Betti numbers of unordered configuration spaces of small graphs


Introduction

The purpose of this document is to provide data about known Betti numbers of unordered configuration spaces of small graphs in order to guide research and avoid duplicated effort.

It contains information for connected multigraphs having at most nine edges which contain no loops, no bivalent vertices, and no internal (i.e., non-leaf) bridges. For each such graph there is a table of Betti numbers for configurations of small numbers of points along with Poincaré series which encode Betti numbers for all larger numbers of points. Because the Poincaré series are rational functions, this means that for fixed i and Γ, the sequence βi (BkΓ) of ith Betti numbers of is eventually polynomial in the number of points k in the configuration. For the reader's convenience, the stable polynomial is also indicated.

The enumeration of the graphs in question was done using utilities that are part of Nauty. For graphs with fewer than seven edges, this was also verified using Richard Mathar's preprint Statistics on Small Graphs (Table 61). The core homology computation was done using Macaulay2.

The approach uses the fact that the chains of the unordered configuration spaces of a graph are a differential graded module over a polynomial ring with variables the edges of the graph. The calculation is simplified further by a presentation of this differential graded module as the tensor product of finitely generated models for local configurations at the vertices of the graph. This picture was pioneered by Świątkowski; the action by the polynomial ring was described in my work with An and Knudsen and analyzed in later work with the same collaborators. Other related work includes the following.

  1. Ko and Park calculated the first Betti numbers for all graphs.
  2. Ramos calculated all Betti numbers for trees. For trees all values are stable. In this document, this includes the graphs with fewer than two essential vertices.
  3. Maciążek and Sawicki calculated all Betti numbers for theta graphs. In this document, this data is reproduced in a different form in the section for graphs with precisely two essential vertices.

A pdf version of this document is available here. I would like to thank Byung Hee An and Ben Knudsen for help and suggestions related to this project. This work was supported by IBS-R003-D1. This document was last modified January 15, 2020.

Examples of motivation

Two examples of the use of this data are as follows.

In my work with An and Knudsen, we showed that the ith Betti numbers of Bk(Γ) grows like a polynomial in k of degree ΔΓi-1, where ΔΓi is the maximal number of connected components of the complement of i points in Γ. At the time, An made the following conjecture, which I believe has not appeared publicly, about the leading coefficient of this polynomial.

Leading coefficient conjecture


For any graph Γ and any index i> 1, the leading term of the polynomial governing the growth of the ith Betti numbers of Bk(Γ) is CΓi kΔΓi-1, where
CΓi = (ΣS Πv in S (d(v)-2))/(ΔΓi-1)!
where S runs over maximally separating i-element subsets of the essential vertices of Γ and d(v) is the degree of a vertex.
This conjecture would be false for i=1 more or less because of the special case of Lemma 3.18 of our second paper. In any event, the data here provides evidence for the conjecture, which holds for all of these small graphs.

As a second example, as expressed above, for each Γ and i the sequence βi (BkΓ) is eventually polynomial in k. A priori this does not tell us when polynomiality starts. Consequently, an interesting question is whether it is possible to find a lower bound on the value of k for which βi (BkΓ) is polynomial in k as a “simple” function of i and “simple” invariants of Γ. For instance, is it possible that the beginning of the polynomial range is bounded below by a constant plus the number of essential vertices of Γ for Γ without isolated vertices? The data here indicates that if so, the constant is at least two.

Reducing to the kinds of graphs considered here

Betti numbers for unordered configuration spaces of graphs with loops can be obtained by reducing to loop-free graphs with the same number of edges (see Lemma 4.6 of our second paper above). Betti numbers for unordered configuration spaces of loop-free graphs with bivalent vertices can be obtained from such information for graphs without bivalent vertices (smoothing bivalent vertices is a homeomorphism and thus does not affect the configuration spaces). Betti numbers for unordered configuration spaces of disconnected graphs can be obtained combinatorially from the counts for connected graphs by summing over all ways of partitioning the desired number of points among the path components (this is true for any locally path-connected topological spaces and is not particular to graphs). Betti numbers for unordered configuration spaces of graphs with internal bridges can be obtained in a similar combinatorial manner from such information for the graphs obtained by cutting the edge into two leaves (see Proposition 5.2 of our first paper above).

Notes about the data

The graphs are organized by the number of essential (valence at least three) vertices. They are presented in sparse6 format, with degree sequences, with adjacency matrices, and with a visual representation. The number of essential vertices also gives the maximal homological degree of the unordered configuration spaces of a graph; as long as there is at least one essential vertex, this maximal degree is realized for configuration spaces of sufficiently many points (uniformly, twice the number of essential vertices is always enough to realize the maximal degree). Unstable values are indicated in bold. All values not explicitly included in the tables of data are stable and are calculated by the indicated stable polynomial value.

Notes about the computation

The core computation of a presentation for the homology and all Poincaré series for 723 graphs (the isolated vertex has irregularities because it lacks edges and therefore was computed by hand) takes several hours on a 2019 MacBook Pro. The median calculation time is between one and two seconds, while the slowest calculation for a graph in this collection sometimes takes an hour.

Example code for the core computation looks as follows. It presents a local two-stage chain complex model for each vertex and then tensors them together, both over the full polynomial ring on the edges. 

	
-- macaulay script for H_*(B_*(K4))
R = ZZ[e_0, e_1, e_2, e_3, e_4, e_5]
C0 = chainComplex { matrix {{e_4 - e_0, e_5 - e_0}} }
C1 = chainComplex { matrix {{e_1 - e_0, e_2 - e_0}} }
C2 = chainComplex { matrix {{e_3 - e_1, e_5 - e_1}} }
C3 = chainComplex { matrix {{e_3 - e_2, e_4 - e_2}} }
C = C0 ** C1 ** C2 ** C3
H = HH (C)
p0 = hilbertSeries (H_0, Reduce => true)
p1 = hilbertSeries (H_1, Reduce => true)
p2 = hilbertSeries (H_2, Reduce => true)
p3 = hilbertSeries (H_3, Reduce => true)
p4 = hilbertSeries (H_4, Reduce => true)

Data for small graphs

Data for graphs with 0 essential vertices

sparse6 nameimageadjacency matrixdegree sequence
:@picture of the graph :@
0
[0]

Note: values calculated by hand
Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01101+t0

sparse6 nameimageadjacency matrixdegree sequence
:Anpicture of the graph :An
01
10
[1, 1]

Betti numbers βi(Bk(Γ)):

i\k0Poincaré seriesstable polynomial value
011/(1-t)1

Data for graphs with 1 essential vertex

sparse6 nameimageadjacency matrixdegree sequence
:Ccfpicture of the graph :Ccf
0111
1000
1000
1000
[3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0Poincaré seriesstable polynomial value
011/(1-t)1
10t2/(1-t)3(-t+t2)/2!

sparse6 nameimageadjacency matrixdegree sequence
:DaGbpicture of the graph :DaGb
01111
10000
10000
10000
10000
[4, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0Poincaré seriesstable polynomial value
011/(1-t)1
10(3t2-t3)/(1-t)4(-5t+3t2+2t3)/3!

sparse6 nameimageadjacency matrixdegree sequence
:EaGaNpicture of the graph :EaGaN
011111
100000
100000
100000
100000
100000
[5, 1, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0Poincaré seriesstable polynomial value
011/(1-t)1
10(6t2-4t3+t4)/(1-t)5(-26t+9t2+14t3+3t4)/4!

sparse6 nameimageadjacency matrixdegree sequence
:FaGaGpicture of the graph :FaGaG
0111111
1000000
1000000
1000000
1000000
1000000
1000000
[6, 1, 1, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0Poincaré seriesstable polynomial value
011/(1-t)1
10(10t2-10t3+5t4-t5)/(1-t)6(-154t+25t2+90t3+35t4+4t5)/5!

sparse6 nameimageadjacency matrixdegree sequence
:GaGaGbpicture of the graph :GaGaGb
01111111
10000000
10000000
10000000
10000000
10000000
10000000
10000000
[7, 1, 1, 1, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0Poincaré seriesstable polynomial value
011/(1-t)1
10(15t2-20t3+15t4-6t5+t6)/(1-t)7(-1044t+20t2+615t3+335t4+69t5+5t6)/6!

sparse6 nameimageadjacency matrixdegree sequence
:H`ACGO`Bpicture of the graph :H`ACGO`B
011111111
100000000
100000000
100000000
100000000
100000000
100000000
100000000
100000000
[8, 1, 1, 1, 1, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0Poincaré seriesstable polynomial value
011/(1-t)1
10(21t2-35t3+35t4-21t5+7t6-t7)/(1-t)8(-8028t-784t2+4599t3+3185t4+903t5+119t6+6t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:I`ACGO`AFpicture of the graph :I`ACGO`AF
0111111111
1000000000
1000000000
1000000000
1000000000
1000000000
1000000000
1000000000
1000000000
1000000000
[9, 1, 1, 1, 1, 1, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0Poincaré seriesstable polynomial value
011/(1-t)1
10(28t2-56t3+70t4-56t5+28t6-8t7+t8)/(1-t)9(-69264t-13580t2+37772t3+31703t4+11144t5+2030t6+188t7+7t8)/8!

Data for graphs with 2 essential vertices

sparse6 nameimageadjacency matrixdegree sequence
:A_picture of the graph :A_
03
30
[3, 3]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
1023(2t+t2)/(1-t)3
2000t4/(1-t)3(6-5t+t2)/2!

sparse6 nameimageadjacency matrixdegree sequence
:A_Npicture of the graph :A_N
04
40
[4, 4]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
1036(3t+3t2)/(1-t)6
2000(t3+6t4-3t5)/(1-t)4(36-10t-12t2+4t3)/3!

sparse6 nameimageadjacency matrixdegree sequence
:Bo?Npicture of the graph :Bo?N
003
001
310
[4, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
1025(2t+t2-t3)/(1-t)21+2t
2000(3t4-t5)/(1-t)4(6+7t-9t2+2t3)/3!

sparse6 nameimageadjacency matrixdegree sequence
:Co_Npicture of the graph :Co_N
0012
0001
1000
2100
[3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01Poincaré seriesstable polynomial value
0111/(1-t)1
101(t+t2)/(1-t)2-1+2t
200t4/(1-t)4(-6+11t-6t2+t3)/3!

sparse6 nameimageadjacency matrixdegree sequence
:A_Bpicture of the graph :A_B
05
50
[5, 5]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10410(4t+6t2)/(1-t)10
2000(4t3+19t4-20t5+6t6)/(1-t)5(240-30t-69t2-6t3+9t4)/4!

sparse6 nameimageadjacency matrixdegree sequence
:Bo?@picture of the graph :Bo?@
004
001
410
[5, 4, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
1039(3t+3t2-3t3)/(1-t)23+3t
2000(t3+14t4-12t5+3t6)/(1-t)5(72+56t-54t2-8t3+6t4)/4!

sparse6 nameimageadjacency matrixdegree sequence
:Cw?Ipicture of the graph :Cw?I
0003
0001
0001
3110
[5, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
1028(2t+2t2-2t3+t4)/(1-t)3(2+t+3t2)/2!
2000(6t4-4t5+t6)/(1-t)5(24+10t-3t2-10t3+3t4)/4!

sparse6 nameimageadjacency matrixdegree sequence
:Co_@picture of the graph :Co_@
0013
0001
1000
3100
[4, 4, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
1027(2t+3t2-t3)/(1-t)2-1+4t
2000(9t4-6t5+t6)/(1-t)5(-24+92t-40t2-8t3+4t4)/4!

sparse6 nameimageadjacency matrixdegree sequence
:DkG?Qpicture of the graph :DkG?Q
00012
00001
00001
10000
21100
[4, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01Poincaré seriesstable polynomial value
0111/(1-t)1
101(t+2t2-t3)/(1-t)3(-2+2t+2t2)/2!
200(3t4-t5)/(1-t)5(-24+32t-2t2-8t3+2t4)/4!

sparse6 nameimageadjacency matrixdegree sequence
:A_?picture of the graph :A_?
06
60
[6, 6]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10515(5t+10t2)/(1-t)15
2000(10t3+45t4-74t5+45t6-10t7)/(1-t)6(1800-116t-400t2-140t3+40t4+16t5)/5!

sparse6 nameimageadjacency matrixdegree sequence
:Bo??Npicture of the graph :Bo??N
005
001
510
[6, 5, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10414(4t+6t2-6t3)/(1-t)26+4t
2000(4t3+39t4-55t5+30t6-6t7)/(1-t)6(720+418t-325t2-130t3+25t4+12t5)/5!

sparse6 nameimageadjacency matrixdegree sequence
:Cw?@Vpicture of the graph :Cw?@V
0004
0001
0001
4110
[6, 4, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10313(3t+4t2-6t3+3t4)/(1-t)3(6+2t+4t2)/2!
2000(t3+25t4-30t5+15t6-3t7)/(1-t)6(360+112t-10t2-120t3+10t4+8t5)/5!

sparse6 nameimageadjacency matrixdegree sequence
:Co_?Npicture of the graph :Co_?N
0014
0001
1000
4100
[5, 5, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10312(3t+6t2-3t3)/(1-t)26t
2000(t3+31t4-38t5+18t6-3t7)/(1-t)6(706t-255t2-115t3+15t4+9t5)/5!

sparse6 nameimageadjacency matrixdegree sequence
:Do??QNpicture of the graph :Do??QN
00003
00001
00001
00001
31110
[6, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10212(2t+4t2-4t3+3t4-t5)/(1-t)4(6-t+9t2+4t3)/3!
2000(10t4-10t5+5t6-t7)/(1-t)6(120+26t+5t2-30t3-5t4+4t5)/5!

sparse6 nameimageadjacency matrixdegree sequence
:DkG?@Jpicture of the graph :DkG?@J
00013
00001
00001
10000
31100
[5, 4, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10210(2t+4t2-4t3+t4)/(1-t)3(-2+5t+3t2)/2!
2000(18t4-18t5+7t6-t7)/(1-t)6(-120+334t-5t2-100t3+5t4+6t5)/5!

sparse6 nameimageadjacency matrixdegree sequence
:EoG?QNpicture of the graph :EoG?QN
000012
000001
000001
000001
100000
211100
[5, 3, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01Poincaré seriesstable polynomial value
0111/(1-t)1
101(t+4t2-3t3+t4)/(1-t)4(-6+3t+6t2+3t3)/3!
200(6t4-4t5+t6)/(1-t)6(-120+142t+5t2-25t3-5t4+3t5)/5!

sparse6 nameimageadjacency matrixdegree sequence
:Eo@gsRpicture of the graph :Eo@gsR
000010
000010
000001
000001
110002
001120
[4, 4, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01Poincaré seriesstable polynomial value
0111/(1-t)1
101(t+4t2-t3)/(1-t)3(-2+4t2)/2!
200(9t4-6t5+t6)/(1-t)6(-120+76t+120t2-80t3+4t5)/5!

sparse6 nameimageadjacency matrixdegree sequence
:A_?Npicture of the graph :A_?N
07
70
[7, 7]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10621(6t+15t2)/(1-t)21
2000(20t3+90t4-204t5+188t6-84t7+15t8)/(1-t)7(15120-540t-2600t2-1425t3+55t4+165t5+25t6)/6!

sparse6 nameimageadjacency matrixdegree sequence
:Bo??@picture of the graph :Bo??@
006
001
610
[7, 6, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10520(5t+10t2-10t3)/(1-t)210+5t
2000(10t3+85t4-169t5+144t6-60t7+10t8)/(1-t)7(7200+3324t-2170t2-1290t3-10t4+126t5+20t6)/6!

sparse6 nameimageadjacency matrixdegree sequence
:Cw??Ipicture of the graph :Cw??I
0005
0001
0001
5110
[7, 5, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10419(4t+7t2-12t3+6t4)/(1-t)3(12+3t+5t2)/2!
2000(4t3+65t4-114t5+90t6-36t7+6t8)/(1-t)7(4320+1068t+60t2-1155t3-75t4+87t5+15t6)/6!

sparse6 nameimageadjacency matrixdegree sequence
:Co_?@picture of the graph :Co_?@
0015
0001
1000
5100
[6, 6, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10418(4t+10t2-6t3)/(1-t)22+8t
2000(4t3+75t4-134t5+105t6-40t7+6t8)/(1-t)7(1440+5724t-1766t2-1140t3-50t4+96t5+16t6)/6!

sparse6 nameimageadjacency matrixdegree sequence
:Do??@G~picture of the graph :Do??@G~
00004
00001
00001
00001
41110
[7, 4, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10318(3t+6t2-10t3+9t4-3t5)/(1-t)4(18+t+12t2+5t3)/3!
2000(t3+39t4-60t5+45t6-18t7+3t8)/(1-t)7(2160+372t+130t2-420t3-140t4+48t5+10t6)/6!

sparse6 nameimageadjacency matrixdegree sequence
:DkG??Cnpicture of the graph :DkG??Cn
00014
00001
00001
10000
41100
[6, 5, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10316(3t+7t2-9t3+3t4)/(1-t)3(8t+4t2)/2!
2000(t3+54t4-85t5+60t6-21t7+3t8)/(1-t)7(3084t+78t2-990t3-90t4+66t5+12t6)/6!

sparse6 nameimageadjacency matrixdegree sequence
:Es??QLNpicture of the graph :Es??QLN
000003
000001
000001
000001
000001
311110
[7, 3, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10217(2t+7t2-8t3+7t4-4t5+t6)/(1-t)5(24-14t+31t2+26t3+5t4)/4!
2000(15t4-20t5+15t6-6t7+t8)/(1-t)7(720+96t+50t2-105t3-55t4+9t5+5t6)/6!

sparse6 nameimageadjacency matrixdegree sequence
:EoG?@G~picture of the graph :EoG?@G~
000013
000001
000001
000001
100000
311100
[6, 4, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10214(2t+6t2-8t3+5t4-t5)/(1-t)4(-6+11t+9t2+4t3)/3!
2000(30t4-40t5+25t6-8t7+t8)/(1-t)7(-720+1764t+122t2-360t3-130t4+36t5+8t6)/6!

sparse6 nameimageadjacency matrixdegree sequence
:Eo@gsPNpicture of the graph :Eo@gsPN
000010
000010
000001
000001
110003
001130
[5, 5, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10213(2t+7t2-4t3+t4)/(1-t)3(-2+2t+6t2)/2!
2000(36t4-48t5+28t6-8t7+t8)/(1-t)7(-720+1140t+1176t2-825t3-105t4+45t5+9t6)/6!

sparse6 nameimageadjacency matrixdegree sequence
:FsG?QLNpicture of the graph :FsG?QLN
0000012
0000001
0000001
0000001
0000001
1000000
2111100
[6, 3, 1, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01Poincaré seriesstable polynomial value
0111/(1-t)1
101(t+7t2-7t3+4t4-t5)/(1-t)5(-24+4t+20t2+20t3+4t4)/4!
200(10t4-10t5+5t6-t7)/(1-t)7(-720+804t+46t2-90t3-50t4+6t5+4t6)/6!

sparse6 nameimageadjacency matrixdegree sequence
:Fs@gsT^picture of the graph :Fs@gsT^
0000010
0000010
0000001
0000001
0000001
1100002
0011120
[5, 4, 1, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01Poincaré seriesstable polynomial value
0111/(1-t)1
101(t+6t2-5t3+t4)/(1-t)4(-6-3t+12t2+3t3)/3!
200(18t4-18t5+7t6-t7)/(1-t)7(-720+276t+834t2-300t3-120t4+24t5+6t6)/6!

sparse6 nameimageadjacency matrixdegree sequence
:A_?Bpicture of the graph :A_?B
08
80
[8, 8]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10728(7t+21t2)/(1-t)28
2000(35t3+161t4-469t5+581t6-391t7+140t8-21t9)/(1-t)8(141120-2892t-19110t2-13566t3-1470t4+1302t5+420t6+36t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Bo???Npicture of the graph :Bo???N
007
001
710
[8, 7, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10627(6t+15t2-15t3)/(1-t)215+6t
2000(20t3+160t4-414t5+482t6-308t7+105t8-15t9)/(1-t)8(75600+28908t-16268t2-12285t3-1715t4+987t5+343t6+30t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Cw??@Vpicture of the graph :Cw??@V
0006
0001
0001
6110
[8, 6, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10526(5t+11t2-20t3+10t4)/(1-t)3(20+4t+6t2)/2!
2000(10t3+135t4-314t5+343t6-210t7+70t8-10t9)/(1-t)8(50400+10308t+1694t2-11004t3-1960t4+672t5+266t6+24t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Co_??Npicture of the graph :Co_??N
0016
0001
1000
6100
[7, 7, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10525(5t+15t2-10t3)/(1-t)25+10t
2000(10t3+150t4-354t5+388t6-234t7+75t8-10t9)/(1-t)8(25200+50508t-13580t2-10955t3-1820t4+742t5+280t6+25t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Do???Cbpicture of the graph :Do???Cb
00005
00001
00001
00001
51110
[8, 5, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10425(4t+9t2-19t3+18t4-6t5)/(1-t)4(36+3t+15t2+6t3)/3!
2000(4t3+97t4-203t5+210t6-126t7+42t8-6t9)/(1-t)8(30240+4308t+2016t2-4683t3-2205t4+357t5+189t6+18t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:DkG???Qpicture of the graph :DkG???Q
00015
00001
00001
10000
51100
[7, 6, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10423(4t+11t2-16t3+6t4)/(1-t)3(4+11t+5t2)/2!
2000(4t3+121t4-259t5+264t6-150t7+46t8-6t9)/(1-t)8(10080+29268t+1708t2-9625t3-1925t4+497t5+217t6+20t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Es??@Gspicture of the graph :Es??@Gs
000004
000001
000001
000001
000001
411110
[8, 4, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10324(3t+9t2-16t3+19t4-12t5+3t6)/(1-t)5(72-8t+42t2+32t3+6t4)/4!
2000(t3+56t4-105t5+105t6-63t7+21t8-3t9)/(1-t)8(15120+1668t+1078t2-1722t3-1190t4+42t5+112t6+12t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:EoG??Cbpicture of the graph :EoG??Cb
000014
000001
000001
000001
100000
411100
[7, 5, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10321(3t+9t2-16t3+12t4-3t5)/(1-t)4(19t+12t2+5t3)/3!
2000(t3+83t4-159t5+150t6-81t7+24t8-3t9)/(1-t)8(18948t+1876t2-4095t3-2030t4+252t5+154t6+15t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Eo@gsPCpicture of the graph :Eo@gsPC
000010
000010
000001
000001
110004
001140
[6, 6, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10320(3t+11t2-9t3+3t4)/(1-t)3(4t+8t2)/2!
2000(t3+93t4-179t5+165t6-85t7+24t8-3t9)/(1-t)8(12948t+11802t2-8246t3-1890t4+322t5+168t6+16t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Fw??QLDpicture of the graph :Fw??QLD
0000003
0000001
0000001
0000001
0000001
0000001
3111110
[8, 3, 1, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10223(2t+11t2-15t3+15t4-11t5+5t6-t7)/(1-t)6(120-106t+125t2+160t3+55t4+6t5)/5!
2000(21t4-35t5+35t6-21t7+7t8-t9)/(1-t)8(5040+456t+350t2-441t3-385t4-21t5+35t6+6t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:FsG?@Gspicture of the graph :FsG?@Gs
0000013
0000001
0000001
0000001
0000001
1000000
3111100
[7, 4, 1, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10219(2t+9t2-14t3+13t4-6t5+t6)/(1-t)5(-24+34t+31t2+26t3+5t4)/4!
2000(45t4-75t5+65t6-33t7+9t8-t9)/(1-t)8(-5040+11568t+994t2-1505t3-1085t4+7t5+91t6+10t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Fs@gsTTpicture of the graph :Fs@gsTT
0000010
0000010
0000001
0000001
0000001
1100003
0011130
[6, 5, 1, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10217(2t+9t2-11t3+5t4-t5)/(1-t)4(-6+2t+18t2+4t3)/3!
2000(60t4-100t5+80t6-36t7+9t8-t9)/(1-t)8(-5040+5868t+9296t2-3507t3-1855t4+147t5+119t6+12t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:GwG?QLDpicture of the graph :GwG?QLD
00000012
00000001
00000001
00000001
00000001
00000001
10000000
21111100
[7, 3, 1, 1, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01Poincaré seriesstable polynomial value
0111/(1-t)1
101(t+11t2-14t3+11t4-5t5+t6)/(1-t)6(-120-10t+75t2+125t3+45t4+5t5)/5!
200(15t4-20t5+15t6-6t7+t8)/(1-t)8(-5040+5448t+322t2-385t3-350t4-28t5+28t6+5t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Gw@gsTepicture of the graph :Gw@gsTe
00000010
00000010
00000001
00000001
00000001
00000001
11000002
00111120
[6, 4, 1, 1, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01Poincaré seriesstable polynomial value
0111/(1-t)1
101(t+9t2-11t3+6t4-t5)/(1-t)5(-24-20t+44t2+20t3+4t4)/4!
200(30t4-40t5+25t6-8t7+t8)/(1-t)8(-5040+1308t+5950t2-1288t3-980t4-28t5+70t6+8t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Gw@IsTepicture of the graph :Gw@IsTe
00000010
00000010
00000010
00000001
00000001
00000001
11100002
00011120
[5, 5, 1, 1, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01Poincaré seriesstable polynomial value
0111/(1-t)1
101(t+9t2-5t3+t4)/(1-t)4(-6-6t+12t2+6t3)/3!
200(36t4-48t5+28t6-8t7+t8)/(1-t)8(-5040+348t+6636t2-399t3-1680t4+42t5+84t6+9t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:A_??picture of the graph :A_??
09
90
[9, 9]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10836(8t+28t2)/(1-t)36
2000(56t3+266t4-952t5+1484t6-1336t7+719t8-216t9+28t10)/(1-t)9(1451520-17136t-157780t2-133868t3-28959t4+9016t5+5250t6+868t7+49t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Bo???@picture of the graph :Bo???@
008
001
810
[9, 8, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10735(7t+21t2-21t3)/(1-t)221+7t
2000(35t3+273t4-875t5+1295t6-1119t7+580t8-168t9+21t10)/(1-t)9(846720+275904t-136360t2-121856t3-29302t4+6496t5+4340t6+736t7+42t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Cw???Ipicture of the graph :Cw???I
0007
0001
0001
7110
[9, 7, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10634(6t+16t2-30t3+15t4)/(1-t)3(30+5t+7t2)/2!
2000(20t3+245t4-714t5+1001t6-832t7+420t8-120t9+15t10)/(1-t)9(604800+105264t+26180t2-109844t3-29645t4+3976t5+3430t6+604t7+35t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Co_??@picture of the graph :Co_??@
0017
0001
1000
7100
[8, 8, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10633(6t+21t2-15t3)/(1-t)29+12t
2000(20t3+266t4-784t5+1106t6-916t7+455t8-126t9+15t10)/(1-t)9(362880+487584t-115984t2-109704t3-28756t4+4536t5+3584t6+624t7+36t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Do????QNpicture of the graph :Do????QN
00006
00001
00001
00001
61110
[9, 6, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10533(5t+13t2-31t3+30t4-10t5)/(1-t)4(60+5t+18t2+7t3)/3!
2000(10t3+195t4-519t5+692t6-560t7+280t8-80t9+10t10)/(1-t)9(403200+48864t+27440t2-50792t3-29988t4+1456t5+2520t6+472t7+28t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:DkG???@Jpicture of the graph :DkG???@J
00016
00001
00001
10000
61100
[8, 7, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10531(5t+16t2-25t3+10t4)/(1-t)3(10+14t+6t2)/2!
2000(10t3+230t4-624t5+832t6-658t7+315t8-85t9+10t10)/(1-t)9(201600+296064t+25352t2-97552t3-28210t4+2576t5+2828t6+512t7+30t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Es???CbRpicture of the graph :Es???CbR
000005
000001
000001
000001
000001
511110
[9, 5, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10432(4t+12t2-28t3+37t4-24t5+6t6)/(1-t)5(144-2t+53t2+38t3+7t4)/4!
2000(4t3+135t4-328t5+420t6-336t7+168t8-48t9+6t10)/(1-t)9(241920+22704t+16940t2-21980t3-18571t4-1064t5+1610t6+340t7+21t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:EoG???QNpicture of the graph :EoG???QN
000015
000001
000001
000001
100000
511100
[8, 6, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10429(4t+13t2-27t3+22t4-6t5)/(1-t)4(12+27t+15t2+6t3)/3!
2000(4t3+177t4-440t5+553t6-420t7+196t8-52t9+6t10)/(1-t)9(80640+205344t+25568t2-45080t3-27664t4+616t5+2072t6+400t7+24t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Eo@gsPCRpicture of the graph :Eo@gsPCR
000010
000010
000001
000001
110005
001150
[7, 7, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10428(4t+16t2-16t3+6t4)/(1-t)3(4+6t+10t2)/2!
2000(4t3+192t4-480t5+598t6-444t7+201t8-52t9+6t10)/(1-t)9(80640+144144t+125324t2-85260t3-26775t4+1176t5+2226t6+420t7+25t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Fw??@GsVpicture of the graph :Fw??@GsV
0000004
0000001
0000001
0000001
0000001
0000001
4111110
[9, 4, 1, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10331(3t+13t2-25t3+35t4-31t5+15t6-3t7)/(1-t)6(360-82t+175t2+195t3+65t4+7t5)/5!
2000(t3+76t4-168t5+210t6-168t7+84t8-24t9+3t10)/(1-t)9(120960+9312t+8120t2-8288t3-8834t4-1232t5+700t6+208t7+14t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:FsG??CbRpicture of the graph :FsG??CbR
0000014
0000001
0000001
0000001
0000001
1000000
4111100
[8, 5, 1, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10327(3t+12t2-25t3+28t4-15t5+3t6)/(1-t)5(64t+42t2+32t3+6t4)/4!
2000(t3+118t4-266t5+315t6-231t7+105t8-27t9+3t10)/(1-t)9(141504t+15704t2-19488t3-17038t4-1344t5+1316t6+288t7+18t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Fs@gsTTVpicture of the graph :Fs@gsTTV
0000010
0000010
0000001
0000001
0000001
1100004
0011140
[7, 6, 1, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10325(3t+13t2-20t3+12t4-3t5)/(1-t)4(7t+24t2+5t3)/3!
2000(t3+142t4-322t5+369t6-255t7+109t8-27t9+3t10)/(1-t)9(79584t+104336t2-39368t3-25340t4-224t5+1624t6+328t7+20t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:G{??QLDZpicture of the graph :G{??QLDZ
00000003
00000001
00000001
00000001
00000001
00000001
00000001
31111110
[9, 3, 1, 1, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10230(2t+16t2-26t3+30t4-26t5+16t6-6t7+t8)/(1-t)7(720-804t+568t2+1065t3+505t4+99t5+7t6)/6!
2000(28t4-56t5+70t6-56t7+28t8-8t9+t10)/(1-t)9(40320+2640t+2548t2-2156t3-2737t4-560t5+182t6+76t7+7t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:GwG?@GsVpicture of the graph :GwG?@GsV
00000013
00000001
00000001
00000001
00000001
00000001
10000000
31111100
[8, 4, 1, 1, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10225(2t+13t2-23t3+27t4-19t5+7t6-t7)/(1-t)6(-120+134t+125t2+160t3+55t4+6t5)/5!
2000(63t4-126t5+140t6-98t7+42t8-10t9+t10)/(1-t)9(-40320+89088t+7520t2-7336t3-8092t4-1288t5+560t6+176t7+12t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Gw@gsTeZpicture of the graph :Gw@gsTeZ
00000010
00000010
00000001
00000001
00000001
00000001
11000003
00111130
[7, 5, 1, 1, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10222(2t+12t2-20t3+16t4-6t5+t6)/(1-t)5(-24-2t+67t2+26t3+5t4)/4!
2000(90t4-180t5+185t6-116t7+45t8-10t9+t10)/(1-t)9(-40320+38544t+74948t2-16996t3-15505t4-1624t5+1022t6+236t7+15t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Gw@IsTeZpicture of the graph :Gw@IsTeZ
00000010
00000010
00000010
00000001
00000001
00000001
11100003
00011130
[6, 6, 1, 1, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10221(2t+13t2-11t3+5t4-t5)/(1-t)4(-6-2t+18t2+8t3)/3!
2000(100t4-200t5+200t6-120t7+45t8-10t9+t10)/(1-t)9(-40320+27744t+82304t2-6776t3-23016t4-1064t5+1176t6+256t7+16t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:HmA??aEOhnpicture of the graph :HmA??aEOhn
000000012
000000001
000000001
000000001
000000001
000000001
000000001
100000000
211111100
[8, 3, 1, 1, 1, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01Poincaré seriesstable polynomial value
0111/(1-t)1
101(t+16t2-25t3+25t4-16t5+6t6-t7)/(1-t)7(-720-204t+294t2+840t3+420t4+84t5+6t6)/6!
200(21t4-35t5+35t6-21t7+7t8-t9)/(1-t)9(-40320+42720t+2360t2-1904t3-2506t4-560t5+140t6+64t7+6t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Hm?K`cIWx~picture of the graph :Hm?K`cIWx~
000000010
000000010
000000001
000000001
000000001
000000001
000000001
110000002
001111120
[7, 4, 1, 1, 1, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01Poincaré seriesstable polynomial value
0111/(1-t)1
101(t+13t2-20t3+17t4-7t5+t6)/(1-t)6(-120-130t+195t2+125t3+45t4+5t5)/5!
200(45t4-75t5+65t6-33t7+9t8-t9)/(1-t)9(-40320+7584t+47240t2-6384t3-7350t4-1344t5+420t6+144t7+10t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Hm?GhcIWx~picture of the graph :Hm?GhcIWx~
000000010
000000010
000000010
000000001
000000001
000000001
000000001
111000002
000111120
[6, 5, 1, 1, 1, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01Poincaré seriesstable polynomial value
0111/(1-t)1
101(t+12t2-14t3+6t4-t5)/(1-t)5(-24-32t+44t2+32t3+4t4)/4!
200(60t4-100t5+80t6-36t7+9t8-t9)/(1-t)9(-40320-3936t+53552t2+5656t3-13972t4-1904t5+728t6+184t7+12t8)/8!

Data for graphs with 3 essential vertices

sparse6 nameimageadjacency matrixdegree sequence
:B__Npicture of the graph :B__N
022
201
210
[4, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
10355(3t+2t2)/(1-t)5
20002(2t3+3t4-t5)/(1-t)3(10-14t+4t2)/2!
30000(3t6-t7)/(1-t)5(-120t+94t2-24t3+2t4)/4!

sparse6 nameimageadjacency matrixdegree sequence
:CoCIpicture of the graph :CoCI
0021
0001
2001
1110
[3, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
1024(2t-t3)/(1-t)22+t
2000(t3+2t4)/(1-t)3(14-13t+3t2)/2!
3000t6/(1-t)5(120-154t+71t2-14t3+t4)/4!

sparse6 nameimageadjacency matrixdegree sequence
:Bo?HNpicture of the graph :Bo?HN
003
003
330
[6, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104101418(4t+2t2-2t3)/(1-t)22+4t
2000423(4t3+7t4-5t5+3t6-t7)/(1-t)4(18+22t-30t2+8t3)/3!
300000(10t6-10t7+5t8-t9)/(1-t)6(120+126t-255t2+170t3-45t4+4t5)/5!

sparse6 nameimageadjacency matrixdegree sequence
:B__Hpicture of the graph :B__H
022
202
220
[4, 4, 4]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104777(4t+3t2)/(1-t)7
2000833(8t3+9t4-6t5+t6)/(1-t)3(18-36t+12t2)/2!
300000(27t6-27t7+9t8-t9)/(1-t)6(240-1948t+1080t2-40t3-60t4+8t5)/5!

sparse6 nameimageadjacency matrixdegree sequence
:B_C@picture of the graph :B_C@
032
301
210
[5, 4, 3]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104888(4t+4t2)/(1-t)8
2000631(6t3+7t4-11t5+5t6-t7)/(1-t)4(42-36t-6t2+6t3)/3!
300000(18t6-18t7+7t8-t9)/(1-t)6(-120-526t+235t2+100t3-55t4+6t5)/5!

sparse6 nameimageadjacency matrixdegree sequence
:Co?_Npicture of the graph :Co?_N
0032
0001
3000
2100
[5, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
103812(3t+2t2-t3)/(1-t)24t
20003(3t3+5t4-3t5+t6)/(1-t)4(-18+30t-24t2+6t3)/3!
30000(6t6-4t7+t8)/(1-t)6(-360+222t-205t2+135t3-35t4+3t5)/5!

sparse6 nameimageadjacency matrixdegree sequence
:Co_IVpicture of the graph :Co_IV
0012
0001
1002
2120
[5, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
103811(3t+2t2-2t3)/(1-t)22+3t
20002(2t3+7t4-4t5+t6)/(1-t)4(-6+24t-24t2+6t3)/3!
30000(6t6-4t7+t8)/(1-t)6(-360+222t-205t2+135t3-35t4+3t5)/5!

sparse6 nameimageadjacency matrixdegree sequence
:CoC@Vpicture of the graph :CoC@V
0022
0001
2001
2110
[4, 4, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
10379(3t+t2-2t3)/(1-t)23+2t
20004(4t3+5t4-6t5+t6)/(1-t)4(54-46t+4t3)/3!
30000(9t6-6t7+t8)/(1-t)6(720-1044t+280t2+80t3-40t4+4t5)/5!

sparse6 nameimageadjacency matrixdegree sequence
:Co?`Vpicture of the graph :Co?`V
0031
0001
3001
1110
[4, 4, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
10378(3t+t2-3t3)/(1-t)25+t
20003(3t3+7t4-7t5+t6)/(1-t)4(66-52t+4t3)/3!
30000(9t6-6t7+t8)/(1-t)6(720-1044t+280t2+80t3-40t4+4t5)/5!

sparse6 nameimageadjacency matrixdegree sequence
:Dk?_QNpicture of the graph :Dk?_QN
00021
00001
00001
20001
11110
[4, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
1026(2t-t3+t4)/(1-t)3(4+2t2)/2!
2000(3t3+3t4-2t5)/(1-t)4(30-13t-9t2+4t3)/3!
3000(3t6-t7)/(1-t)6(360-222t-95t2+100t3-25t4+2t5)/5!

sparse6 nameimageadjacency matrixdegree sequence
:Dk?EANpicture of the graph :Dk?EAN
00021
00010
00001
21001
10110
[4, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
1026(2t+2t2-t3)/(1-t)23t
2000(t3+5t4-2t5)/(1-t)4(18+5t-15t2+4t3)/3!
3000(3t6-t7)/(1-t)6(360-222t-95t2+100t3-25t4+2t5)/5!

sparse6 nameimageadjacency matrixdegree sequence
:DgH_@Fpicture of the graph :DgH_@F
00102
00012
10000
01000
22000
[4, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
1026(2t+2t2)/(1-t)2-2+4t
2000(2t3+3t4-t5)/(1-t)4(6+11t-15t2+4t3)/3!
3000(3t6-t7)/(1-t)6(360-222t-95t2+100t3-25t4+2t5)/5!

sparse6 nameimageadjacency matrixdegree sequence
:EkGEARpicture of the graph :EkGEAR
000111
000010
000001
100000
110001
101010
[3, 3, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01Poincaré seriesstable polynomial value
0111/(1-t)1
101(t+2t2)/(1-t)2-2+3t
2003t4/(1-t)4(-18+33t-18t2+3t3)/3!
300t6/(1-t)6(-120+274t-225t2+85t3-15t4+t5)/5!

sparse6 nameimageadjacency matrixdegree sequence
:Bo?@Hpicture of the graph :Bo?@H
004
003
430
[7, 4, 3]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
105141924(5t+4t2-4t3)/(1-t)24+5t
20001065(10t3+15t4-28t5+22t6-12t7+3t8)/(1-t)5(168+132t-154t2+12t3+10t4)/4!
300000(t5+39t6-60t7+45t8-18t9+3t10)/(1-t)7(2160+1212t-2150t2+1020t3-20t4-72t5+10t6)/6!

sparse6 nameimageadjacency matrixdegree sequence
:B_C@Npicture of the graph :B_C@N
032
302
220
[5, 5, 4]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
105101010(5t+5t2)/(1-t)10
20001779(17t3+11t4-36t5+22t6-5t7)/(1-t)4(78-117t+18t2+9t3)/3!
300000(t5+102t6-165t7+112t8-37t9+5t10)/(1-t)7(2160-12948t+4782t2+1500t3-480t4-72t5+18t6)/6!

sparse6 nameimageadjacency matrixdegree sequence
:B_C?Npicture of the graph :B_C?N
033
301
310
[6, 4, 4]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
105111111(5t+6t2)/(1-t)11
20001473(14t3+17t4-29t5+19t6-5t7)/(1-t)4(54-16t-36t2+16t3)/3!
300000(t5+84t6-135t7+95t8-34t9+5t10)/(1-t)7(-1440-888t-1736t2+2400t3-440t4-72t5+16t6)/6!

sparse6 nameimageadjacency matrixdegree sequence
:B_?_Npicture of the graph :B_?_N
042
401
210
[6, 5, 3]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
105121212(5t+7t2)/(1-t)12
20001381(13t3+16t4-39t5+34t6-15t7+3t8)/(1-t)5(264-140t-36t2-4t3+12t4)/4!
300000(t5+54t6-85t7+60t8-21t9+3t10)/(1-t)7(-720-3252t+1458t2+450t3-30t4-78t5+12t6)/6!

sparse6 nameimageadjacency matrixdegree sequence
:Cw?HIpicture of the graph :Cw?HI
0003
0003
0001
3310
[7, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104152948(4t+3t2-4t3+2t4)/(1-t)3(4+3t+5t2)/2!
2000433(4t3+13t4-12t5+8t6-4t7+t8)/(1-t)5(72+28t-10t2-28t3+10t4)/4!
300000(15t6-20t7+15t8-6t9+t10)/(1-t)7(720+156t-160t2-105t3+155t4-51t5+5t6)/6!

sparse6 nameimageadjacency matrixdegree sequence
:Co?_@picture of the graph :Co?_@
0033
0001
3000
3100
[6, 4, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104121824(4t+4t2-2t3)/(1-t)26t
2000851(8t3+11t4-20t5+14t6-6t7+t8)/(1-t)5(-120+208t-128t2+8t3+8t4)/4!
300000(30t6-40t7+25t8-8t9+t10)/(1-t)7(-3600+2460t-1798t2+840t3-10t4-60t5+8t6)/6!

sparse6 nameimageadjacency matrixdegree sequence
:Co?C@picture of the graph :Co?C@
0042
0001
4000
2100
[6, 4, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1041217(4t+4t2-3t3)/(1-t)22+5t
20007(7t3+14t4-22t5+12t6-3t7)/(1-t)5(-168+208t-128t2+8t3+8t4)/4!
30000(t5+25t6-30t7+15t8-3t9)/(1-t)7(-6480+3180t-1798t2+840t3-10t4-60t5+8t6)/6!

sparse6 nameimageadjacency matrixdegree sequence
:Co_@Qpicture of the graph :Co_@Q
0013
0001
1002
3120
[6, 4, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104121620(4t+4t2-4t3)/(1-t)24+4t
2000647(6t3+17t4-26t5+16t6-6t7+t8)/(1-t)5(-24+160t-128t2+8t3+8t4)/4!
300000(30t6-40t7+25t8-8t9+t10)/(1-t)7(-3600+2460t-1798t2+840t3-10t4-60t5+8t6)/6!

sparse6 nameimageadjacency matrixdegree sequence
:CoC@Qpicture of the graph :CoC@Q
0022
0001
2002
2120
[5, 4, 4, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104101316(4t+2t2-3t3)/(1-t)24+3t
20001157(11t3+13t4-18t5+7t6-t7)/(1-t)4(54-48t-18t2+12t3)/3!
300000(54t6-72t7+39t8-10t9+t10)/(1-t)7(3600-7260t-42t2+1920t3-330t4-60t5+12t6)/6!

sparse6 nameimageadjacency matrixdegree sequence
:CoC?Ipicture of the graph :CoC?I
0023
0001
2001
3110
[5, 5, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104111417(4t+3t2-4t3)/(1-t)25+3t
2000958(9t3+13t4-27t5+19t6-6t7+t8)/(1-t)5(312-222t+3t2-6t3+9t4)/4!
300000(36t6-48t7+28t8-8t9+t10)/(1-t)7(5760-8232t+2166t2+375t3-15t4-63t5+9t6)/6!

sparse6 nameimageadjacency matrixdegree sequence
:Co?_Ipicture of the graph :Co?_I
0032
0001
3001
2110
[5, 4, 4, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104101214(4t+2t2-4t3)/(1-t)26+2t
20001055(10t3+15t4-19t5+7t6-t7)/(1-t)4(66-54t-18t2+12t3)/3!
300000(54t6-72t7+39t8-10t9+t10)/(1-t)7(3600-7260t-42t2+1920t3-330t4-60t5+12t6)/6!

sparse6 nameimageadjacency matrixdegree sequence
:Co?CIpicture of the graph :Co?CI
0041
0001
4001
1110
[5, 5, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1041112(4t+3t2-6t3)/(1-t)29+t
20007(7t3+19t4-32t5+18t6-3t7)/(1-t)5(312-246t+3t2-6t3+9t4)/4!
30000(t5+31t6-38t7+18t8-3t9)/(1-t)7(2880-7512t+2166t2+375t3-15t4-63t5+9t6)/6!

sparse6 nameimageadjacency matrixdegree sequence
:DkG?PCnpicture of the graph :DkG?PCn
00012
00003
00001
10000
23100
[6, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031224(3t+3t2-3t3+t4)/(1-t)3(4t+4t2)/2!
20003(3t3+10t4-8t5+4t6-t7)/(1-t)5(-72+72t-8t2-24t3+8t4)/4!
30000(10t6-10t7+5t8-t9)/(1-t)7(-2160+852t-134t2-90t3+130t4-42t5+4t6)/6!

sparse6 nameimageadjacency matrixdegree sequence
:Dk?A?Cnpicture of the graph :Dk?A?Cn
00032
00001
00001
30000
21100
[5, 4, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031018(3t+t2-3t3+t4)/(1-t)3(6t+2t2)/2!
20007(7t3+6t4-12t5+6t6-t7)/(1-t)5(72-4t-54t2+4t3+6t4)/4!
30000(18t6-18t7+7t8-t9)/(1-t)7(2160-2052t-726t2+660t3-48t5+6t6)/6!

sparse6 nameimageadjacency matrixdegree sequence
:DkG?QK~picture of the graph :DkG?QK~
00012
00001
00001
10002
21120
[6, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031223(3t+3t2-4t3+2t4)/(1-t)3(4+2t+4t2)/2!
20002(2t3+13t4-11t5+5t6-t7)/(1-t)5(-24+48t-8t2-24t3+8t4)/4!
30000(10t6-10t7+5t8-t9)/(1-t)7(-2160+852t-134t2-90t3+130t4-42t5+4t6)/6!

sparse6 nameimageadjacency matrixdegree sequence
:Dk?_@G~picture of the graph :Dk?_@G~
00022
00001
00001
20001
21110
[5, 4, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031018(3t+t2-3t3+2t4)/(1-t)3(6+t+3t2)/2!
20007(7t3+7t4-14t5+7t6-t7)/(1-t)5(144-64t-42t2+4t3+6t4)/4!
30000(18t6-18t7+7t8-t9)/(1-t)7(2160-2052t-726t2+660t3-48t5+6t6)/6!

sparse6 nameimageadjacency matrixdegree sequence
:Dk?A@G~picture of the graph :Dk?A@G~
00031
00001
00001
30001
11110
[4, 4, 4, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
103914(3t-4t3+3t4)/(1-t)3(10+2t2)/2!
20007(7t3+13t4-9t5+t6)/(1-t)4(78-30t-30t2+12t3)/3!
30000(27t6-27t7+9t8-t9)/(1-t)7(5760-3312t-2668t2+1920t3-220t4-48t5+8t6)/6!

sparse6 nameimageadjacency matrixdegree sequence
:Dk?EAK~picture of the graph :Dk?EAK~
00021
00010
00001
21002
10120
[5, 4, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031015(3t+4t2-2t3)/(1-t)25t
20004(4t3+13t4-17t5+7t6-t7)/(1-t)5(72+44t-78t2+4t3+6t4)/4!
30000(18t6-18t7+7t8-t9)/(1-t)7(2160-2052t-726t2+660t3-48t5+6t6)/6!

sparse6 nameimageadjacency matrixdegree sequence
:Dk?E?G~picture of the graph :Dk?E?G~
00022
00010
00001
21001
20110
[4, 4, 4, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
103913(3t+3t2-2t3)/(1-t)21+4t
20006(6t3+13t4-8t5+t6)/(1-t)4(54-6t-36t2+12t3)/3!
30000(27t6-27t7+9t8-t9)/(1-t)7(5760-3312t-2668t2+1920t3-220t4-48t5+8t6)/6!

sparse6 nameimageadjacency matrixdegree sequence
:Dk??WG~picture of the graph :Dk??WG~
00031
00010
00001
31001
10110
[5, 4, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031014(3t+4t2-3t3)/(1-t)22+4t
20003(3t3+16t4-20t5+8t6-t7)/(1-t)5(120+20t-78t2+4t3+6t4)/4!
30000(18t6-18t7+7t8-t9)/(1-t)7(2160-2052t-726t2+660t3-48t5+6t6)/6!

sparse6 nameimageadjacency matrixdegree sequence
:DgH_?C^picture of the graph :DgH_?C^
00103
00012
10000
01000
32000
[5, 4, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031016(3t+4t2-t3)/(1-t)2-2+6t
20005(5t3+10t4-14t5+6t6-t7)/(1-t)5(24+68t-78t2+4t3+6t4)/4!
30000(18t6-18t7+7t8-t9)/(1-t)7(2160-2052t-726t2+660t3-48t5+6t6)/6!

sparse6 nameimageadjacency matrixdegree sequence
:Eo?_QLNpicture of the graph :Eo?_QLN
000021
000001
000001
000001
200001
111110
[5, 3, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
1029(2t+t2-t3+2t4-t5)/(1-t)4(12-3t+6t2+3t3)/3!
2000(6t3+3t4-5t5+2t6)/(1-t)5(120-64t-6t2-8t3+6t4)/4!
3000(6t6-4t7+t8)/(1-t)7(2160-1692t+252t2-75t3+105t4-33t5+3t6)/6!

sparse6 nameimageadjacency matrixdegree sequence
:Eo?E?G~picture of the graph :Eo?E?G~
000022
000010
000001
000001
210000
201100
[4, 4, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
1028(2t+2t2-2t3)/(1-t)3(-4+6t+2t2)/2!
2000(4t3+5t4-6t5+t6)/(1-t)5(-24+124t-88t2+8t3+4t4)/4!
3000(9t6-6t7+t8)/(1-t)7(720+1476t-2174t2+720t3+10t4-36t5+4t6)/6!

sparse6 nameimageadjacency matrixdegree sequence
:Eo@_ALNpicture of the graph :Eo@_ALN
000012
000010
000001
000001
110001
201110
[5, 3, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
1029(2t+3t2-3t3+t4)/(1-t)3(3t+3t2)/2!
2000(t3+10t4-7t5+2t6)/(1-t)5(72-16t+6t2-20t3+6t4)/4!
3000(6t6-4t7+t8)/(1-t)7(2160-1692t+252t2-75t3+105t4-33t5+3t6)/6!

sparse6 nameimageadjacency matrixdegree sequence
:Eo?EALNpicture of the graph :Eo?EALN
000021
000010
000001
000001
210001
101110
[4, 4, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
1028(2t+2t2-3t3+t4)/(1-t)3(4t+2t2)/2!
2000(3t3+8t4-9t5+2t6)/(1-t)5(24+100t-88t2+8t3+4t4)/4!
3000(9t6-6t7+t8)/(1-t)7(720+1476t-2174t2+720t3+10t4-36t5+4t6)/6!

sparse6 nameimageadjacency matrixdegree sequence
:EkH_@Cnpicture of the graph :EkH_@Cn
000102
000012
000001
100000
010000
221000
[5, 3, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
1029(2t+3t2-2t3)/(1-t)3(-4+5t+3t2)/2!
2000(2t3+7t4-4t5+t6)/(1-t)5(24+8t+6t2-20t3+6t4)/4!
3000(6t6-4t7+t8)/(1-t)7(2160-1692t+252t2-75t3+105t4-33t5+3t6)/6!

sparse6 nameimageadjacency matrixdegree sequence
:EkG?WHNpicture of the graph :EkG?WHN
000121
000010
000001
100000
210001
101010
[4, 4, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
1028(2t+4t2-t3)/(1-t)2-2+5t
2000(t3+12t4-11t5+2t6)/(1-t)5(-24+172t-112t2+8t3+4t4)/4!
3000(9t6-6t7+t8)/(1-t)7(720+1476t-2174t2+720t3+10t4-36t5+4t6)/6!

sparse6 nameimageadjacency matrixdegree sequence
:FoGEAL^picture of the graph :FoGEAL^
0000111
0000010
0000001
0000001
1000000
1100001
1011010
[4, 3, 3, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01Poincaré seriesstable polynomial value
0111/(1-t)1
101(t+3t2-2t3)/(1-t)3(-4+4t+2t2)/2!
200(7t4-3t5)/(1-t)5(-72+108t-28t2-12t3+4t4)/4!
300(3t6-t7)/(1-t)7(-720+1404t-802t2+60t3+80t4-24t5+2t6)/6!

sparse6 nameimageadjacency matrixdegree sequence
:Bo?@HNpicture of the graph :Bo?@HN
004
004
440
[8, 4, 4]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
106182430(6t+6t2-6t3)/(1-t)26+6t
200020131(20t3+31t4-60t5+60t6-36t7+9t8)/(1-t)5(360+184t-192t2-16t3+24t4)/4!
300000(6t5+146t6-308t7+315t8-189t9+63t10-9t11)/(1-t)8(45360+13836t-20902t2+4956t3+3290t4-1176t5-28t6+24t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Bo??HNpicture of the graph :Bo??HN
005
003
530
[8, 5, 3]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
106192531(6t+7t2-7t3)/(1-t)27+6t
200020152(20t3+32t4-86t5+95t6-67t7+30t8-6t9)/(1-t)6(1560+862t-885t2-40t3+45t4+18t5)/5!
300000(4t5+97t6-203t7+210t8-126t9+42t10-6t11)/(1-t)8(30240+10944t-18102t2+7077t3+525t4-399t5-63t6+18t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:B_C?Hpicture of the graph :B_C?H
033
302
320
[6, 5, 5]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
106131313(6t+7t2)/(1-t)13
200032158(32t3+30t4-80t5+57t6-15t7)/(1-t)4(120-117t-15t2+24t3)/3!
300000(6t5+317t6-707t7+709t8-391t9+117t10-15t11)/(1-t)8(35280-91428t+8064t2+27279t3-3045t4-1407t5+21t6+36t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:B_?_Hpicture of the graph :B_?_H
042
402
220
[6, 6, 4]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
106141414(6t+8t2)/(1-t)14
200030163(30t3+13t4-94t5+113t6-58t7+12t8)/(1-t)5(504-540t+92t2+16t4)/4!
300000(6t5+257t6-567t7+569t8-315t9+94t10-12t11)/(1-t)8(35280-106908t+39690t2+7448t3+630t4-1372t5+32t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:B_?_@picture of the graph :B_?_@
043
401
310
[7, 5, 4]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
106151515(6t+9t2)/(1-t)15
200026152(26t3+22t4-90t5+99t6-54t7+12t8)/(1-t)5(360-14t-183t2+38t3+15t4)/4!
300000(6t5+227t6-497t7+504t8-288t9+90t10-12t11)/(1-t)8(3288t-18298t2+15645t3+665t4-1323t5-7t6+30t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:B_?C@picture of the graph :B_?C@
052
501
210
[7, 6, 3]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
106171717(6t+11t2)/(1-t)17
200024178(24t3+34t4-106t5+127t6-87t7+34t8-6t9)/(1-t)6(2040-710t-175t2-150t3+55t4+20t5)/5!
300000(4t5+121t6-259t7+264t8-150t9+46t10-6t11)/(1-t)8(-24408t+12138t2+2135t3+525t4-427t5-63t6+20t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Cw?@HVpicture of the graph :Cw?@HV
0004
0003
0001
4310
[8, 4, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
105203760(5t+5t2-8t3+4t4)/(1-t)3(8+4t+6t2)/2!
20001089(10t3+29t4-55t5+50t6-34t7+15t8-3t9)/(1-t)6(840+228t-50t2-240t3+50t4+12t5)/5!
300000(t5+56t6-105t7+105t8-63t9+21t10-3t11)/(1-t)8(15120+2004t-1694t2-1722t3+1750t4-294t5-56t6+12t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Co?_?Npicture of the graph :Co?_?N
0034
0001
3000
4100
[7, 5, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
105172533(5t+7t2-4t3)/(1-t)21+8t
200016122(16t3+26t4-67t5+71t6-46t7+18t8-3t9)/(1-t)6(-600+1470t-755t2-45t3+35t4+15t5)/5!
300000(t5+83t6-159t7+150t8-81t9+24t10-3t11)/(1-t)8(-30240+24576t-15554t2+5985t3+490t4-336t5-56t6+15t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Co?C?Npicture of the graph :Co?C?N
0043
0001
4000
3100
[7, 4, 4, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
105162330(5t+6t2-4t3)/(1-t)22+7t
200016107(16t3+27t4-48t5+40t6-18t7+3t8)/(1-t)5(-312+352t-164t2-16t3+20t4)/4!
300000(3t5+116t6-219t7+195t8-99t9+27t10-3t11)/(1-t)8(-75600+42204t-17962t2+4130t3+2870t4-994t5-28t6+20t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Co??_Npicture of the graph :Co??_N
0052
0001
5000
2100
[7, 5, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1051723(5t+7t2-6t3)/(1-t)25+6t
200014(14t3+34t4-76t5+67t6-30t7+6t8)/(1-t)6(-1560+1590t-755t2-45t3+35t4+15t5)/5!
30000(4t5+65t6-114t7+90t8-36t9+6t10)/(1-t)8(-90720+39696t-15554t2+5985t3+490t4-336t5-56t6+15t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Co_@QVpicture of the graph :Co_@QV
0013
0001
1003
3130
[7, 4, 4, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
105162126(5t+6t2-6t3)/(1-t)26+5t
200014103(14t3+33t4-56t5+48t6-24t7+5t8)/(1-t)5(-24+256t-164t2-16t3+20t4)/4!
300000(t5+128t6-249t7+235t8-129t9+39t10-5t11)/(1-t)8(-35280+32124t-17962t2+4130t3+2870t4-994t5-28t6+20t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Co_?IVpicture of the graph :Co_?IV
0014
0001
1002
4120
[7, 5, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
105172227(5t+7t2-7t3)/(1-t)27+5t
200013116(13t3+38t4-85t5+83t6-49t7+18t8-3t9)/(1-t)6(120+1110t-755t2-45t3+35t4+15t5)/5!
300000(t5+83t6-159t7+150t8-81t9+24t10-3t11)/(1-t)8(-30240+24576t-15554t2+5985t3+490t4-336t5-56t6+15t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:CoC?IVpicture of the graph :CoC?IV
0023
0001
2002
3120
[6, 5, 4, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
105141822(5t+4t2-5t3)/(1-t)26+4t
200021123(21t3+18t4-67t5+62t6-27t7+5t8)/(1-t)5(312-220t-84t2+28t3+12t4)/4!
300000(t5+173t6-339t7+305t8-153t9+42t10-5t11)/(1-t)8(35280-62268t-686t2+12936t3+700t4-1092t5-14t6+24t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:CoC?@Vpicture of the graph :CoC?@V
0024
0001
2001
4110
[6, 6, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
105162024(5t+6t2-7t3)/(1-t)28+4t
200017133(17t3+31t4-83t5+89t6-53t7+18t8-3t9)/(1-t)6(2280-1316t+80t2-140t3+40t4+16t5)/5!
300000(t5+93t6-179t7+165t8-85t9+24t10-3t11)/(1-t)8(55440-72060t+19726t2+1834t3+490t4-350t5-56t6+16t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Co?_IVpicture of the graph :Co?_IV
0032
0001
3002
2120
[5, 5, 5, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
105131619(5t+3t2-5t3)/(1-t)27+3t
200023124(23t3+32t4-48t5+25t6-5t7)/(1-t)4(60-45t-54t2+27t3)/3!
300000(t5+209t6-411t7+361t8-173t9+45t10-5t11)/(1-t)8(15120-48516t-28140t2+29463t3-2100t4-1134t5+27t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Co?_@Vpicture of the graph :Co?_@V
0033
0001
3001
3110
[6, 5, 4, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
105141720(5t+4t2-6t3)/(1-t)28+3t
200020121(20t3+21t4-70t5+63t6-27t7+5t8)/(1-t)5(360-244t-84t2+28t3+12t4)/4!
300000(t5+173t6-339t7+305t8-153t9+42t10-5t11)/(1-t)8(35280-62268t-686t2+12936t3+700t4-1092t5-14t6+24t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Co?C@Vpicture of the graph :Co?C@V
0042
0001
4001
2110
[6, 5, 4, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
105141618(5t+4t2-7t3)/(1-t)210+2t
200019119(19t3+24t4-71t5+58t6-21t7+3t8)/(1-t)5(216-220t-84t2+28t3+12t4)/4!
300000(3t5+161t6-309t7+265t8-123t9+30t10-3t11)/(1-t)8(-5040-52188t-686t2+12936t3+700t4-1092t5-14t6+24t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Co??`Vpicture of the graph :Co??`V
0051
0001
5001
1110
[6, 6, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1051617(5t+6t2-10t3)/(1-t)214+t
200014(14t3+43t4-98t5+89t6-38t7+6t8)/(1-t)6(1560-1316t+80t2-140t3+40t4+16t5)/5!
30000(4t5+75t6-134t7+105t8-40t9+6t10)/(1-t)8(-5040-56940t+19726t2+1834t3+490t4-350t5-56t6+16t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Do??PCbpicture of the graph :Do??PCb
00003
00003
00001
00001
33110
[8, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
1042153108(4t+5t2-7t3+6t4-2t5)/(1-t)4(12+3t+15t2+6t3)/3!
2000445(4t3+21t4-25t5+20t6-12t7+5t8-t9)/(1-t)6(360+68t+10t2-80t3-10t4+12t5)/5!
300000(21t6-35t7+35t8-21t9+7t10-t11)/(1-t)8(5040+372t-196t2-441t3+245t4+63t5-49t6+6t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:DkG?PCQpicture of the graph :DkG?PCQ
00012
00004
00001
10000
24100
[7, 4, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1041732(4t+5t2-7t3+3t4)/(1-t)3(4+5t+5t2)/2!
20007(7t3+27t4-46t5+34t6-15t7+3t8)/(1-t)6(-840+680t-40t2-210t3+40t4+10t5)/5!
30000(t5+39t6-60t7+45t8-18t9+3t10)/(1-t)8(-45360+16860t-1456t2-1505t3+1505t4-245t5-49t6+10t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:DkG?@CQpicture of the graph :DkG?@CQ
00013
00003
00001
10000
33100
[7, 4, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104173354(4t+5t2-6t3+2t4)/(1-t)3(7t+5t2)/2!
2000871(8t3+23t4-41t5+34t6-20t7+7t8-t9)/(1-t)6(-600+680t-40t2-210t3+40t4+10t5)/5!
300000(45t6-75t7+65t8-33t9+9t10-t11)/(1-t)8(-25200+11820t-1456t2-1505t3+1505t4-245t5-49t6+10t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Dk?A??Qpicture of the graph :Dk?A??Q
00033
00001
00001
30000
31100
[6, 5, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104152742(4t+3t2-6t3+2t4)/(1-t)3(9t+3t2)/2!
20001499(14t3+15t4-43t5+43t6-23t7+7t8-t9)/(1-t)6(480+38t-265t2-50t3+25t4+12t5)/5!
300000(60t6-100t7+80t8-36t9+9t10-t11)/(1-t)8(20160-19752t-5446t2+4893t3+455t4-273t5-49t6+12t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Dk??G?Qpicture of the graph :Dk??G?Q
00042
00001
00001
40000
21100
[6, 4, 4, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1041423(4t+2t2-7t3+3t4)/(1-t)3(4+8t+2t2)/2!
200013(13t3+22t4-34t5+18t6-3t7)/(1-t)5(264-152t-40t2-16t3+16t4)/4!
30000(3t5+74t6-115t7+75t8-24t9+3t10)/(1-t)8(45360-50388t+98t2+3304t3+2450t4-812t5-28t6+16t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:DkG?@Grpicture of the graph :DkG?@Gr
00013
00001
00001
10002
31120
[7, 4, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104173150(4t+5t2-8t3+4t4)/(1-t)3(8+3t+5t2)/2!
2000667(6t3+31t4-53t5+42t6-22t7+7t8-t9)/(1-t)6(-120+440t-40t2-210t3+40t4+10t5)/5!
300000(45t6-75t7+65t8-33t9+9t10-t11)/(1-t)8(-25200+11820t-1456t2-1505t3+1505t4-245t5-49t6+10t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Dk?_@Grpicture of the graph :Dk?_@Gr
00022
00001
00001
20002
21120
[6, 4, 4, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104142540(4t+2t2-5t3+3t4)/(1-t)3(8+2t+4t2)/2!
20001593(15t3+18t4-35t5+25t6-8t7+t8)/(1-t)5(120-80t-40t2-16t3+16t4)/4!
300000(90t6-150t7+115t8-49t9+11t10-t11)/(1-t)8(5040-20148t-4942t2+3304t3+2450t4-812t5-28t6+16t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Dk?_?Cbpicture of the graph :Dk?_?Cb
00023
00001
00001
20001
31110
[6, 5, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104152641(4t+3t2-7t3+4t4)/(1-t)3(10+2t+4t2)/2!
20001398(13t3+20t4-52t5+50t6-25t7+7t8-t9)/(1-t)6(1080-382t-205t2-50t3+25t4+12t5)/5!
300000(60t6-100t7+80t8-36t9+9t10-t11)/(1-t)8(20160-19752t-5446t2+4893t3+455t4-273t5-49t6+12t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Dk?A?Cbpicture of the graph :Dk?A?Cb
00032
00001
00001
30001
21110
[5, 5, 4, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104132132(4t+t2-6t3+4t4)/(1-t)3(12+t+3t2)/2!
20001697(16t3+17t4-46t5+29t6-8t7+t8)/(1-t)5(336-138t-153t2+42t3+9t4)/4!
300000(108t6-180t7+132t8-52t9+11t10-t11)/(1-t)8(40320-29544t-25914t2+15267t3+735t4-861t5-21t6+18t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Dk??GCbpicture of the graph :Dk??GCb
00041
00001
00001
40001
11110
[5, 5, 4, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1041318(4t+t2-9t3+6t4)/(1-t)3(18+2t2)/2!
200013(13t3+25t4-50t5+24t6-3t7)/(1-t)5(600-294t-141t2+42t3+9t4)/4!
30000(3t5+92t6-145t7+92t8-27t9+3t10)/(1-t)8(80640-59784t-20874t2+15267t3+735t4-861t5-21t6+18t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Dk?EAKrpicture of the graph :Dk?EAKr
00021
00010
00001
21003
10130
[6, 5, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104152229(4t+7t2-4t3)/(1-t)21+7t
2000986(9t3+32t4-64t5+54t6-25t7+7t8-t9)/(1-t)6(600+338t-445t2-50t3+25t4+12t5)/5!
300000(60t6-100t7+80t8-36t9+9t10-t11)/(1-t)8(20160-19752t-5446t2+4893t3+455t4-273t5-49t6+12t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Dk?E?Grpicture of the graph :Dk?E?Gr
00022
00010
00001
21002
20120
[5, 5, 4, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104131925(4t+5t2-3t3)/(1-t)21+6t
20001490(14t3+20t4-46t5+28t6-8t7+t8)/(1-t)5(216-6t-189t2+42t3+9t4)/4!
300000(108t6-180t7+132t8-52t9+11t10-t11)/(1-t)8(40320-29544t-25914t2+15267t3+735t4-861t5-21t6+18t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Dk??WGrpicture of the graph :Dk??WGr
00031
00010
00001
31002
10120
[6, 4, 4, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104142026(4t+6t2-4t3)/(1-t)22+6t
20001079(10t3+29t4-42t5+26t6-8t7+t8)/(1-t)5(72+40t-88t2-16t3+16t4)/4!
300000(90t6-150t7+115t8-49t9+11t10-t11)/(1-t)8(5040-20148t-4942t2+3304t3+2450t4-812t5-28t6+16t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Dk??W?bpicture of the graph :Dk??W?b
00032
00010
00001
31001
20110
[5, 5, 4, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104131823(4t+5t2-4t3)/(1-t)23+5t
20001388(13t3+23t4-49t5+29t6-8t7+t8)/(1-t)5(264-30t-189t2+42t3+9t4)/4!
300000(108t6-180t7+132t8-52t9+11t10-t11)/(1-t)8(40320-29544t-25914t2+15267t3+735t4-861t5-21t6+18t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Dk??@_bpicture of the graph :Dk??@_b
00041
00010
00001
41001
10110
[6, 5, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1041520(4t+7t2-6t3)/(1-t)25+5t
20007(7t3+40t4-75t5+58t6-21t7+3t8)/(1-t)6(600+218t-445t2-50t3+25t4+12t5)/5!
30000(t5+54t6-85t7+60t8-21t9+3t10)/(1-t)8(-14712t-5446t2+4893t3+455t4-273t5-49t6+12t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:DgH_?CPpicture of the graph :DgH_?CP
00103
00013
10000
01000
33000
[6, 4, 4, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104142230(4t+6t2-2t3)/(1-t)2-2+8t
20001283(12t3+23t4-36t5+24t6-8t7+t8)/(1-t)5(-24+88t-88t2-16t3+16t4)/4!
300000(90t6-150t7+115t8-49t9+11t10-t11)/(1-t)8(5040-20148t-4942t2+3304t3+2450t4-812t5-28t6+16t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:DgH_??Ppicture of the graph :DgH_??P
00104
00012
10000
01000
42000
[6, 5, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1041523(4t+7t2-3t3)/(1-t)2-1+8t
200010(10t3+28t4-57t5+46t6-18t7+3t8)/(1-t)6(-120+578t-445t2-50t3+25t4+12t5)/5!
30000(t5+54t6-85t7+60t8-21t9+3t10)/(1-t)8(-14712t-5446t2+4893t3+455t4-273t5-49t6+12t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:EoG?PCbpicture of the graph :EoG?PCb
000012
000003
000001
000001
100000
231100
[7, 3, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031744(3t+5t2-6t3+4t4-t5)/(1-t)4(7t+12t2+5t3)/3!
20003(3t3+17t4-18t5+12t6-5t7+t8)/(1-t)6(-360+300t+10t2-70t3-10t4+10t5)/5!
30000(15t6-20t7+15t8-6t9+t10)/(1-t)8(-15120+5364t-168t2-385t3+210t4+56t5-42t6+5t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Eo?A?Cbpicture of the graph :Eo?A?Cb
000032
000001
000001
000001
300000
211100
[5, 5, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031330(3t+t2-4t3+4t4-t5)/(1-t)4(15t+6t2+3t3)/3!
200013(13t3+5t4-24t5+21t6-7t7+t8)/(1-t)6(646t-615t2+65t3+15t4+9t5)/5!
30000(36t6-48t7+28t8-8t9+t10)/(1-t)8(14040t-20538t2+6321t3+420t4-210t5-42t6+9t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:EoG?QLCpicture of the graph :EoG?QLC
000012
000001
000001
000001
100002
211120
[7, 3, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031743(3t+5t2-7t3+6t4-2t5)/(1-t)4(12+t+12t2+5t3)/3!
20002(2t3+21t4-24t5+16t6-6t7+t8)/(1-t)6(-120+180t+10t2-70t3-10t4+10t5)/5!
30000(15t6-20t7+15t8-6t9+t10)/(1-t)8(-15120+5364t-168t2-385t3+210t4+56t5-42t6+5t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Eo?_@Gspicture of the graph :Eo?_@Gs
000022
000001
000001
000001
200001
211110
[6, 4, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031434(3t+2t2-4t3+5t4-2t5)/(1-t)4(18-t+9t2+4t3)/3!
200011(11t3+8t4-25t5+21t6-8t7+t8)/(1-t)6(720-448t+30t2-100t3+30t4+8t5)/5!
30000(30t6-40t7+25t8-8t9+t10)/(1-t)8(15120-18684t+3822t2-1288t3+1260t4-196t5-42t6+8t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Eo?A@Gspicture of the graph :Eo?A@Gs
000031
000001
000001
000001
300001
111110
[5, 4, 4, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031226(3t-4t3+7t4-3t5)/(1-t)4(30-3t+6t2+3t3)/3!
200013(13t3+15t4-25t5+10t6-t7)/(1-t)5(240-12t-132t2+12t3+12t4)/4!
30000(54t6-72t7+39t8-10t9+t10)/(1-t)8(25200-180t-22162t2+5838t3+2030t4-630t5-28t6+12t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Eo?E??bpicture of the graph :Eo?E??b
000023
000010
000001
000001
210000
301100
[5, 5, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031325(3t+4t2-5t3+t4)/(1-t)3(-4+9t+3t2)/2!
20008(8t3+17t4-33t5+23t6-7t7+t8)/(1-t)6(-240+886t-555t2+5t3+15t4+9t5)/5!
30000(36t6-48t7+28t8-8t9+t10)/(1-t)8(14040t-20538t2+6321t3+420t4-210t5-42t6+9t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Eo??W?bpicture of the graph :Eo??W?b
000032
000010
000001
000001
310000
201100
[5, 4, 4, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031222(3t+3t2-5t3+t4)/(1-t)3(-4+10t+2t2)/2!
20009(9t3+18t4-22t5+8t6-t7)/(1-t)5(72+120t-132t2+12t4)/4!
30000(54t6-72t7+39t8-10t9+t10)/(1-t)8(25200-180t-22162t2+5838t3+2030t4-630t5-28t6+12t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Eo??YLCpicture of the graph :Eo??YLC
000030
000010
000001
000001
310002
001120
[6, 4, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031430(3t+5t2-3t3+t4)/(1-t)3(2t+6t2)/2!
20007(7t3+15t4-26t5+18t6-7t7+t8)/(1-t)6(360-308t+210t2-180t3+30t4+8t5)/5!
30000(30t6-40t7+25t8-8t9+t10)/(1-t)8(15120-18684t+3822t2-1288t3+1260t4-196t5-42t6+8t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Eo@_ALCpicture of the graph :Eo@_ALC
000012
000010
000001
000001
110002
201120
[6, 4, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031427(3t+5t2-6t3+2t4)/(1-t)3(6t+4t2)/2!
20004(4t3+25t4-38t5+24t6-8t7+t8)/(1-t)6(360-68t+90t2-180t3+30t4+8t5)/5!
30000(30t6-40t7+25t8-8t9+t10)/(1-t)8(15120-18684t+3822t2-1288t3+1260t4-196t5-42t6+8t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Eo@_?Gspicture of the graph :Eo@_?Gs
000013
000010
000001
000001
110001
301110
[6, 4, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031426(3t+5t2-7t3+3t4)/(1-t)3(4+4t+4t2)/2!
20003(3t3+29t4-44t5+28t6-9t7+t8)/(1-t)6(600-188t+90t2-180t3+30t4+8t5)/5!
30000(30t6-40t7+25t8-8t9+t10)/(1-t)8(15120-18684t+3822t2-1288t3+1260t4-196t5-42t6+8t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Eo?EALCpicture of the graph :Eo?EALC
000021
000010
000001
000001
210002
101120
[5, 5, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031324(3t+4t2-6t3+2t4)/(1-t)3(7t+3t2)/2!
20007(7t3+21t4-39t5+27t6-8t7+t8)/(1-t)6(766t-555t2+5t3+15t4+9t5)/5!
30000(36t6-48t7+28t8-8t9+t10)/(1-t)8(14040t-20538t2+6321t3+420t4-210t5-42t6+9t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Eo?E?Gspicture of the graph :Eo?E?Gs
000022
000010
000001
000001
210001
201110
[5, 4, 4, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031222(3t+3t2-5t3+2t4)/(1-t)3(2+5t+3t2)/2!
20009(9t3+19t4-24t5+9t6-t7)/(1-t)5(144+60t-120t2+12t4)/4!
30000(54t6-72t7+39t8-10t9+t10)/(1-t)8(25200-180t-22162t2+5838t3+2030t4-630t5-28t6+12t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Eo??WGspicture of the graph :Eo??WGs
000031
000010
000001
000001
310001
101110
[5, 4, 4, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031220(3t+3t2-7t3+3t4)/(1-t)3(4+6t+2t2)/2!
20007(7t3+24t4-28t5+10t6-t7)/(1-t)5(168+72t-132t2+12t4)/4!
30000(54t6-72t7+39t8-10t9+t10)/(1-t)8(25200-180t-22162t2+5838t3+2030t4-630t5-28t6+12t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:EkH_?CQpicture of the graph :EkH_?CQ
000103
000012
000001
100000
010000
321000
[6, 4, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031428(3t+5t2-5t3+t4)/(1-t)3(-4+8t+4t2)/2!
20005(5t3+21t4-32t5+20t6-7t7+t8)/(1-t)6(120+52t+90t2-180t3+30t4+8t5)/5!
30000(30t6-40t7+25t8-8t9+t10)/(1-t)8(15120-18684t+3822t2-1288t3+1260t4-196t5-42t6+8t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:EkG?W?cpicture of the graph :EkG?W?c
000122
000010
000001
100000
210001
201010
[5, 4, 4, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031219(3t+6t2-2t3)/(1-t)2-2+7t
20006(6t3+25t4-27t5+9t6-t7)/(1-t)5(72+168t-156t2+12t4)/4!
30000(54t6-72t7+39t8-10t9+t10)/(1-t)8(25200-180t-22162t2+5838t3+2030t4-630t5-28t6+12t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:EkG?@_cpicture of the graph :EkG?@_c
000131
000010
000001
100000
310001
101010
[5, 5, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031320(3t+7t2-3t3)/(1-t)2-1+7t
20003(3t3+34t4-54t5+34t6-9t7+t8)/(1-t)6(-120+1186t-735t2+5t3+15t4+9t5)/5!
30000(36t6-48t7+28t8-8t9+t10)/(1-t)8(14040t-20538t2+6321t3+420t4-210t5-42t6+9t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Fs?_QLDpicture of the graph :Fs?_QLD
0000021
0000001
0000001
0000001
0000001
2000001
1111110
[6, 3, 3, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10213(2t+3t2-2t3+3t4-3t5+t6)/(1-t)5(48-20t+20t2+20t3+4t4)/4!
2000(10t3+t4-8t5+7t6-2t7)/(1-t)6(600-328t-10t2-40t3+10t4+8t5)/5!
3000(10t6-10t7+5t8-t9)/(1-t)8(15120-12324t+2380t2-329t3+175t4+49t5-35t6+4t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Fs?E?Gspicture of the graph :Fs?E?Gs
0000022
0000010
0000001
0000001
0000001
2100000
2011100
[5, 4, 3, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10211(2t+3t2-4t3+2t4)/(1-t)4(-12+15t+6t2+3t3)/3!
2000(7t3+7t4-14t5+7t6-t7)/(1-t)6(-120+524t-260t2-50t3+20t4+6t5)/5!
3000(18t6-18t7+7t8-t9)/(1-t)8(5040+7092t-8540t2+609t3+1015t4-147t5-35t6+6t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Fs@_ALDpicture of the graph :Fs@_ALD
0000012
0000010
0000001
0000001
0000001
1100001
2011110
[6, 3, 3, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10213(2t+5t2-6t3+4t4-t5)/(1-t)4(5t+9t2+4t3)/3!
2000(t3+17t4-17t5+9t6-2t7)/(1-t)6(360-128t+70t2-60t3-10t4+8t5)/5!
3000(10t6-10t7+5t8-t9)/(1-t)8(15120-12324t+2380t2-329t3+175t4+49t5-35t6+4t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Fs?EALDpicture of the graph :Fs?EALD
0000021
0000010
0000001
0000001
0000001
2100001
1011110
[5, 4, 3, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10211(2t+3t2-5t3+4t4-t5)/(1-t)4(9t+6t2+3t3)/3!
2000(6t3+11t4-20t5+11t6-2t7)/(1-t)6(120+404t-260t2-50t3+20t4+6t5)/5!
3000(18t6-18t7+7t8-t9)/(1-t)8(5040+7092t-8540t2+609t3+1015t4-147t5-35t6+6t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Fs?Cg?spicture of the graph :Fs?Cg?s
0000022
0000010
0000010
0000001
0000001
2110000
2001100
[4, 4, 4, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10210(2t+4t2-2t3)/(1-t)3(-4+4t+4t2)/2!
2000(6t3+13t4-8t5+t6)/(1-t)5(-72+180t-72t2-24t3+12t4)/4!
3000(27t6-27t7+9t8-t9)/(1-t)8(-5040+25668t-17542t2-28t3+2450t4-448t5-28t6+8t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Fs?CgLDpicture of the graph :Fs?CgLD
0000021
0000010
0000010
0000001
0000001
2110001
1001110
[5, 4, 3, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10211(2t+5t2-3t3+t4)/(1-t)3(t+5t2)/2!
2000(3t3+17t4-23t5+11t6-2t7)/(1-t)6(120+284t-80t2-110t3+20t4+6t5)/5!
3000(18t6-18t7+7t8-t9)/(1-t)8(5040+7092t-8540t2+609t3+1015t4-147t5-35t6+6t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:FoH_@Cbpicture of the graph :FoH_@Cb
0000102
0000012
0000001
0000001
1000000
0100000
2211000
[6, 3, 3, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10213(2t+5t2-5t3+2t4)/(1-t)4(-12+11t+9t2+4t3)/3!
2000(2t3+13t4-11t5+5t6-t7)/(1-t)6(120-8t+70t2-60t3-10t4+8t5)/5!
3000(10t6-10t7+5t8-t9)/(1-t)8(15120-12324t+2380t2-329t3+175t4+49t5-35t6+4t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:FoGE?Gtpicture of the graph :FoGE?Gt
0000112
0000010
0000001
0000001
1000000
1100001
2011010
[5, 4, 3, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10211(2t+5t2-5t3+t4)/(1-t)3(-4+7t+3t2)/2!
2000(t3+23t4-29t5+13t6-2t7)/(1-t)6(-120+644t-200t2-110t3+20t4+6t5)/5!
3000(18t6-18t7+7t8-t9)/(1-t)8(5040+7092t-8540t2+609t3+1015t4-147t5-35t6+6t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:FoG?WGtpicture of the graph :FoG?WGt
0000121
0000010
0000001
0000001
1000000
2100001
1011010
[4, 4, 4, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10210(2t+4t2-5t3+t4)/(1-t)3(-4+8t+2t2)/2!
2000(3t3+20t4-13t5+2t6)/(1-t)5(-72+228t-96t2-24t3+12t4)/4!
3000(27t6-27t7+9t8-t9)/(1-t)8(-5040+25668t-17542t2-28t3+2450t4-448t5-28t6+8t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:FoHI?LTpicture of the graph :FoHI?LT
0000102
0000010
0000010
0000001
1000000
0110002
2001020
[5, 4, 3, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10211(2t+5t2-2t3)/(1-t)3(-4+3t+5t2)/2!
2000(4t3+13t4-17t5+7t6-t7)/(1-t)6(-120+404t-80t2-110t3+20t4+6t5)/5!
3000(18t6-18t7+7t8-t9)/(1-t)8(5040+7092t-8540t2+609t3+1015t4-147t5-35t6+6t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:GsGEALEpicture of the graph :GsGEALE
00000111
00000010
00000001
00000001
00000001
10000000
11000001
10111010
[5, 3, 3, 1, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01Poincaré seriesstable polynomial value
0111/(1-t)1
101(t+5t2-5t3+2t4)/(1-t)4(-12+9t+6t2+3t3)/3!
200(13t4-10t5+3t6)/(1-t)6(-360+504t-110t2-30t3-10t4+6t5)/5!
300(6t6-4t7+t8)/(1-t)8(-5040+9468t-5152t2+567t3+140t4+42t5-28t6+3t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:GsGCgLEpicture of the graph :GsGCgLE
00000111
00000010
00000010
00000001
00000001
10000000
11100001
10011010
[4, 4, 3, 1, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01Poincaré seriesstable polynomial value
0111/(1-t)1
101(t+5t2-2t3)/(1-t)3(-4+2t+4t2)/2!
200(15t4-14t5+3t6)/(1-t)6(-360+396t+100t2-160t3+20t4+4t5)/5!
300(9t6-6t7+t8)/(1-t)8(-5040+7668t-1162t2-2534t3+1190t4-98t5-28t6+4t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Bo??HHpicture of the graph :Bo??HH
005
004
540
[9, 5, 4]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
107233037(7t+9t2-9t3)/(1-t)29+7t
200035252(35t3+42t4-164t5+225t6-189t7+90t8-18t9)/(1-t)6(3240+1154t-1085t2-215t3+125t4+21t5)/5!
300000(18t5+353t6-951t7+1252t8-1008t9+504t10-144t11+18t12)/(1-t)9(725760+143520t-197624t2+23744t3+38458t4-6160t5-2156t6+176t7+42t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Bo??@Hpicture of the graph :Bo??@H
006
003
630
[9, 6, 3]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
107253239(7t+11t2-11t3)/(1-t)211+7t
200035308(35t3+63t4-214t5+299t6-266t7+161t8-60t9+10t10)/(1-t)7(15120+6324t-5858t2-750t3+70t4+186t5+28t6)/6!
300000(10t5+195t6-519t7+692t8-560t9+280t10-80t11+10t12)/(1-t)9(403200+104640t-166208t2+58296t3+5852t4-1680t5-952t6+24t7+28t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:B_C?HNpicture of the graph :B_C?HN
033
303
330
[6, 6, 6]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
107161616(7t+9t2)/(1-t)16
200055285(55t3+65t4-162t5+125t6-35t7)/(1-t)4(198-102t-72t2+48t3)/3!
300000(21t5+825t6-2355t7+3120t8-2410t9+1128t10-300t11+35t12)/(1-t)9(685440-635424t-304144t2+410256t3-16464t4-17136t5-2016t6+384t7+64t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:B_?_@Npicture of the graph :B_?_@N
043
402
320
[7, 6, 5]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
107171717(7t+10t2)/(1-t)17
200052286(52t3+26t4-201t5+253t6-141t7+31t8)/(1-t)5(816-520t-68t2+64t3+20t4)/4!
300000(21t5+725t6-2055t7+2720t8-2110t9+993t10-265t11+31t12)/(1-t)9(685440-825504t+63472t2+196616t3+19180t4-16576t5-2072t6+344t7+60t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:B_?_?Npicture of the graph :B_?_?N
044
401
410
[8, 5, 5]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
107191919(7t+12t2)/(1-t)19
200044270(44t3+50t4-169t5+201t6-117t7+27t8)/(1-t)5(624+72t-228t2+36t4)/4!
300000(21t5+581t6-1623t7+2148t8-1694t9+819t10-225t11+27t12)/(1-t)9(282240+165696t-208920t2+91392t3+49686t4-15456t5-2100t6+288t7+54t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:B_?C@Npicture of the graph :B_?C@N
052
502
220
[7, 7, 4]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
107191919(7t+12t2)/(1-t)19
200048306(48t3+18t4-198t5+344t6-288t7+123t8-22t9)/(1-t)6(3960-3110t+645t2-155t3+75t4+25t5)/5!
300000(18t5+524t6-1464t7+1938t8-1510t9+711t10-189t11+22t12)/(1-t)9(564480-1001184t+390088t2+40320t3+15330t4-7056t5-2268t6+240t7+50t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:B_?C?Npicture of the graph :B_?C?N
053
501
310
[8, 6, 4]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
107202020(7t+13t2)/(1-t)20
200043289(43t3+31t4-200t5+319t6-265t7+118t8-22t9)/(1-t)6(3000+136t-1030t2+80t3+70t4+24t5)/5!
300000(18t5+479t6-1329t7+1763t8-1393t9+672t10-184t11+22t12)/(1-t)9(201600+88032t-174320t2+120176t3+15232t4-6832t5-2240t6+224t7+48t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:B_??_Npicture of the graph :B_??_N
062
601
210
[8, 7, 3]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
107232323(7t+16t2)/(1-t)23
200040346(40t3+66t4-248t5+368t6-332t7+191t8-65t9+10t10)/(1-t)7(18000-4404t-870t2-1560t3+120t4+204t5+30t6)/6!
300000(10t5+230t6-624t7+832t8-658t9+315t10-85t11+10t12)/(1-t)9(80640-211488t+115960t2+11648t3+5950t4-1792t5-980t6+32t7+30t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Cw?@HIpicture of the graph :Cw?@HI
0004
0004
0001
4410
[9, 4, 4, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
106254572(6t+7t2-12t3+6t4)/(1-t)3(12+5t+7t2)/2!
200020173(20t3+53t4-105t5+120t6-96t7+45t8-9t9)/(1-t)6(1800+332t-50t2-360t3+50t4+28t5)/5!
300000(6t5+203t6-496t7+630t8-504t9+252t10-72t11+9t12)/(1-t)9(362880+30048t-20048t2-30520t3+21812t4+392t5-1792t6+80t7+28t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Cw??HIpicture of the graph :Cw??HI
0005
0003
0001
5310
[9, 5, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
106264673(6t+8t2-14t3+7t4)/(1-t)3(14+5t+7t2)/2!
200020201(20t3+61t4-160t5+195t6-162t7+97t8-36t9+6t10)/(1-t)7(9360+1896t-186t2-2025t3+165t4+129t5+21t6)/6!
300000(4t5+135t6-328t7+420t8-336t9+168t10-48t11+6t12)/(1-t)9(241920+22032t-16212t2-20804t3+16989t4-1232t5-798t6+4t7+21t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Co?_?@picture of the graph :Co?_?@
0035
0001
3000
5100
[8, 6, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
106233343(6t+11t2-7t3)/(1-t)23+10t
200028252(28t3+56t4-178t5+241t6-206t7+117t8-40t9+6t10)/(1-t)7(-2160+11364t-5094t2-720t3+30t4+156t5+24t6)/6!
300000(4t5+177t6-440t7+553t8-420t9+196t10-52t11+6t12)/(1-t)9(-241920+253440t-145680t2+50344t3+5376t4-1400t5-840t6+16t7+24t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Co?C?@picture of the graph :Co?C?@
0044
0001
4000
4100
[8, 5, 4, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
106213039(6t+9t2-6t3)/(1-t)23+9t
200029212(29t3+38t4-139t5+177t6-132t7+54t8-9t9)/(1-t)6(-1800+2462t-945t2-200t3+105t4+18t5)/5!
300000(9t5+308t6-769t7+938t8-693t9+315t10-81t11+9t12)/(1-t)9(-725760+489408t-173216t2+19656t3+33964t4-5208t5-1904t6+144t7+36t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Co??_@picture of the graph :Co??_@
0053
0001
5000
3100
[8, 5, 4, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
106212937(6t+9t2-7t3)/(1-t)25+8t
200028210(28t3+42t4-142t5+169t6-115t7+42t8-6t9)/(1-t)6(-3000+2702t-945t2-200t3+105t4+18t5)/5!
300000(12t5+287t6-706t7+833t8-588t9+252t10-60t11+6t12)/(1-t)9(-1209600+610368t-173216t2+19656t3+33964t4-5208t5-1904t6+144t7+36t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Co??C@picture of the graph :Co??C@
0062
0001
6000
2100
[8, 6, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1062330(6t+11t2-10t3)/(1-t)29+7t
200025(25t3+71t4-202t5+241t6-161t7+60t8-10t9)/(1-t)7(-15120+13524t-5094t2-720t3+30t4+156t5+24t6)/6!
30000(10t5+135t6-314t7+343t8-210t9+70t10-10t11)/(1-t)9(-1209600+495360t-145680t2+50344t3+5376t4-1400t5-840t6+16t7+24t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Co_?IQpicture of the graph :Co_?IQ
0014
0001
1003
4130
[8, 5, 4, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
106212733(6t+9t2-9t3)/(1-t)29+6t
200026206(26t3+50t4-160t5+201t6-153t7+66t8-12t9)/(1-t)6(360+1742t-945t2-200t3+105t4+18t5)/5!
300000(6t5+329t6-832t7+1043t8-798t9+378t10-102t11+12t12)/(1-t)9(-241920+368448t-173216t2+19656t3+33964t4-5208t5-1904t6+144t7+36t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Co_?@Qpicture of the graph :Co_?@Q
0015
0001
1002
5120
[8, 6, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
106232935(6t+11t2-11t3)/(1-t)211+6t
200024244(24t3+76t4-218t5+281t6-226t7+121t8-40t9+6t10)/(1-t)7(3600+8484t-5094t2-720t3+30t4+156t5+24t6)/6!
300000(4t5+177t6-440t7+553t8-420t9+196t10-52t11+6t12)/(1-t)9(-241920+253440t-145680t2+50344t3+5376t4-1400t5-840t6+16t7+24t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:CoC?IQpicture of the graph :CoC?IQ
0023
0001
2003
3130
[7, 5, 5, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
106182328(6t+6t2-7t3)/(1-t)28+5t
200037228(37t3+43t4-135t5+142t6-72t7+15t8)/(1-t)5(480-248t-90t2-4t3+30t4)/4!
300000(6t5+491t6-1264t7+1556t8-1140t9+513t10-132t11+15t12)/(1-t)9(483840-588144t-1508t2+76692t3+43645t4-12936t5-1862t6+228t7+45t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:CoC?@Qpicture of the graph :CoC?@Q
0024
0001
2002
4120
[7, 6, 4, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
106192429(6t+7t2-8t3)/(1-t)29+5t
200035238(35t3+28t4-162t5+237t6-176t7+70t8-12t9)/(1-t)6(2520-1270t-415t2+50t3+55t4+20t5)/5!
300000(6t5+401t6-1024t7+1261t8-924t9+414t10-106t11+12t12)/(1-t)9(483840-600384t+8080t2+101864t3+14000t4-5656t5-1960t6+176t7+40t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:CoC??Ipicture of the graph :CoC??I
0025
0001
2001
5110
[7, 7, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
106222732(6t+10t2-11t3)/(1-t)212+5t
200029268(29t3+65t4-210t5+288t6-239t7+126t8-40t9+6t10)/(1-t)7(19440-9180t+1000t2-1425t3+55t4+165t5+25t6)/6!
300000(4t5+192t6-480t7+598t8-444t9+201t10-52t11+6t12)/(1-t)9(604800-694224t+197004t2+10220t3+5425t4-1456t5-854t6+20t7+25t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Co?_@Qpicture of the graph :Co?_@Q
0033
0001
3002
3120
[6, 6, 5, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
106172125(6t+5t2-7t3)/(1-t)29+4t
200040234(40t3+34t4-154t5+157t6-76t7+15t8)/(1-t)5(384-180t-268t2+96t3+16t4)/4!
300000(6t5+551t6-1424t7+1736t8-1244t9+544t10-136t11+15t12)/(1-t)9(282240-431904t-298752t2+243544t3+18312t4-13496t5-1848t6+256t7+48t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Co?_?Ipicture of the graph :Co?_?I
0034
0001
3001
4110
[7, 6, 4, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
106192327(6t+7t2-9t3)/(1-t)211+4t
200034236(34t3+32t4-168t5+241t6-177t7+70t8-12t9)/(1-t)6(2760-1390t-415t2+50t3+55t4+20t5)/5!
300000(6t5+401t6-1024t7+1261t8-924t9+414t10-106t11+12t12)/(1-t)9(483840-600384t+8080t2+101864t3+14000t4-5656t5-1960t6+176t7+40t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Co?C@Qpicture of the graph :Co?C@Q
0042
0001
4002
2120
[6, 6, 5, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
106172023(6t+5t2-8t3)/(1-t)211+3t
200039232(39t3+37t4-154t5+149t6-67t7+12t8)/(1-t)5(144-132t-268t2+96t3+16t4)/4!
300000(9t5+530t6-1361t7+1631t8-1139t9+481t10-115t11+12t12)/(1-t)9(-201600-310944t-298752t2+243544t3+18312t4-13496t5-1848t6+256t7+48t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Co?C?Ipicture of the graph :Co?C?I
0043
0001
4001
3110
[7, 5, 5, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
106182124(6t+6t2-9t3)/(1-t)212+3t
200035224(35t3+49t4-138t5+135t6-63t7+12t8)/(1-t)5(288-224t-90t2-4t3+30t4)/4!
300000(9t5+470t6-1201t7+1451t8-1035t9+450t10-111t11+12t12)/(1-t)9(-467184t-1508t2+76692t3+43645t4-12936t5-1862t6+228t7+45t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Co??_Ipicture of the graph :Co??_I
0052
0001
5001
2110
[7, 6, 4, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
106192123(6t+7t2-11t3)/(1-t)215+2t
200032232(32t3+40t4-174t5+225t6-143t7+46t8-6t9)/(1-t)6(360-910t-415t2+50t3+55t4+20t5)/5!
300000(12t5+359t6-898t7+1051t8-714t9+288t10-64t11+6t12)/(1-t)9(-483840-358464t+8080t2+101864t3+14000t4-5656t5-1960t6+176t7+40t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Co??CIpicture of the graph :Co??CI
0061
0001
6001
1110
[7, 7, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1062223(6t+10t2-15t3)/(1-t)220+t
200025(25t3+85t4-244t5+298t6-199t7+70t8-10t9)/(1-t)7(7920-7740t+1000t2-1425t3+55t4+165t5+25t6)/6!
30000(10t5+150t6-354t7+388t8-234t9+75t10-10t11)/(1-t)9(-362880-452304t+197004t2+10220t3+5425t4-1456t5-854t6+20t7+25t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Do??@CQNpicture of the graph :Do??@CQN
00004
00003
00001
00001
43110
[9, 4, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
1052765130(5t+7t2-13t3+12t4-4t5)/(1-t)4(24+5t+18t2+7t3)/3!
200010117(10t3+47t4-98t5+105t6-84t7+49t8-18t9+3t10)/(1-t)7(5040+696t+176t2-810t3-190t4+114t5+14t6)/6!
300000(t5+76t6-168t7+210t8-168t9+84t10-24t11+3t12)/(1-t)9(120960+5952t-2296t2-7504t3+2926t4+1568t5-644t6-16t7+14t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:DkG?PCPJpicture of the graph :DkG?PCPJ
00012
00005
00001
10000
25100
[8, 5, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1052341(5t+8t2-13t3+6t4)/(1-t)3(10+6t+6t2)/2!
200014(14t3+62t4-146t5+155t6-97t7+36t8-6t9)/(1-t)7(-9360+6732t-138t2-1800t3+120t4+108t5+18t6)/6!
30000(4t5+97t6-203t7+210t8-126t9+42t10-6t11)/(1-t)9(-725760+261408t-14200t2-18480t3+14882t4-1008t5-700t6+18t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:DkG?@CPJpicture of the graph :DkG?@CPJ
00013
00004
00001
10000
34100
[8, 4, 4, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
105224166(5t+7t2-10t3+4t4)/(1-t)3(4+8t+6t2)/2!
200016143(16t3+47t4-87t5+88t6-58t7+21t8-3t9)/(1-t)6(-1560+1256t-40t2-320t3+40t4+24t5)/5!
300000(3t5+167t6-371t7+420t8-294t9+126t10-30t11+3t12)/(1-t)9(-604800+268512t-17552t2-27104t3+19096t4+448t5-1568t6+64t7+24t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:DkG??CPJpicture of the graph :DkG??CPJ
00014
00003
00001
10000
43100
[8, 5, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
105234369(5t+8t2-11t3+4t4)/(1-t)3(2+10t+6t2)/2!
200016164(16t3+52t4-129t5+150t6-117t7+64t8-21t9+3t10)/(1-t)7(-3600+6012t-138t2-1800t3+120t4+108t5+18t6)/6!
300000(t5+118t6-266t7+315t8-231t9+105t10-27t11+3t12)/(1-t)9(-241920+140448t-14200t2-18480t3+14882t4-1008t5-700t6+18t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dk?A??@Jpicture of the graph :Dk?A??@J
00034
00001
00001
30000
41100
[7, 6, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
105213757(5t+6t2-11t3+4t4)/(1-t)3(2+12t+4t2)/2!
200024206(24t3+38t4-125t5+166t6-133t7+68t8-21t9+3t10)/(1-t)7(5040+564t-1450t2-690t3-10t4+126t5+20t6)/6!
300000(t5+142t6-322t7+369t8-255t9+109t10-27t11+3t12)/(1-t)9(241920-202560t-44512t2+42392t3+4900t4-1120t5-728t6+8t7+20t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dk??G?@Jpicture of the graph :Dk??G?@J
00043
00001
00001
40000
31100
[7, 5, 4, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
105193248(5t+4t2-10t3+4t4)/(1-t)3(4+11t+3t2)/2!
200025179(25t3+29t4-105t5+115t6-67t7+21t8-3t9)/(1-t)6(1680-1030t-85t2-185t3+85t4+15t5)/5!
300000(6t5+230t6-515t7+549t8-348t9+135t10-30t11+3t12)/(1-t)9(483840-555744t+32632t2+15568t3+29470t4-4256t5-1652t6+112t7+30t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dk???_@Jpicture of the graph :Dk???_@J
00052
00001
00001
50000
21100
[7, 5, 4, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1051929(5t+4t2-13t3+6t4)/(1-t)3(10+10t+2t2)/2!
200022(22t3+40t4-114t5+103t6-42t7+6t8)/(1-t)6(2760-1990t+35t2-185t3+85t4+15t5)/5!
30000(12t5+191t6-407t7+384t8-198t9+54t10-6t11)/(1-t)9(725760-858144t+93112t2+15568t3+29470t4-4256t5-1652t6+112t7+30t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:DkG?@GrNpicture of the graph :DkG?@GrN
00013
00001
00001
10003
31130
[8, 4, 4, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
105223962(5t+7t2-12t3+6t4)/(1-t)3(12+4t+6t2)/2!
200014139(14t3+55t4-101t5+104t6-72t7+29t8-5t9)/(1-t)6(-120+776t-40t2-320t3+40t4+24t5)/5!
300000(t5+181t6-413t7+490t8-364t9+168t10-44t11+5t12)/(1-t)9(-282240+187872t-17552t2-27104t3+19096t4+448t5-1568t6+64t7+24t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:DkG??CbNpicture of the graph :DkG??CbN
00014
00001
00001
10002
41120
[8, 5, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
105234063(5t+8t2-14t3+7t4)/(1-t)3(14+4t+6t2)/2!
200013158(13t3+67t4-159t5+180t6-132t7+67t8-21t9+3t10)/(1-t)7(720+3852t-138t2-1800t3+120t4+108t5+18t6)/6!
300000(t5+118t6-266t7+315t8-231t9+105t10-27t11+3t12)/(1-t)9(-241920+140448t-14200t2-18480t3+14882t4-1008t5-700t6+18t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dk?_?CbNpicture of the graph :Dk?_?CbN
00023
00001
00001
20002
31120
[7, 5, 4, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
105193352(5t+4t2-9t3+5t4)/(1-t)3(12+3t+5t2)/2!
200026183(26t3+27t4-110t5+134t6-89t7+32t8-5t9)/(1-t)6(960-490t-145t2-185t3+85t4+15t5)/5!
300000(t5+262t6-602t7+679t8-463t9+195t10-47t11+5t12)/(1-t)9(80640-213024t-27848t2+15568t3+29470t4-4256t5-1652t6+112t7+30t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dk?_??QNpicture of the graph :Dk?_??QN
00024
00001
00001
20001
41110
[7, 6, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
105213554(5t+6t2-13t3+7t4)/(1-t)3(16+3t+5t2)/2!
200022203(22t3+49t4-149t5+192t6-147t7+71t8-21t9+3t10)/(1-t)7(10080-2676t-1090t2-690t3-10t4+126t5+20t6)/6!
300000(t5+142t6-322t7+369t8-255t9+109t10-27t11+3t12)/(1-t)9(241920-202560t-44512t2+42392t3+4900t4-1120t5-728t6+8t7+20t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dk?A?CbNpicture of the graph :Dk?A?CbN
00032
00001
00001
30002
21120
[6, 5, 5, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
105172843(5t+2t2-8t3+5t4)/(1-t)3(14+2t+4t2)/2!
200031192(31t3+37t4-96t5+77t6-30t7+5t8)/(1-t)5(336-148t-192t2+28t3+24t4)/4!
300000(t5+352t6-812t7+884t8-566t9+222t10-50t11+5t12)/(1-t)9(282240-273504t-277936t2+122472t3+37604t4-10416t5-1624t6+168t7+36t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dk?A??QNpicture of the graph :Dk?A??QN
00033
00001
00001
30001
31110
[6, 6, 4, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
105182944(5t+3t2-10t3+6t4)/(1-t)3(16+2t+4t2)/2!
200028193(28t3+25t4-123t5+153t6-94t7+32t8-5t9)/(1-t)6(2280-796t-880t2+180t3+40t4+16t5)/5!
300000(t5+292t6-672t7+744t8-490t9+199t10-47t11+5t12)/(1-t)9(443520-294240t-253040t2+137312t3+12768t4-4480t5-1680t6+128t7+32t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dk??G?QNpicture of the graph :Dk??G?QN
00042
00001
00001
40001
21110
[6, 5, 5, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
105172536(5t+2t2-11t3+7t4)/(1-t)3(20+t+3t2)/2!
200028185(28t3+45t4-98t5+67t6-21t7+3t8)/(1-t)5(648-364t-168t2+28t3+24t4)/4!
300000(6t5+320t6-725t7+754t8-451t9+162t10-33t11+3t12)/(1-t)9(685440-616224t-217456t2+122472t3+37604t4-10416t5-1624t6+168t7+36t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dk???_QNpicture of the graph :Dk???_QN
00051
00001
00001
50001
11110
[6, 6, 4, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1051823(5t+3t2-16t3+10t4)/(1-t)3(28+2t2)/2!
200022(22t3+47t4-142t5+133t6-50t7+6t8)/(1-t)6(4920-2836t-640t2+180t3+40t4+16t5)/5!
30000(12t5+221t6-477t7+449t8-225t9+58t10-6t11)/(1-t)9(1088640-939360t-132080t2+137312t3+12768t4-4480t5-1680t6+128t7+32t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dk?EAKrNpicture of the graph :Dk?EAKrN
00021
00010
00001
21004
10140
[7, 6, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
105213039(5t+11t2-7t3)/(1-t)23+9t
200017188(17t3+69t4-179t5+212t6-152t7+71t8-21t9+3t10)/(1-t)7(6480+2724t-2890t2-690t3-10t4+126t5+20t6)/6!
300000(t5+142t6-322t7+369t8-255t9+109t10-27t11+3t12)/(1-t)9(241920-202560t-44512t2+42392t3+4900t4-1120t5-728t6+8t7+20t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dk?E?GrNpicture of the graph :Dk?E?GrN
00022
00010
00001
21003
20130
[6, 6, 4, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
105182634(5t+8t2-5t3)/(1-t)22+8t
200025183(25t3+33t4-129t5+153t6-93t7+32t8-5t9)/(1-t)6(1560+44t-1120t2+180t3+40t4+16t5)/5!
300000(t5+292t6-672t7+744t8-490t9+199t10-47t11+5t12)/(1-t)9(443520-294240t-253040t2+137312t3+12768t4-4480t5-1680t6+128t7+32t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dk??WGrNpicture of the graph :Dk??WGrN
00031
00010
00001
31003
10130
[7, 5, 4, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
105192735(5t+9t2-6t3)/(1-t)23+8t
200020166(20t3+46t4-131t5+143t6-90t7+32t8-5t9)/(1-t)6(600+290t-445t2-185t3+85t4+15t5)/5!
300000(t5+262t6-602t7+679t8-463t9+195t10-47t11+5t12)/(1-t)9(80640-213024t-27848t2+15568t3+29470t4-4256t5-1652t6+112t7+30t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dk??W?bNpicture of the graph :Dk??W?bN
00032
00010
00001
31002
20120
[6, 5, 5, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
105172431(5t+7t2-5t3)/(1-t)23+7t
200027180(27t3+45t4-100t5+77t6-30t7+5t8)/(1-t)5(240-4t-240t2+28t3+24t4)/4!
300000(t5+352t6-812t7+884t8-566t9+222t10-50t11+5t12)/(1-t)9(282240-273504t-277936t2+122472t3+37604t4-10416t5-1624t6+168t7+36t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dk??W?ANpicture of the graph :Dk??W?AN
00033
00010
00001
31001
30110
[6, 5, 5, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
105172329(5t+7t2-6t3)/(1-t)25+6t
200026178(26t3+48t4-103t5+78t6-30t7+5t8)/(1-t)5(288-28t-240t2+28t3+24t4)/4!
300000(t5+352t6-812t7+884t8-566t9+222t10-50t11+5t12)/(1-t)9(282240-273504t-277936t2+122472t3+37604t4-10416t5-1624t6+168t7+36t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dk??@_bNpicture of the graph :Dk??@_bN
00041
00010
00001
41002
10120
[7, 5, 4, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
105192633(5t+9t2-7t3)/(1-t)25+7t
200019164(19t3+50t4-135t5+139t6-79t7+24t8-3t9)/(1-t)6(-120+410t-445t2-185t3+85t4+15t5)/5!
300000(3t5+248t6-560t7+609t8-393t9+153t10-33t11+3t12)/(1-t)9(-241920-132384t-27848t2+15568t3+29470t4-4256t5-1652t6+112t7+30t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dk??@_ANpicture of the graph :Dk??@_AN
00042
00010
00001
41001
20110
[6, 6, 4, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
105182430(5t+8t2-7t3)/(1-t)26+6t
200023179(23t3+41t4-139t5+153t6-83t7+24t8-3t9)/(1-t)6(1080+44t-1120t2+180t3+40t4+16t5)/5!
300000(3t5+278t6-630t7+674t8-420t9+157t10-33t11+3t12)/(1-t)9(120960-213600t-253040t2+137312t3+12768t4-4480t5-1680t6+128t7+32t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dk???EANpicture of the graph :Dk???EAN
00051
00010
00001
51001
10110
[7, 6, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1052127(5t+11t2-10t3)/(1-t)29+6t
200014(14t3+84t4-206t5+227t6-137t7+44t8-6t9)/(1-t)7(2160+2724t-2890t2-690t3-10t4+126t5+20t6)/6!
30000(4t5+121t6-259t7+264t8-150t9+46t10-6t11)/(1-t)9(-241920-81600t-44512t2+42392t3+4900t4-1120t5-728t6+8t7+20t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:DgH_??PFpicture of the graph :DgH_??PF
00104
00013
10000
01000
43000
[7, 5, 4, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
105192939(5t+9t2-4t3)/(1-t)2-1+10t
200022170(22t3+38t4-117t5+127t6-76t7+24t8-3t9)/(1-t)6(-840+770t-445t2-185t3+85t4+15t5)/5!
300000(3t5+248t6-560t7+609t8-393t9+153t10-33t11+3t12)/(1-t)9(-241920-132384t-27848t2+15568t3+29470t4-4256t5-1652t6+112t7+30t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:DgH_??@Fpicture of the graph :DgH_??@F
00105
00012
10000
01000
52000
[7, 6, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1052131(5t+11t2-6t3)/(1-t)21+10t
200018(18t3+64t4-166t5+187t6-117t7+40t8-6t9)/(1-t)7(-3600+5604t-2890t2-690t3-10t4+126t5+20t6)/6!
30000(4t5+121t6-259t7+264t8-150t9+46t10-6t11)/(1-t)9(-241920-81600t-44512t2+42392t3+4900t4-1120t5-728t6+8t7+20t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Es??PCbRpicture of the graph :Es??PCbR
000003
000003
000001
000001
000001
331110
[9, 3, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
1042888213(4t+8t2-12t3+13t4-8t5+2t6)/(1-t)5(48-2t+53t2+38t3+7t4)/4!
2000459(4t3+31t4-46t5+45t6-32t7+17t8-6t9+t10)/(1-t)7(2160+240t+116t2-270t3-130t4+30t5+14t6)/6!
300000(28t6-56t7+70t8-56t9+28t10-8t11+t12)/(1-t)9(40320+1296t-252t2-1764t3+343t4+504t5-98t6-36t7+7t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:EoG?PCQNpicture of the graph :EoG?PCQN
000012
000004
000001
000001
100000
241100
[8, 4, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1042356(4t+7t2-12t3+10t4-3t5)/(1-t)4(12+9t+15t2+6t3)/3!
20007(7t3+44t4-85t5+80t6-49t7+18t8-3t9)/(1-t)7(-5040+3504t+168t2-720t3-180t4+96t5+12t6)/6!
30000(t5+56t6-105t7+105t8-63t9+21t10-3t11)/(1-t)9(-362880+126240t-2000t2-6664t3+2548t4+1400t5-560t6-16t7+12t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:EoG?@CQNpicture of the graph :EoG?@CQN
000013
000003
000001
000001
100000
331100
[8, 4, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
1042357114(4t+7t2-11t3+8t4-2t5)/(1-t)4(15t+15t2+6t3)/3!
2000895(8t3+39t4-76t5+75t6-54t7+27t8-8t9+t10)/(1-t)7(-3600+3504t+168t2-720t3-180t4+96t5+12t6)/6!
300000(63t6-126t7+140t8-98t9+42t10-10t11+t12)/(1-t)9(-201600+85920t-2000t2-6664t3+2548t4+1400t5-560t6-16t7+12t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Eo?A??QNpicture of the graph :Eo?A??QN
000033
000001
000001
000001
300000
311100
[6, 6, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104194382(4t+3t2-9t3+8t4-2t5)/(1-t)4(23t+9t2+4t3)/3!
200022171(22t3+17t4-74t5+98t6-70t7+30t8-8t9+t10)/(1-t)7(5364t-4286t2+300t3-50t4+96t5+16t6)/6!
300000(100t6-200t7+200t8-120t9+45t10-10t11+t12)/(1-t)9(141120t-205424t2+61320t3+4424t4-840t5-616t6+16t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Eo??G?QNpicture of the graph :Eo??G?QN
000042
000001
000001
000001
400000
211100
[6, 5, 4, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1041735(4t+t2-9t3+10t4-3t5)/(1-t)4(12+21t+6t2+3t3)/3!
200022(22t3+21t4-74t5+61t6-21t7+3t8)/(1-t)6(240+1238t-1265t2+70t3+65t4+12t5)/5!
30000(6t5+146t6-279t7+235t8-108t9+27t10-3t11)/(1-t)9(273984t-366320t2+71960t3+24976t4-3304t5-1400t6+80t7+24t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:EoG?@GsRpicture of the graph :EoG?@GsR
000013
000001
000001
000001
100002
311120
[8, 4, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
1042355110(4t+7t2-13t3+12t4-4t5)/(1-t)4(24+3t+15t2+6t3)/3!
2000691(6t3+49t4-96t5+95t6-64t7+29t8-8t9+t10)/(1-t)7(-720+2064t+168t2-720t3-180t4+96t5+12t6)/6!
300000(63t6-126t7+140t8-98t9+42t10-10t11+t12)/(1-t)9(-201600+85920t-2000t2-6664t3+2548t4+1400t5-560t6-16t7+12t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Eo?_@GsRpicture of the graph :Eo?_@GsR
000022
000001
000001
000001
200002
211120
[7, 4, 4, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104194590(4t+3t2-7t3+8t4-3t5)/(1-t)4(24+t+12t2+5t3)/3!
200020143(20t3+23t4-58t5+60t6-33t7+9t8-t9)/(1-t)6(600-620t+150t2-180t3+30t4+20t5)/5!
300000(135t6-270t7+270t8-164t9+60t10-12t11+t12)/(1-t)9(40320-218784t+65584t2-23688t3+16380t4+504t5-1344t6+48t7+20t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Eo?_?CbRpicture of the graph :Eo?_?CbR
000023
000001
000001
000001
200001
311110
[7, 5, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104204691(4t+4t2-10t3+11t4-4t5)/(1-t)4(30+t+12t2+5t3)/3!
200018153(18t3+27t4-87t5+107t6-75t7+32t8-8t9+t10)/(1-t)7(6480-3432t+630t2-975t3+75t4+87t5+15t6)/6!
300000(90t6-180t7+185t8-116t9+45t10-10t11+t12)/(1-t)9(161280-204816t+48292t2-16156t3+12775t4-784t5-602t6-4t7+15t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Eo?A?CbRpicture of the graph :Eo?A?CbR
000032
000001
000001
000001
300001
211110
[6, 5, 4, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104173772(4t+t2-7t3+10t4-4t5)/(1-t)4(36-t+9t2+4t3)/3!
200024161(24t3+17t4-79t5+79t6-37t7+9t8-t9)/(1-t)6(1200-42t-785t2+30t3+65t4+12t5)/5!
300000(180t6-360t7+340t8-188t9+63t10-12t11+t12)/(1-t)9(161280-8256t-225200t2+51800t3+24976t4-3304t5-1400t6+80t7+24t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Eo??GCbRpicture of the graph :Eo??GCbR
000041
000001
000001
000001
400001
111110
[5, 5, 5, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1041630(4t-10t3+15t4-6t5)/(1-t)4(54-3t+6t2+3t3)/3!
200022(22t3+43t4-59t5+24t6-3t7)/(1-t)5(384+66t-267t2+6t3+27t4)/4!
30000(6t5+182t6-351t7+291t8-128t9+30t10-3t11)/(1-t)9(282240+131856t-388044t2+57372t3+46683t4-7896t5-1386t6+108t7+27t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Eo?E??ANpicture of the graph :Eo?E??AN
000024
000010
000001
000001
210000
401100
[6, 6, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1041935(4t+7t2-10t3+3t4)/(1-t)3(-2+12t+4t2)/2!
200014(14t3+46t4-113t5+119t6-68t7+21t8-3t9)/(1-t)7(-3600+7644t-3926t2-180t3-50t4+96t5+16t6)/6!
30000(t5+93t6-179t7+165t8-85t9+24t10-3t11)/(1-t)9(-161280+181440t-205424t2+61320t3+4424t4-840t5-616t6+16t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Eo??W?ANpicture of the graph :Eo??W?AN
000033
000010
000001
000001
310000
301100
[6, 5, 4, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104173148(4t+5t2-8t3+2t4)/(1-t)3(-4+13t+3t2)/2!
200018137(18t3+29t4-83t5+75t6-35t7+9t8-t9)/(1-t)6(240+758t-785t2-50t3+65t4+12t5)/5!
300000(180t6-360t7+340t8-188t9+63t10-12t11+t12)/(1-t)9(161280-8256t-225200t2+51800t3+24976t4-3304t5-1400t6+80t7+24t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Eo??@_ANpicture of the graph :Eo??@_AN
000042
000010
000001
000001
410000
201100
[6, 5, 4, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1041729(4t+5t2-10t3+3t4)/(1-t)3(-2+14t+2t2)/2!
200016(16t3+36t4-89t5+70t6-24t7+3t8)/(1-t)6(1320+98t-725t2-50t3+65t4+12t5)/5!
30000(3t5+161t6-309t7+265t8-123t9+30t10-3t11)/(1-t)9(483840-250176t-184880t2+51800t3+24976t4-3304t5-1400t6+80t7+24t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Eo??YLCRpicture of the graph :Eo??YLCR
000030
000010
000001
000001
310003
001130
[7, 5, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104204272(4t+8t2-6t3+2t4)/(1-t)3(4t+8t2)/2!
200014134(14t3+36t4-88t5+96t6-66t7+30t8-8t9+t10)/(1-t)7(2880-2112t+2070t2-1575t3+75t4+87t5+15t6)/6!
300000(90t6-180t7+185t8-116t9+45t10-10t11+t12)/(1-t)9(161280-204816t+48292t2-16156t3+12775t4-784t5-602t6-4t7+15t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Eo??@gsRpicture of the graph :Eo??@gsR
000040
000010
000001
000001
410002
001120
[7, 4, 4, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1041938(4t+7t2-7t3+3t4)/(1-t)3(4+3t+7t2)/2!
200013(13t3+39t4-66t5+52t6-21t7+3t8)/(1-t)6(1320-1180t+450t2-280t3+30t4+20t5)/5!
30000(3t5+116t6-219t7+195t8-99t9+27t10-3t11)/(1-t)9(362880-460704t+105904t2-23688t3+16380t4+504t5-1344t6+48t7+20t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Eo@_ALCRpicture of the graph :Eo@_ALCR
000012
000010
000001
000001
110003
201130
[7, 5, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104203759(4t+8t2-11t3+4t4)/(1-t)3(2+9t+5t2)/2!
20009121(9t3+58t4-126t5+128t6-79t7+32t8-8t9+t10)/(1-t)7(3600-312t+990t2-1575t3+75t4+87t5+15t6)/6!
300000(90t6-180t7+185t8-116t9+45t10-10t11+t12)/(1-t)9(161280-204816t+48292t2-16156t3+12775t4-784t5-602t6-4t7+15t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Eo@_?GsRpicture of the graph :Eo@_?GsR
000013
000010
000001
000001
110002
301120
[7, 4, 4, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104193556(4t+7t2-10t3+4t4)/(1-t)3(4+7t+5t2)/2!
200010109(10t3+49t4-81t5+68t6-34t7+9t8-t9)/(1-t)6(360-220t+210t2-280t3+30t4+20t5)/5!
300000(135t6-270t7+270t8-164t9+60t10-12t11+t12)/(1-t)9(40320-218784t+65584t2-23688t3+16380t4+504t5-1344t6+48t7+20t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Eo@_??bRpicture of the graph :Eo@_??bR
000014
000010
000001
000001
110001
401110
[7, 5, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1042035(4t+8t2-13t3+6t4)/(1-t)3(10+5t+5t2)/2!
20007(7t3+68t4-145t5+143t6-79t7+24t8-3t9)/(1-t)7(3600-1032t+990t2-1575t3+75t4+87t5+15t6)/6!
30000(t5+83t6-159t7+150t8-81t9+24t10-3t11)/(1-t)9(-164496t+48292t2-16156t3+12775t4-784t5-602t6-4t7+15t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Eo?EALCRpicture of the graph :Eo?EALCR
000021
000010
000001
000001
210003
101130
[6, 6, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104193453(4t+7t2-11t3+4t4)/(1-t)3(2+10t+4t2)/2!
200013142(13t3+51t4-124t5+134t6-83t7+32t8-8t9+t10)/(1-t)7(720+6204t-3926t2-180t3-50t4+96t5+16t6)/6!
300000(100t6-200t7+200t8-120t9+45t10-10t11+t12)/(1-t)9(141120t-205424t2+61320t3+4424t4-840t5-616t6+16t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Eo?E?GsRpicture of the graph :Eo?E?GsR
000022
000010
000001
000001
210002
201120
[6, 5, 4, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104173149(4t+5t2-8t3+3t4)/(1-t)3(2+8t+4t2)/2!
200018138(18t3+30t4-86t5+78t6-36t7+9t8-t9)/(1-t)6(600+458t-725t2-50t3+65t4+12t5)/5!
300000(180t6-360t7+340t8-188t9+63t10-12t11+t12)/(1-t)9(161280-8256t-225200t2+51800t3+24976t4-3304t5-1400t6+80t7+24t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Eo?E??bRpicture of the graph :Eo?E??bR
000023
000010
000001
000001
210001
301110
[6, 5, 4, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104173047(4t+5t2-9t3+4t4)/(1-t)3(6+6t+4t2)/2!
200017136(17t3+34t4-92t5+82t6-37t7+9t8-t9)/(1-t)6(840+338t-725t2-50t3+65t4+12t5)/5!
300000(180t6-360t7+340t8-188t9+63t10-12t11+t12)/(1-t)9(161280-8256t-225200t2+51800t3+24976t4-3304t5-1400t6+80t7+24t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Eo??WGsRpicture of the graph :Eo??WGsR
000031
000010
000001
000001
310002
101120
[6, 5, 4, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104172944(4t+5t2-10t3+4t4)/(1-t)3(4+9t+3t2)/2!
200016133(16t3+37t4-95t5+83t6-37t7+9t8-t9)/(1-t)6(720+518t-785t2-50t3+65t4+12t5)/5!
300000(180t6-360t7+340t8-188t9+63t10-12t11+t12)/(1-t)9(161280-8256t-225200t2+51800t3+24976t4-3304t5-1400t6+80t7+24t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Eo??W?bRpicture of the graph :Eo??W?bR
000032
000010
000001
000001
310001
201110
[5, 5, 5, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104162741(4t+4t2-9t3+4t4)/(1-t)3(6+7t+3t2)/2!
200019139(19t3+44t4-61t5+32t6-8t7+t8)/(1-t)5(336-6t-171t2-18t3+27t4)/4!
300000(216t6-432t7+396t8-208t9+66t10-12t11+t12)/(1-t)9(443520-150384t-246924t2+37212t3+46683t4-7896t5-1386t6+108t7+27t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Eo??@_bRpicture of the graph :Eo??@_bR
000041
000010
000001
000001
410001
101110
[6, 5, 4, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1041726(4t+5t2-13t3+6t4)/(1-t)3(10+8t+2t2)/2!
200013(13t3+48t4-107t5+82t6-27t7+3t8)/(1-t)6(2040-262t-725t2-50t3+65t4+12t5)/5!
30000(3t5+161t6-309t7+265t8-123t9+30t10-3t11)/(1-t)9(483840-250176t-184880t2+51800t3+24976t4-3304t5-1400t6+80t7+24t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:EkH_?CPJpicture of the graph :EkH_?CPJ
000103
000013
000001
100000
010000
331000
[7, 4, 4, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104193760(4t+7t2-8t3+2t4)/(1-t)3(-4+11t+5t2)/2!
200012113(12t3+41t4-69t5+60t6-32t7+9t8-t9)/(1-t)6(-120+20t+210t2-280t3+30t4+20t5)/5!
300000(135t6-270t7+270t8-164t9+60t10-12t11+t12)/(1-t)9(40320-218784t+65584t2-23688t3+16380t4+504t5-1344t6+48t7+20t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:EkH_??PJpicture of the graph :EkH_??PJ
000104
000012
000001
100000
010000
421000
[7, 5, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1042038(4t+8t2-10t3+3t4)/(1-t)3(-2+11t+5t2)/2!
200010(10t3+53t4-115t5+113t6-64t7+21t8-3t9)/(1-t)7(-720+1128t+990t2-1575t3+75t4+87t5+15t6)/6!
30000(t5+83t6-159t7+150t8-81t9+24t10-3t11)/(1-t)9(-164496t+48292t2-16156t3+12775t4-784t5-602t6-4t7+15t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:EkG?W?cRpicture of the graph :EkG?W?cR
000122
000010
000001
100000
210002
201020
[5, 5, 5, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104162534(4t+8t2-3t3)/(1-t)2-2+9t
200017132(17t3+47t4-61t5+31t6-8t7+t8)/(1-t)5(216+126t-207t2-18t3+27t4)/4!
300000(216t6-432t7+396t8-208t9+66t10-12t11+t12)/(1-t)9(443520-150384t-246924t2+37212t3+46683t4-7896t5-1386t6+108t7+27t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:EkG?@_ARpicture of the graph :EkG?@_AR
000132
000010
000001
100000
310001
201010
[6, 5, 4, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104172635(4t+9t2-4t3)/(1-t)2-1+9t
200013124(13t3+46t4-104t5+86t6-37t7+9t8-t9)/(1-t)6(360+1058t-965t2-50t3+65t4+12t5)/5!
300000(180t6-360t7+340t8-188t9+63t10-12t11+t12)/(1-t)9(161280-8256t-225200t2+51800t3+24976t4-3304t5-1400t6+80t7+24t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:EkG??EARpicture of the graph :EkG??EAR
000141
000010
000001
100000
410001
101010
[6, 6, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1041928(4t+11t2-6t3)/(1-t)21+9t
20007(7t3+77t4-167t5+165t6-87t7+24t8-3t9)/(1-t)7(-2160+9804t-5366t2-180t3-50t4+96t5+16t6)/6!
30000(t5+93t6-179t7+165t8-85t9+24t10-3t11)/(1-t)9(-161280+181440t-205424t2+61320t3+4424t4-840t5-616t6+16t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:FsG?PCbRpicture of the graph :FsG?PCbR
0000012
0000003
0000001
0000001
0000001
1000000
2311100
[8, 3, 3, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1032374(3t+8t2-11t3+10t4-5t5+t6)/(1-t)5(16t+42t2+32t3+6t4)/4!
20003(3t3+26t4-35t5+30t6-17t7+6t8-t9)/(1-t)7(-2160+1656t+108t2-240t3-120t4+24t5+12t6)/6!
30000(21t6-35t7+35t8-21t9+7t10-t11)/(1-t)9(-120960+41472t-216t2-1568t3+294t4+448t5-84t6-32t7+6t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Fs?A?CbRpicture of the graph :Fs?A?CbR
0000032
0000001
0000001
0000001
0000001
3000000
2111100
[6, 5, 3, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031750(3t+2t2-5t3+8t4-5t5+t6)/(1-t)5(52t+20t2+20t3+4t4)/4!
200021(21t3-37t5+49t6-28t7+8t8-t9)/(1-t)7(3204t-2322t2-390t3+150t4+66t5+12t6)/6!
30000(60t6-100t7+80t8-36t9+9t10-t11)/(1-t)9(74880t-90816t2+6328t3+10668t4-560t5-504t6-8t7+12t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:FsG?QLDVpicture of the graph :FsG?QLDV
0000012
0000001
0000001
0000001
0000001
1000002
2111120
[8, 3, 3, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1032373(3t+8t2-12t3+13t4-8t5+2t6)/(1-t)5(48-8t+42t2+32t3+6t4)/4!
20002(2t3+31t4-45t5+40t6-22t7+7t8-t9)/(1-t)7(-720+936t+108t2-240t3-120t4+24t5+12t6)/6!
30000(21t6-35t7+35t8-21t9+7t10-t11)/(1-t)9(-120960+41472t-216t2-1568t3+294t4+448t5-84t6-32t7+6t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Fs?_@GsVpicture of the graph :Fs?_@GsV
0000022
0000001
0000001
0000001
0000001
2000001
2111110
[7, 4, 3, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031959(3t+4t2-6t3+9t4-7t5+2t6)/(1-t)5(72-14t+31t2+26t3+5t4)/4!
200016(16t3+7t4-38t5+46t6-29t7+9t8-t9)/(1-t)7(4320-2868t+370t2-450t3-20t4+78t5+10t6)/6!
30000(45t6-75t7+65t8-33t9+9t10-t11)/(1-t)9(120960-156672t+38616t2-5824t3+2170t4+1232t5-476t6-16t7+10t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Fs?A@GsVpicture of the graph :Fs?A@GsV
0000031
0000001
0000001
0000001
0000001
3000001
1111110
[6, 4, 4, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031646(3t+t2-4t3+11t4-10t5+3t6)/(1-t)5(120-20t+20t2+20t3+4t4)/4!
200021(21t3+14t4-44t5+35t6-11t7+t8)/(1-t)6(1200-196t-400t2-60t3+40t4+16t5)/5!
30000(90t6-150t7+115t8-49t9+11t10-t11)/(1-t)9(201600-47520t-93200t2+6608t3+13664t4+560t5-1120t6+32t7+16t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Fs?E??bRpicture of the graph :Fs?E??bR
0000023
0000010
0000001
0000001
0000001
2100000
3011100
[6, 5, 3, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031741(3t+5t2-9t3+6t4-t5)/(1-t)4(-12+23t+9t2+4t3)/3!
200012(12t3+25t4-62t5+60t6-30t7+8t8-t9)/(1-t)7(-1440+4404t-1842t2-510t3+30t4+66t5+12t6)/6!
30000(60t6-100t7+80t8-36t9+9t10-t11)/(1-t)9(74880t-90816t2+6328t3+10668t4-560t5-504t6-8t7+12t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Fs??W?bRpicture of the graph :Fs??W?bR
0000032
0000010
0000001
0000001
0000001
3100000
2011100
[5, 5, 4, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031534(3t+3t2-8t3+6t4-t5)/(1-t)4(-12+27t+6t2+3t3)/3!
200015(15t3+21t4-52t5+33t6-9t7+t8)/(1-t)6(1086t-675t2-135t3+75t4+9t5)/5!
30000(108t6-180t7+132t8-52t9+11t10-t11)/(1-t)9(80640+169632t-190712t2-6048t3+30562t4-2352t5-1148t6+48t7+18t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Fs@gaLDVpicture of the graph :Fs@gaLDV
0000010
0000010
0000003
0000001
0000001
1100002
0031120
[7, 4, 3, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031950(3t+7t2-8t3+4t4-t5)/(1-t)4(t+18t2+5t3)/3!
20007(7t3+28t4-51t5+44t6-25t7+8t8-t9)/(1-t)7(2160-2328t+1600t2-630t3-170t4+78t5+10t6)/6!
30000(45t6-75t7+65t8-33t9+9t10-t11)/(1-t)9(120960-156672t+38616t2-5824t3+2170t4+1232t5-476t6-16t7+10t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Fs??YLDVpicture of the graph :Fs??YLDV
0000030
0000010
0000001
0000001
0000001
3100002
0011120
[6, 5, 3, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031742(3t+5t2-8t3+4t4-t5)/(1-t)4(3t+18t2+3t3)/3!
200013(13t3+20t4-53t5+53t6-28t7+8t8-t9)/(1-t)7(2004t-762t2-630t3+30t4+66t5+12t6)/6!
30000(60t6-100t7+80t8-36t9+9t10-t11)/(1-t)9(74880t-90816t2+6328t3+10668t4-560t5-504t6-8t7+12t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Fs@_ALDVpicture of the graph :Fs@_ALDV
0000012
0000010
0000001
0000001
0000001
1100002
2011120
[7, 4, 3, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031947(3t+7t2-11t3+8t4-2t5)/(1-t)4(13t+12t2+5t3)/3!
20004(4t3+41t4-73t5+62t6-32t7+9t8-t9)/(1-t)7(2160-888t+880t2-630t3-170t4+78t5+10t6)/6!
30000(45t6-75t7+65t8-33t9+9t10-t11)/(1-t)9(120960-156672t+38616t2-5824t3+2170t4+1232t5-476t6-16t7+10t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Fs@_?GsVpicture of the graph :Fs@_?GsV
0000013
0000010
0000001
0000001
0000001
1100001
3011110
[7, 4, 3, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031946(3t+7t2-12t3+10t4-3t5)/(1-t)4(12+7t+12t2+5t3)/3!
20003(3t3+46t4-83t5+72t6-37t7+10t8-t9)/(1-t)7(3600-1608t+880t2-630t3-170t4+78t5+10t6)/6!
30000(45t6-75t7+65t8-33t9+9t10-t11)/(1-t)9(120960-156672t+38616t2-5824t3+2170t4+1232t5-476t6-16t7+10t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Fs?EALDVpicture of the graph :Fs?EALDV
0000021
0000010
0000001
0000001
0000001
2100002
1011120
[6, 5, 3, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031740(3t+5t2-10t3+8t4-2t5)/(1-t)4(17t+9t2+4t3)/3!
200011(11t3+30t4-72t5+70t6-35t7+9t8-t9)/(1-t)7(3684t-1842t2-510t3+30t4+66t5+12t6)/6!
30000(60t6-100t7+80t8-36t9+9t10-t11)/(1-t)9(74880t-90816t2+6328t3+10668t4-560t5-504t6-8t7+12t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Fs?E?GsVpicture of the graph :Fs?E?GsV
0000022
0000010
0000001
0000001
0000001
2100001
2011110
[6, 4, 4, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031638(3t+4t2-8t3+7t4-2t5)/(1-t)4(6+11t+9t2+4t3)/3!
200013(13t3+26t4-47t5+33t6-10t7+t8)/(1-t)6(720+124t-320t2-80t3+20t4+16t5)/5!
30000(90t6-150t7+115t8-49t9+11t10-t11)/(1-t)9(201600-47520t-93200t2+6608t3+13664t4+560t5-1120t6+32t7+16t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Fs??WGsVpicture of the graph :Fs??WGsV
0000031
0000010
0000001
0000001
0000001
3100001
1011110
[5, 5, 4, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031532(3t+3t2-10t3+10t4-3t5)/(1-t)4(12+15t+6t2+3t3)/3!
200013(13t3+29t4-64t5+41t6-11t7+t8)/(1-t)6(480+846t-675t2-135t3+75t4+9t5)/5!
30000(108t6-180t7+132t8-52t9+11t10-t11)/(1-t)9(80640+169632t-190712t2-6048t3+30562t4-2352t5-1148t6+48t7+18t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Fs??Q_BRpicture of the graph :Fs??Q_BR
0000032
0000010
0000010
0000001
0000001
3110000
2001100
[5, 5, 4, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031531(3t+6t2-5t3+t4)/(1-t)3(-4+7t+5t2)/2!
200012(12t3+27t4-55t5+33t6-9t7+t8)/(1-t)6(966t-495t2-195t3+75t4+9t5)/5!
30000(108t6-180t7+132t8-52t9+11t10-t11)/(1-t)9(80640+169632t-190712t2-6048t3+30562t4-2352t5-1148t6+48t7+18t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Fs?CgLDVpicture of the graph :Fs?CgLDV
0000021
0000010
0000010
0000001
0000001
2110002
1001120
[6, 5, 3, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031736(3t+8t2-6t3+2t4)/(1-t)3(3t+7t2)/2!
20007(7t3+42t4-84t5+74t6-35t7+9t8-t9)/(1-t)7(2724t-402t2-990t3+30t4+66t5+12t6)/6!
30000(60t6-100t7+80t8-36t9+9t10-t11)/(1-t)9(74880t-90816t2+6328t3+10668t4-560t5-504t6-8t7+12t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Fs?Cg?sVpicture of the graph :Fs?Cg?sV
0000022
0000010
0000010
0000001
0000001
2110001
2001110
[5, 5, 4, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031531(3t+6t2-5t3+2t4)/(1-t)3(2+2t+6t2)/2!
200012(12t3+28t4-58t5+36t6-10t7+t8)/(1-t)6(360+666t-435t2-195t3+75t4+9t5)/5!
30000(108t6-180t7+132t8-52t9+11t10-t11)/(1-t)9(80640+169632t-190712t2-6048t3+30562t4-2352t5-1148t6+48t7+18t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Fs??Q_sVpicture of the graph :Fs??Q_sV
0000031
0000010
0000010
0000001
0000001
3110001
1001110
[6, 4, 4, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031632(3t+7t2-7t3+3t4)/(1-t)3(4+2t+6t2)/2!
20007(7t3+41t4-60t5+38t6-11t7+t8)/(1-t)6(840+24t-140t2-160t3+20t4+16t5)/5!
30000(90t6-150t7+115t8-49t9+11t10-t11)/(1-t)9(201600-47520t-93200t2+6608t3+13664t4+560t5-1120t6+32t7+16t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:FoH_?CQNpicture of the graph :FoH_?CQN
0000103
0000012
0000001
0000001
1000000
0100000
3211000
[7, 4, 3, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031948(3t+7t2-10t3+6t4-t5)/(1-t)4(-12+19t+12t2+5t3)/3!
20005(5t3+36t4-63t5+52t6-27t7+8t8-t9)/(1-t)7(720-168t+880t2-630t3-170t4+78t5+10t6)/6!
30000(45t6-75t7+65t8-33t9+9t10-t11)/(1-t)9(120960-156672t+38616t2-5824t3+2170t4+1232t5-476t6-16t7+10t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:FoGE?GtVpicture of the graph :FoGE?GtV
0000112
0000010
0000001
0000001
1000000
1100002
2011020
[6, 4, 4, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031631(3t+7t2-8t3+2t4)/(1-t)3(-4+10t+4t2)/2!
20006(6t3+43t4-60t5+36t6-10t7+t8)/(1-t)6(360+504t-260t2-160t3+20t4+16t5)/5!
30000(90t6-150t7+115t8-49t9+11t10-t11)/(1-t)9(201600-47520t-93200t2+6608t3+13664t4+560t5-1120t6+32t7+16t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:FoGE??bVpicture of the graph :FoGE??bV
0000113
0000010
0000001
0000001
1000000
1100001
3011010
[6, 5, 3, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031732(3t+8t2-10t3+3t4)/(1-t)3(-2+10t+4t2)/2!
20003(3t3+59t4-112t5+96t6-43t7+10t8-t9)/(1-t)7(-720+5244t-1482t2-990t3+30t4+66t5+12t6)/6!
30000(60t6-100t7+80t8-36t9+9t10-t11)/(1-t)9(74880t-90816t2+6328t3+10668t4-560t5-504t6-8t7+12t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:FoG?W?bVpicture of the graph :FoG?W?bV
0000122
0000010
0000001
0000001
1000000
2100001
2011010
[5, 5, 4, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031528(3t+6t2-8t3+2t4)/(1-t)3(-4+11t+3t2)/2!
20009(9t3+37t4-67t5+39t6-10t7+t8)/(1-t)6(1206t-615t2-195t3+75t4+9t5)/5!
30000(108t6-180t7+132t8-52t9+11t10-t11)/(1-t)9(80640+169632t-190712t2-6048t3+30562t4-2352t5-1148t6+48t7+18t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:FoG?@_bVpicture of the graph :FoG?@_bV
0000131
0000010
0000001
0000001
1000000
3100001
1011010
[5, 5, 4, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031526(3t+6t2-10t3+3t4)/(1-t)3(-2+12t+2t2)/2!
20007(7t3+44t4-76t5+44t6-11t7+t8)/(1-t)6(120+1266t-675t2-195t3+75t4+9t5)/5!
30000(108t6-180t7+132t8-52t9+11t10-t11)/(1-t)9(80640+169632t-190712t2-6048t3+30562t4-2352t5-1148t6+48t7+18t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:FoHI?LTVpicture of the graph :FoHI?LTV
0000102
0000010
0000010
0000001
1000000
0110003
2001030
[6, 5, 3, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031737(3t+8t2-5t3+t4)/(1-t)3(-4+5t+7t2)/2!
20008(8t3+37t4-74t5+64t6-30t7+8t8-t9)/(1-t)7(-1440+3444t-402t2-990t3+30t4+66t5+12t6)/6!
30000(60t6-100t7+80t8-36t9+9t10-t11)/(1-t)9(74880t-90816t2+6328t3+10668t4-560t5-504t6-8t7+12t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:FoHI??tVpicture of the graph :FoHI??tV
0000103
0000010
0000010
0000001
1000000
0110002
3001020
[6, 4, 4, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031634(3t+7t2-5t3+t4)/(1-t)3(-4+6t+6t2)/2!
20009(9t3+33t4-48t5+30t6-9t7+t8)/(1-t)6(360+264t-140t2-160t3+20t4+16t5)/5!
30000(90t6-150t7+115t8-49t9+11t10-t11)/(1-t)9(201600-47520t-93200t2+6608t3+13664t4+560t5-1120t6+32t7+16t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Gw?_QLDZpicture of the graph :Gw?_QLDZ
00000021
00000001
00000001
00000001
00000001
00000001
20000001
11111110
[7, 3, 3, 1, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10218(2t+6t2-5t3+5t4-6t5+4t6-t7)/(1-t)6(240-130t+75t2+125t3+45t4+5t5)/5!
2000(15t3-4t4-9t5+15t6-9t7+2t8)/(1-t)7(3600-1968t-20t2-240t3+10t4+48t5+10t6)/6!
3000(15t6-20t7+15t8-6t9+t10)/(1-t)9(120960-99792t+19980t2-1372t3+245t4+392t5-70t6-28t7+5t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Gw?E?GsVpicture of the graph :Gw?E?GsV
00000022
00000010
00000001
00000001
00000001
00000001
21000000
20111100
[6, 4, 3, 1, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10215(2t+5t2-7t3+6t4-2t5)/(1-t)5(-48+52t+20t2+20t3+4t4)/4!
2000(11t3+8t4-25t5+21t6-8t7+t8)/(1-t)7(-720+3000t-1408t2-180t3-40t4+60t5+8t6)/6!
3000(30t6-40t7+25t8-8t9+t10)/(1-t)9(40320+50976t-61888t2+8456t3+1792t4+1064t5-392t6-16t7+8t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Gw@_ALDZpicture of the graph :Gw@_ALDZ
00000012
00000010
00000001
00000001
00000001
00000001
11000001
20111110
[7, 3, 3, 1, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10218(2t+8t2-11t3+10t4-5t5+t6)/(1-t)5(10t+31t2+26t3+5t4)/4!
2000(t3+26t4-34t5+26t6-11t7+2t8)/(1-t)7(2160-888t+460t2-210t3-110t4+18t5+10t6)/6!
3000(15t6-20t7+15t8-6t9+t10)/(1-t)9(120960-99792t+19980t2-1372t3+245t4+392t5-70t6-28t7+5t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Gw?EALDZpicture of the graph :Gw?EALDZ
00000021
00000010
00000001
00000001
00000001
00000001
21000001
10111110
[6, 4, 3, 1, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10215(2t+5t2-8t3+9t4-5t5+t6)/(1-t)5(28t+20t2+20t3+4t4)/4!
2000(10t3+13t4-35t5+31t6-13t7+2t8)/(1-t)7(720+2280t-1408t2-180t3-40t4+60t5+8t6)/6!
3000(30t6-40t7+25t8-8t9+t10)/(1-t)9(40320+50976t-61888t2+8456t3+1792t4+1064t5-392t6-16t7+8t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Gw?Cg?sVpicture of the graph :Gw?Cg?sV
00000022
00000010
00000010
00000001
00000001
00000001
21100000
20011100
[5, 4, 4, 1, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10213(2t+5t2-6t3+2t4)/(1-t)4(-12+9t+12t2+3t3)/3!
2000(9t3+19t4-24t5+9t6-t7)/(1-t)6(-360+768t-150t2-180t3+30t4+12t5)/5!
3000(54t6-72t7+39t8-10t9+t10)/(1-t)9(-40320+170784t-77264t2-30296t3+17668t4+616t5-896t6+16t7+12t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Gw@I?LDZpicture of the graph :Gw@I?LDZ
00000012
00000010
00000010
00000001
00000001
00000001
11100001
20011110
[6, 4, 3, 1, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10215(2t+7t2-8t3+4t4-t5)/(1-t)4(-t+15t2+4t3)/3!
2000(3t3+30t4-48t5+34t6-13t7+2t8)/(1-t)7(720+1320t-208t2-300t3-160t4+60t5+8t6)/6!
3000(30t6-40t7+25t8-8t9+t10)/(1-t)9(40320+50976t-61888t2+8456t3+1792t4+1064t5-392t6-16t7+8t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Gw?CgLDZpicture of the graph :Gw?CgLDZ
00000021
00000010
00000010
00000001
00000001
00000001
21100001
10011110
[5, 5, 3, 1, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10214(2t+6t2-8t3+4t4-t5)/(1-t)4(15t2+3t3)/3!
2000(6t3+26t4-49t5+37t6-13t7+2t8)/(1-t)7(720+1020t+636t2-1065t3+75t4+45t5+9t6)/6!
3000(36t6-48t7+28t8-8t9+t10)/(1-t)9(40320+28656t-13204t2-28308t3+13601t4-336t5-406t6-12t7+9t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:GsH_@CbRpicture of the graph :GsH_@CbR
00000102
00000012
00000001
00000001
00000001
10000000
01000000
22111000
[7, 3, 3, 1, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10218(2t+8t2-10t3+7t4-2t5)/(1-t)5(-48+34t+31t2+26t3+5t4)/4!
2000(2t3+21t4-24t5+16t6-6t7+t8)/(1-t)7(720-168t+460t2-210t3-110t4+18t5+10t6)/6!
3000(15t6-20t7+15t8-6t9+t10)/(1-t)9(120960-99792t+19980t2-1372t3+245t4+392t5-70t6-28t7+5t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:GsG?W?bRpicture of the graph :GsG?W?bR
00000122
00000010
00000001
00000001
00000001
10000000
21000000
20111000
[5, 5, 3, 1, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10214(2t+6t2-7t3+2t4)/(1-t)4(-12+6t+15t2+3t3)/3!
2000(7t3+21t4-39t5+27t6-8t7+t8)/(1-t)7(-720+1740t+636t2-1065t3+75t4+45t5+9t6)/6!
3000(36t6-48t7+28t8-8t9+t10)/(1-t)9(40320+28656t-13204t2-28308t3+13601t4-336t5-406t6-12t7+9t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:GsGE?GsZpicture of the graph :GsGE?GsZ
00000112
00000010
00000001
00000001
00000001
10000000
11000001
20111010
[6, 4, 3, 1, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10215(2t+7t2-10t3+6t4-t5)/(1-t)4(-12+17t+9t2+4t3)/3!
2000(t3+38t4-60t5+42t6-15t7+2t8)/(1-t)7(-720+3480t-928t2-300t3-160t4+60t5+8t6)/6!
3000(30t6-40t7+25t8-8t9+t10)/(1-t)9(40320+50976t-61888t2+8456t3+1792t4+1064t5-392t6-16t7+8t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:GsG?WGsZpicture of the graph :GsG?WGsZ
00000121
00000010
00000001
00000001
00000001
10000000
21000001
10111010
[5, 4, 4, 1, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10213(2t+5t2-9t3+6t4-t5)/(1-t)4(-12+21t+6t2+3t3)/3!
2000(6t3+29t4-36t5+15t6-2t7)/(1-t)6(-360+1008t-270t2-180t3+30t4+12t5)/5!
3000(54t6-72t7+39t8-10t9+t10)/(1-t)9(-40320+170784t-77264t2-30296t3+17668t4+616t5-896t6+16t7+12t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:GsHI?LEZpicture of the graph :GsHI?LEZ
00000102
00000010
00000010
00000001
00000001
10000000
01100002
20011020
[6, 4, 3, 1, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10215(2t+7t2-7t3+2t4)/(1-t)4(-12+5t+15t2+4t3)/3!
2000(4t3+25t4-38t5+24t6-8t7+t8)/(1-t)7(-720+2040t-208t2-300t3-160t4+60t5+8t6)/6!
3000(30t6-40t7+25t8-8t9+t10)/(1-t)9(40320+50976t-61888t2+8456t3+1792t4+1064t5-392t6-16t7+8t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:GsGCgLEZpicture of the graph :GsGCgLEZ
00000111
00000010
00000010
00000001
00000001
10000000
11100002
10011020
[5, 5, 3, 1, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10214(2t+8t2-5t3+t4)/(1-t)3(-4+4t+6t2)/2!
2000(t3+43t4-70t5+48t6-15t7+2t8)/(1-t)7(-720+2460t+996t2-1425t3+75t4+45t5+9t6)/6!
3000(36t6-48t7+28t8-8t9+t10)/(1-t)9(40320+28656t-13204t2-28308t3+13601t4-336t5-406t6-12t7+9t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:GsG?Q_sZpicture of the graph :GsG?Q_sZ
00000121
00000010
00000010
00000001
00000001
10000000
21100001
10011010
[5, 4, 4, 1, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10213(2t+7t2-5t3+t4)/(1-t)3(-4+5t+5t2)/2!
2000(3t3+35t4-39t5+15t6-2t7)/(1-t)6(-360+888t-90t2-240t3+30t4+12t5)/5!
3000(54t6-72t7+39t8-10t9+t10)/(1-t)9(-40320+170784t-77264t2-30296t3+17668t4+616t5-896t6+16t7+12t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Gs@g{TUZpicture of the graph :Gs@g{TUZ
00000100
00000100
00000010
00000010
00000001
11000002
00110002
00001220
[5, 4, 4, 1, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10213(2t+7t2-2t3)/(1-t)3(-4+t+7t2)/2!
2000(6t3+25t4-27t5+9t6-t7)/(1-t)6(-360+648t+30t2-240t3+30t4+12t5)/5!
3000(54t6-72t7+39t8-10t9+t10)/(1-t)9(-40320+170784t-77264t2-30296t3+17668t4+616t5-896t6+16t7+12t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:HkA?WAEOh~picture of the graph :HkA?WAEOh~
000000111
000000010
000000001
000000001
000000001
000000001
100000000
110000001
101111010
[6, 3, 3, 1, 1, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01Poincaré seriesstable polynomial value
0111/(1-t)1
101(t+8t2-10t3+7t4-2t5)/(1-t)5(-48+28t+20t2+20t3+4t4)/4!
200(21t4-23t5+13t6-3t7)/(1-t)7(-2160+2928t-628t2-60t3-100t4+12t5+8t6)/6!
300(10t6-10t7+5t8-t9)/(1-t)9(-40320+74784t-40464t2+5544t3+196t4+336t5-56t6-24t7+4t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:HkA?POEOh~picture of the graph :HkA?POEOh~
000000111
000000010
000000010
000000001
000000001
000000001
100000000
111000001
100111010
[5, 4, 3, 1, 1, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01Poincaré seriesstable polynomial value
0111/(1-t)1
101(t+7t2-7t3+2t4)/(1-t)4(-12+3t+12t2+3t3)/3!
200(27t4-35t5+17t6-3t7)/(1-t)7(-2160+2088t+804t2-690t3-90t4+42t5+6t6)/6!
300(18t6-18t7+7t8-t9)/(1-t)9(-40320+57024t-4472t2-17584t3+4774t4+896t5-308t6-16t7+6t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Hk?K`egSp~picture of the graph :Hk?K`egSp~
000000100
000000100
000000010
000000010
000000001
000000001
110000011
001100101
000011110
[4, 4, 4, 1, 1, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01Poincaré seriesstable polynomial value
0111/(1-t)1
101(t+7t2-2t3)/(1-t)3(-4+6t2)/2!
200(27t4-18t5+3t6)/(1-t)6(-360+228t+360t2-240t3+12t5)/5!
300(27t6-27t7+9t8-t9)/(1-t)9(-40320+38304t+32752t2-40320t3+8232t4+2016t5-672t6+8t8)/8!

Data for graphs with 4 essential vertices

sparse6 nameimageadjacency matrixdegree sequence
:Co@`Npicture of the graph :Co@`N
0021
0012
2100
1200
[3, 3, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
10355(3t+2t2)/(1-t)5
20014(t2+t3+t4-t5)/(1-t)3(-4-2t+2t2)/2!
30000(2t5+2t6)/(1-t)4(-168+146t-42t2+4t3)/3!
40000t8/(1-t)6(-2520+2754t-1175t2+245t3-25t4+t5)/5!

sparse6 nameimageadjacency matrixdegree sequence
:CcKIpicture of the graph :CcKI
0111
1011
1101
1110
[3, 3, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
10344(3t+t2)/(1-t)4
20003(3t3+3t4)/(1-t)2-15+6t
300004t6/(1-t)4(-240+188t-48t2+4t3)/3!
40000t8/(1-t)6(-2520+2754t-1175t2+245t3-25t4+t5)/5!

sparse6 nameimageadjacency matrixdegree sequence
:CoCHIpicture of the graph :CoCHI
0021
0003
2001
1310
[5, 3, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
10491215(4t+t2-2t3)/(1-t)23+3t
20021132(2t2+3t3-3t5+2t6-t7)/(1-t)4(72-54t+9t2+3t3)/3!
300000(8t5+4t6-5t7+2t8)/(1-t)5(552-582t+327t2-90t3+9t4)/4!
400000(6t8-4t9+t10)/(1-t)7(10080-10176t+6582t2-2715t3+615t4-69t5+3t6)/6!

sparse6 nameimageadjacency matrixdegree sequence
:Co@K@picture of the graph :Co@K@
0022
0021
2200
2100
[4, 4, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104777(4t+3t2)/(1-t)7
2001928(t2+6t3+4t4-3t5)/(1-t)3(-18t+8t2)/2!
300000(7t5+7t6-7t7+t8)/(1-t)5(-672+328t+88t2-64t3+8t4)/4!
400000(9t8-6t9+t10)/(1-t)7(-15120+14844t-2414t2-1440t3+610t4-84t5+4t6)/6!

sparse6 nameimageadjacency matrixdegree sequence
:Co?KHpicture of the graph :Co?KH
0031
0012
3100
1200
[4, 4, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104888(4t+4t2)/(1-t)8
20021029(2t2+2t3+t4-4t5+4t6-t7)/(1-t)4(-30+23t-9t2+4t3)/3!
300000(11t5+4t6-9t7+2t8)/(1-t)5(-816+636t-44t2-48t3+8t4)/4!
400000(9t8-6t9+t10)/(1-t)7(-15120+14844t-2414t2-1440t3+610t4-84t5+4t6)/6!

sparse6 nameimageadjacency matrixdegree sequence
:Co@`Ipicture of the graph :Co@`I
0021
0012
2101
1210
[4, 4, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104777(4t+3t2)/(1-t)7
2001928(t2+6t3+4t4-4t5+t6)/(1-t)3(8-20t+8t2)/2!
300000(6t5+10t6-10t7+2t8)/(1-t)5(-576+304t+88t2-64t3+8t4)/4!
400000(9t8-6t9+t10)/(1-t)7(-15120+14844t-2414t2-1440t3+610t4-84t5+4t6)/6!

sparse6 nameimageadjacency matrixdegree sequence
:Co@KIpicture of the graph :Co@KI
0021
0021
2201
1110
[5, 3, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104777(4t+3t2)/(1-t)7
2000624(6t3+6t4-4t5+t6)/(1-t)3(20-29t+9t2)/2!
300000(2t5+13t6-8t7+2t8)/(1-t)5(408-642t+399t2-102t3+9t4)/4!
400000(6t8-4t9+t10)/(1-t)7(10080-10176t+6582t2-2715t3+615t4-69t5+3t6)/6!

sparse6 nameimageadjacency matrixdegree sequence
:C_``Vpicture of the graph :C_``V
0211
2011
1101
1110
[4, 4, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104666(4t+2t2)/(1-t)6
2000827(8t3+3t4-9t5+2t6)/(1-t)3(-34+6t+4t2)/2!
300000(t5+21t6-17t7+3t8)/(1-t)5(-1056+616t+40t2-64t3+8t4)/4!
400000(9t8-6t9+t10)/(1-t)7(-15120+14844t-2414t2-1440t3+610t4-84t5+4t6)/6!

sparse6 nameimageadjacency matrixdegree sequence
:Dk?E@Cnpicture of the graph :Dk?E@Cn
00021
00012
00001
21000
12100
[4, 3, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
10379(3t+t2-2t3)/(1-t)23+2t
20016(t2+2t3+2t4-4t5+t6)/(1-t)4(24-32t+6t2+2t3)/3!
30000(4t5+4t6-2t7)/(1-t)5(-144-132t+186t2-60t3+6t4)/4!
40000(3t8-t9)/(1-t)7(-5040+468t+3158t2-1860t3+440t4-48t5+2t6)/6!

sparse6 nameimageadjacency matrixdegree sequence
:Dk?CWCnpicture of the graph :Dk?CWCn
00021
00021
00001
22000
11100
[4, 3, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
10367(3t-2t3)/(1-t)24+t
20004(4t3+5t4-t5)/(1-t)3(26-30t+8t2)/2!
30000(2t5+6t6-2t7)/(1-t)5(48-340t+258t2-68t3+6t4)/4!
40000(3t8-t9)/(1-t)7(-5040+468t+3158t2-1860t3+440t4-48t5+2t6)/6!

sparse6 nameimageadjacency matrixdegree sequence
:Dg?e@Cnpicture of the graph :Dg?e@Cn
00201
00012
20001
01000
12100
[4, 3, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
103710(3t+t2-t3)/(1-t)21+3t
20017(t2+3t3-3t5+t6)/(1-t)4(12-26t+6t2+2t3)/3!
30000(4t5+4t6-2t7)/(1-t)5(-144-132t+186t2-60t3+6t4)/4!
40000(3t8-t9)/(1-t)7(-5040+468t+3158t2-1860t3+440t4-48t5+2t6)/6!

sparse6 nameimageadjacency matrixdegree sequence
:DgG?gCnpicture of the graph :DgG?gCn
00121
00001
10011
20100
11100
[4, 3, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
10367(3t-2t3)/(1-t)24+t
20004(4t3+5t4-2t5)/(1-t)3(14-23t+7t2)/2!
30000(t5+8t6-3t7)/(1-t)5(-96-256t+246t2-68t3+6t4)/4!
40000(3t8-t9)/(1-t)7(-5040+468t+3158t2-1860t3+440t4-48t5+2t6)/6!

sparse6 nameimageadjacency matrixdegree sequence
:DgGI@G~picture of the graph :DgGI@G~
00111
00001
10011
10101
11110
[4, 3, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
10368(3t-t3)/(1-t)22+2t
20005(5t3+4t4-3t5)/(1-t)3(-2-14t+6t2)/2!
30000(10t6-4t7)/(1-t)5(-240-172t+234t2-68t3+6t4)/4!
40000(3t8-t9)/(1-t)7(-5040+468t+3158t2-1860t3+440t4-48t5+2t6)/6!

sparse6 nameimageadjacency matrixdegree sequence
:EkGCWCnpicture of the graph :EkGCWCn
000111
000021
000001
100000
120000
111000
[3, 3, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
1025(2t+t2-t3)/(1-t)21+2t
2000(2t3+2t4-3t5)/(1-t)4(60-52t+9t2+t3)/3!
3000(t5+3t6)/(1-t)5(384-512t+248t2-52t3+4t4)/4!
4000t8/(1-t)7(5040-8028t+5104t2-1665t3+295t4-27t5+t6)/6!

sparse6 nameimageadjacency matrixdegree sequence
:Ek@_gLNpicture of the graph :Ek@_gLN
000111
000100
000010
110001
101001
100110
[3, 3, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
1025(2t+t2-t3)/(1-t)21+2t
2000(2t3+4t4)/(1-t)3(28-26t+6t2)/2!
30004t6/(1-t)5(480-616t+284t2-56t3+4t4)/4!
4000t8/(1-t)7(5040-8028t+5104t2-1665t3+295t4-27t5+t6)/6!

sparse6 nameimageadjacency matrixdegree sequence
:Co?_HNpicture of the graph :Co?_HN
0032
0003
3000
2300
[5, 5, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10513192531(5t+3t2-2t3)/(1-t)21+6t
20042682183(4t2+10t3+2t4-5t5+5t6-t7)/(1-t)4(-72+69t-42t2+15t3)/3!
30000025(25t5+3t6-26t7+22t8-7t9+t10)/(1-t)6(-5160+4532t-1530t2+490t3-150t4+18t5)/5!
4000000(36t8-48t9+28t10-8t11+t12)/(1-t)8(-151200+153900t-47712t2+6321t3-2520t4+1050t5-168t6+9t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Co_HIVpicture of the graph :Co_HIV
0012
0003
1002
2320
[7, 3, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10513182328(5t+3t2-3t3)/(1-t)23+5t
2000948127(9t3+12t4-11t5+7t6-2t7)/(1-t)4(12+45t-54t2+15t3)/3!
3000004(4t5+27t6-28t7+17t8-6t9+t10)/(1-t)6(-720+690t-915t2+615t3-165t4+15t5)/5!
4000000(15t8-20t9+15t10-6t11+t12)/(1-t)8(-25200+9480t-10738t2+9695t3-4270t4+980t5-112t6+5t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:CoCHHVpicture of the graph :CoCHHV
0021
0004
2001
1410
[6, 4, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
105131721(5t+3t2-4t3)/(1-t)25+4t
20032071(3t2+5t3+t4-6t5+11t6-9t7+3t8)/(1-t)5(456-232t+40t2-8t3+8t4)/4!
300001(t4+29t5-4t6-25t7+21t8-6t9)/(1-t)6(5880-4336t+1700t2-180t3-80t4+16t5)/5!
400000(t7+25t8-30t9+15t10-3t11)/(1-t)8(176400-121500t+44534t2-8008t3-1540t4+980t5-154t6+8t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:CoC@HVpicture of the graph :CoC@HV
0022
0003
2001
2310
[6, 4, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10512162024(5t+2t2-3t3)/(1-t)24+4t
20021969160(2t2+11t3+5t4-10t5+6t6-2t7)/(1-t)4(90-51t-15t2+12t3)/3!
30000017(17t5+15t6-31t7+22t8-8t9+t10)/(1-t)6(3720-3536t+1140t2+100t3-120t4+16t5)/5!
4000000(30t8-40t9+25t10-8t11+t12)/(1-t)8(100800-93780t+42014t2-8008t3-1540t4+980t5-154t6+8t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Co?`HVpicture of the graph :Co?`HV
0031
0003
3001
1310
[5, 4, 4, 3]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10512151821(5t+2t2-4t3)/(1-t)26+3t
20042471147(4t2+8t3-t4-9t5+8t6-3t7)/(1-t)4(102-79t+12t2+7t3)/3!
30000031(31t5-t6-44t7+36t8-11t9+t10)/(1-t)6(-120-432t+1340t2-420t3-20t4+12t5)/5!
4000000(54t8-72t9+39t10-10t11+t12)/(1-t)8(-60480+53916t+27146t2-24402t3+3290t4+714t5-196t6+12t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Co@K@Npicture of the graph :Co@K@N
0022
0022
2200
2200
[4, 4, 4, 4]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
1059999(5t+4t2)/(1-t)9
20022060116(2t2+14t3+6t4-6t5)/(1-t)3(-8-32t+16t2)/2!
30000136(t4+31t5+22t6-30t7+9t8-t9)/(1-t)5(-1536+640t+448t2-256t3+32t4)/4!
4000000(81t8-108t9+54t10-12t11+t12)/(1-t)8(-257040+204888t+34384t2-53816t3+11200t4+112t5-224t6+16t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Co?KHNpicture of the graph :Co?KHN
0031
0013
3100
1300
[4, 4, 4, 4]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10511111111(5t+6t2)/(1-t)11
20042261119(4t2+6t3-3t4-9t5+15t6-5t7)/(1-t)4(-66+76t-24t2+8t3)/3!
30000037(37t5+26t6-44t7+14t8-t9)/(1-t)5(-1752+1328t+160t2-224t3+32t4)/4!
4000000(81t8-108t9+54t10-12t11+t12)/(1-t)8(-257040+204888t+34384t2-53816t3+11200t4+112t5-224t6+16t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Co?K@Npicture of the graph :Co?K@N
0032
0012
3100
2200
[5, 4, 4, 3]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10510101010(5t+5t2)/(1-t)10
20021963132(2t2+11t3-t4-14t5+10t6-2t7)/(1-t)4(-18-33t+9t2+6t3)/3!
30000027(27t5+9t6-51t7+36t8-10t9+t10)/(1-t)6(-3000+848t+1280t2-440t3-20t4+12t5)/5!
4000000(54t8-72t9+39t10-10t11+t12)/(1-t)8(-60480+53916t+27146t2-24402t3+3290t4+714t5-196t6+12t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Co?H_Npicture of the graph :Co?H_N
0032
0021
3200
2100
[5, 5, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10510101010(5t+5t2)/(1-t)10
20011767151(t2+13t3+5t4-19t5+11t6-2t7)/(1-t)4(6-45t+9t3)/3!
30000014(14t5+31t6-50t7+30t8-8t9+t10)/(1-t)6(-4680+2972t-690t2+370t3-150t4+18t5)/5!
4000000(36t8-48t9+28t10-8t11+t12)/(1-t)8(-151200+153900t-47712t2+6321t3-2520t4+1050t5-168t6+9t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Co?@`Npicture of the graph :Co?@`N
0041
0012
4100
1200
[5, 5, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
105121212(5t+7t2)/(1-t)12
20031970(3t2+4t3+5t4-10t5+16t6-12t7+3t8)/(1-t)5(-120+198t-57t2-6t3+9t4)/4!
300001(t4+35t5-7t6-32t7+27t8-6t9)/(1-t)6(-3840+4202t-915t2+160t3-105t4+18t5)/5!
400000(t7+31t8-38t9+18t10-3t11)/(1-t)8(-75600+126180t-45192t2+6321t3-2520t4+1050t5-168t6+9t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Co@`IVpicture of the graph :Co@`IV
0021
0012
2102
1220
[5, 5, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10510101010(5t+5t2)/(1-t)10
20011767150(t2+13t3+5t4-20t5+13t6-3t7)/(1-t)4(30-51t+9t3)/3!
30000013(13t5+35t6-56t7+34t8-9t9+t10)/(1-t)6(-4200+2852t-690t2+370t3-150t4+18t5)/5!
4000000(36t8-48t9+28t10-8t11+t12)/(1-t)8(-151200+153900t-47712t2+6321t3-2520t4+1050t5-168t6+9t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Co@KIVpicture of the graph :Co@KIV
0021
0021
2202
1120
[6, 4, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10510101010(5t+5t2)/(1-t)10
20001359136(13t3+7t4-22t5+13t6-3t7)/(1-t)4(66-80t+6t2+8t3)/3!
3000007(7t5+42t6-56t7+31t8-9t9+t10)/(1-t)6(2520-3636t+1560t2+20t3-120t4+16t5)/5!
4000000(30t8-40t9+25t10-8t11+t12)/(1-t)8(100800-93780t+42014t2-8008t3-1540t4+980t5-154t6+8t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Co@K@Vpicture of the graph :Co@K@V
0022
0021
2201
2110
[5, 4, 4, 3]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
1059999(5t+4t2)/(1-t)9
20011862122(t2+15t3+11t4-11t5+3t6)/(1-t)3(24-51t+19t2)/2!
30000018(18t5+31t6-69t7+42t8-11t9+t10)/(1-t)6(-1080-1552t+2240t2-560t3-20t4+12t5)/5!
4000000(54t8-72t9+39t10-10t11+t12)/(1-t)8(-60480+53916t+27146t2-24402t3+3290t4+714t5-196t6+12t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Co?KHVpicture of the graph :Co?KHV
0031
0012
3101
1210
[5, 4, 4, 3]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10510101010(5t+5t2)/(1-t)10
20021963130(2t2+11t3-t4-16t5+14t6-4t7)/(1-t)4(30-45t+9t2+6t3)/3!
30000025(25t5+17t6-63t7+44t8-12t9+t10)/(1-t)6(-2040+608t+1280t2-440t3-20t4+12t5)/5!
4000000(54t8-72t9+39t10-10t11+t12)/(1-t)8(-60480+53916t+27146t2-24402t3+3290t4+714t5-196t6+12t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Co?H`Vpicture of the graph :Co?H`V
0031
0021
3201
1110
[6, 4, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10510101010(5t+5t2)/(1-t)10
20001359135(13t3+7t4-23t5+15t6-4t7)/(1-t)4(90-86t+6t2+8t3)/3!
3000006(6t5+46t6-62t7+35t8-10t9+t10)/(1-t)6(3000-3756t+1560t2+20t3-120t4+16t5)/5!
4000000(30t8-40t9+25t10-8t11+t12)/(1-t)8(100800-93780t+42014t2-8008t3-1540t4+980t5-154t6+8t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:C_``Qpicture of the graph :C_``Q
0211
2011
1102
1120
[4, 4, 4, 4]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
1058888(5t+3t2)/(1-t)8
2001195898(t2+16t3+4t4-20t5+7t6)/(1-t)3(-44+8t+8t2)/2!
30000019(19t5+56t6-58t7+16t8-t9)/(1-t)5(-1944+1120t+352t2-256t3+32t4)/4!
4000000(81t8-108t9+54t10-12t11+t12)/(1-t)8(-257040+204888t+34384t2-53816t3+11200t4+112t5-224t6+16t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:C__KIpicture of the graph :C__KI
0221
2011
2101
1110
[5, 4, 4, 3]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
1058888(5t+3t2)/(1-t)8
20001761110(17t3+10t4-22t5+7t6)/(1-t)3(-30-10t+12t2)/2!
3000007(7t5+68t6-114t7+65t8-15t9+t10)/(1-t)6(-4200+908t+1820t2-560t3-20t4+12t5)/5!
4000000(54t8-72t9+39t10-10t11+t12)/(1-t)8(-60480+53916t+27146t2-24402t3+3290t4+714t5-196t6+12t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:C_CKIpicture of the graph :C_CKI
0311
3011
1101
1110
[5, 5, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
1059999(5t+4t2)/(1-t)9
20001666140(16t3+2t4-28t5+25t6-6t7)/(1-t)4(-120+57t-18t2+9t3)/3!
3000004(4t5+65t6-92t7+52t8-12t9+t10)/(1-t)6(-7080+5012t-1050t2+370t3-150t4+18t5)/5!
4000000(36t8-48t9+28t10-8t11+t12)/(1-t)8(-151200+153900t-47712t2+6321t3-2520t4+1050t5-168t6+9t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Dk?_PCbpicture of the graph :Dk?_PCb
00021
00003
00001
20001
13110
[6, 3, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104132439(4t+t2-3t3+2t4)/(1-t)3(6+2t+4t2)/2!
20021556(2t2+5t3+t4-7t5+5t6-3t7+t8)/(1-t)5(192-32t-64t2+20t3+4t4)/4!
300000(12t5+4t6-9t7+7t8-2t9)/(1-t)6(1800-622t-365t2+370t3-115t4+12t5)/5!
400000(10t8-10t9+5t10-t11)/(1-t)8(50400-18960t-6454t2+8071t3-3535t4+805t5-91t6+4t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Dk?E@CQpicture of the graph :Dk?E@CQ
00021
00013
00001
21000
13100
[5, 4, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104111417(4t+3t2-4t3)/(1-t)25+3t
20021350(2t2+3t3+5t4-11t5+11t6-5t7+t8)/(1-t)5(96-100t+30t2-8t3+6t4)/4!
300000(20t5+2t6-19t7+11t8-2t9)/(1-t)6(-840-402t+785t2-90t3-65t4+12t5)/5!
400000(18t8-18t9+7t10-t11)/(1-t)8(-30240+13728t+11494t2-4431t3-1295t4+777t5-119t6+6t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Dk?E?CQpicture of the graph :Dk?E?CQ
00022
00012
00001
21000
22100
[5, 4, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104101316(4t+2t2-3t3)/(1-t)24+3t
20011249(t2+8t3+7t4-10t5+3t6)/(1-t)4(18-27t-12t2+9t3)/3!
300000(10t5+15t6-20t7+8t8-t9)/(1-t)6(-840-442t+395t2+130t3-95t4+12t5)/5!
400000(18t8-18t9+7t10-t11)/(1-t)8(-30240+13728t+11494t2-4431t3-1295t4+777t5-119t6+6t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Dk?CW?Qpicture of the graph :Dk?CW?Q
00022
00021
00001
22000
21100
[4, 4, 4, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
10491113(4t+t2-3t3)/(1-t)25+2t
20011348(t2+9t3+2t4-11t5+3t6)/(1-t)4(72-106t+24t2+4t3)/3!
300000(15t5+10t6-26t7+10t8-t9)/(1-t)6(-960-2448t+2400t2-560t3+8t5)/5!
400000(27t8-27t9+9t10-t11)/(1-t)8(-75600-9780t+65170t2-28588t3+3010t4+560t5-140t6+8t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Dk??WCQpicture of the graph :Dk??WCQ
00031
00012
00001
31000
12100
[4, 4, 4, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104101214(4t+2t2-4t3)/(1-t)26+2t
20021449(2t2+6t3+5t4-12t5+6t6-t7)/(1-t)4(18-39t+3t2+6t3)/3!
300000(15t5+13t6-33t7+15t8-2t9)/(1-t)6(-2160-1108t+1980t2-520t3+8t5)/5!
400000(27t8-27t9+9t10-t11)/(1-t)8(-75600-9780t+65170t2-28588t3+3010t4+560t5-140t6+8t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Dk??P_Qpicture of the graph :Dk??P_Q
00031
00021
00001
32000
11100
[5, 4, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
10491011(4t+t2-4t3)/(1-t)27+t
2000944(9t3+8t4-16t5+6t6-t7)/(1-t)4(96-102t+12t2+6t3)/3!
300000(5t5+28t6-32t7+13t8-2t9)/(1-t)6(360-1702t+875t2+70t3-95t4+12t5)/5!
400000(18t8-18t9+7t10-t11)/(1-t)8(-30240+13728t+11494t2-4431t3-1295t4+777t5-119t6+6t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Dk?EAGbpicture of the graph :Dk?EAGb
00021
00010
00003
21001
10310
[5, 4, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104111621(4t+3t2-2t3)/(1-t)21+5t
20021554(2t2+7t3+6t4-7t5+4t6-t7)/(1-t)4(12+10t-27t2+11t3)/3!
300000(12t5+12t6-21t7+11t8-2t9)/(1-t)6(-600+58t+95t2+170t3-95t4+12t5)/5!
400000(18t8-18t9+7t10-t11)/(1-t)8(-30240+13728t+11494t2-4431t3-1295t4+777t5-119t6+6t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Dk?CP_bpicture of the graph :Dk?CP_b
00021
00030
00001
23001
10110
[6, 3, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104111621(4t+3t2-2t3)/(1-t)21+5t
2000738(7t3+10t4-8t5+4t6-t7)/(1-t)4(12+30t-42t2+12t3)/3!
300000(3t5+20t6-18t7+9t8-2t9)/(1-t)6(1320-342t-645t2+510t3-135t4+12t5)/5!
400000(10t8-10t9+5t10-t11)/(1-t)8(50400-18960t-6454t2+8071t3-3535t4+805t5-91t6+4t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Dk@_@Cbpicture of the graph :Dk@_@Cb
00012
00012
00001
11001
22110
[6, 3, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104111519(4t+3t2-3t3)/(1-t)23+4t
2000636(6t3+12t4-10t5+5t6-t7)/(1-t)4(-12+45t-45t2+12t3)/3!
300000(2t5+23t6-21t7+10t8-2t9)/(1-t)6(600+78t-705t2+510t3-135t4+12t5)/5!
400000(10t8-10t9+5t10-t11)/(1-t)8(50400-18960t-6454t2+8071t3-3535t4+805t5-91t6+4t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Dk?E@Cbpicture of the graph :Dk?E@Cb
00021
00012
00001
21001
12110
[5, 4, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104101316(4t+2t2-3t3)/(1-t)24+3t
20011249(t2+8t3+7t4-11t5+5t6-t7)/(1-t)4(42-33t-12t2+9t3)/3!
300000(9t5+19t6-26t7+12t8-2t9)/(1-t)6(-360-562t+395t2+130t3-95t4+12t5)/5!
400000(18t8-18t9+7t10-t11)/(1-t)8(-30240+13728t+11494t2-4431t3-1295t4+777t5-119t6+6t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Dk?CWCbpicture of the graph :Dk?CWCb
00021
00021
00001
22001
11110
[5, 4, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
10491113(4t+t2-3t3)/(1-t)25+2t
20001046(10t3+6t4-14t5+5t6-t7)/(1-t)4(120-117t+15t2+6t3)/3!
300000(6t5+25t6-29t7+12t8-2t9)/(1-t)6(1080-2122t+935t2+70t3-95t4+12t5)/5!
400000(18t8-18t9+7t10-t11)/(1-t)8(-30240+13728t+11494t2-4431t3-1295t4+777t5-119t6+6t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Dg?AW?Ppicture of the graph :Dg?AW?P
00302
00012
30000
01000
22000
[5, 4, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104111723(4t+3t2-t3)/(1-t)2-1+6t
20021656(2t2+8t3+4t4-5t5+2t6)/(1-t)4(-24+22t-27t2+11t3)/3!
300000(13t5+8t6-15t7+7t8-t9)/(1-t)6(-1080+178t+95t2+170t3-95t4+12t5)/5!
400000(18t8-18t9+7t10-t11)/(1-t)8(-30240+13728t+11494t2-4431t3-1295t4+777t5-119t6+6t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:DgH_@Capicture of the graph :DgH_@Ca
00102
00012
10002
01000
22200
[6, 3, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104111621(4t+3t2-2t3)/(1-t)21+5t
2000738(7t3+10t4-8t5+3t6)/(1-t)4(-48+57t-45t2+12t3)/3!
300000(3t5+19t6-15t7+6t8-t9)/(1-t)6(120+198t-705t2+510t3-135t4+12t5)/5!
400000(10t8-10t9+5t10-t11)/(1-t)8(50400-18960t-6454t2+8071t3-3535t4+805t5-91t6+4t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Dg?e@CQpicture of the graph :Dg?e@CQ
00201
00013
20001
01000
13100
[5, 4, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104111621(4t+3t2-2t3)/(1-t)21+5t
20021554(2t2+5t3-t4-5t5+9t6-5t7+t8)/(1-t)5(-52t+30t2-8t3+6t4)/4!
300000(20t5+2t6-19t7+11t8-2t9)/(1-t)6(-840-402t+785t2-90t3-65t4+12t5)/5!
400000(18t8-18t9+7t10-t11)/(1-t)8(-30240+13728t+11494t2-4431t3-1295t4+777t5-119t6+6t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Dg?e?CQpicture of the graph :Dg?e?CQ
00202
00012
20001
01000
22100
[5, 4, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104101418(4t+2t2-2t3)/(1-t)22+4t
20011351(t2+9t3+5t4-9t5+3t6)/(1-t)4(6-21t-12t2+9t3)/3!
300000(10t5+15t6-20t7+8t8-t9)/(1-t)6(-840-442t+395t2+130t3-95t4+12t5)/5!
400000(18t8-18t9+7t10-t11)/(1-t)8(-30240+13728t+11494t2-4431t3-1295t4+777t5-119t6+6t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Dg?AWCQpicture of the graph :Dg?AWCQ
00301
00012
30001
01000
12100
[4, 4, 4, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104101316(4t+2t2-3t3)/(1-t)24+3t
20021551(2t2+7t3+3t4-10t5+4t6)/(1-t)4(-18-27t+3t2+6t3)/3!
300000(16t5+9t6-27t7+11t8-t9)/(1-t)6(-2640-988t+1980t2-520t3+8t5)/5!
400000(27t8-27t9+9t10-t11)/(1-t)8(-75600-9780t+65170t2-28588t3+3010t4+560t5-140t6+8t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:DgG?gCapicture of the graph :DgG?gCa
00121
00001
10012
20100
11200
[4, 4, 4, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
10491113(4t+t2-3t3)/(1-t)25+2t
20011348(t2+9t3+2t4-14t5+7t6-t7)/(1-t)4(24-70t+18t2+4t3)/3!
300000(12t5+20t6-38t7+16t8-2t9)/(1-t)6(-1920-1728t+2280t2-560t3+8t5)/5!
400000(27t8-27t9+9t10-t11)/(1-t)8(-75600-9780t+65170t2-28588t3+3010t4+560t5-140t6+8t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:DgG?a_Qpicture of the graph :DgG?a_Q
00121
00001
10021
20200
11100
[4, 4, 4, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
1048910(4t-3t3)/(1-t)26+t
20001145(11t3+12t4-8t5+t6)/(1-t)3(18-46t+16t2)/2!
300000(6t5+34t6-48t7+18t8-2t9)/(1-t)6(-1440-2968t+2880t2-640t3+8t5)/5!
400000(27t8-27t9+9t10-t11)/(1-t)8(-75600-9780t+65170t2-28588t3+3010t4+560t5-140t6+8t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:DgG?g?Qpicture of the graph :DgG?g?Q
00122
00001
10011
20100
21100
[5, 4, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
10491113(4t+t2-3t3)/(1-t)25+2t
20001046(10t3+6t4-16t5+7t6-t7)/(1-t)4(48-75t+9t2+6t3)/3!
300000(4t5+31t6-35t7+14t8-2t9)/(1-t)6(-360-1282t+815t2+70t3-95t4+12t5)/5!
400000(18t8-18t9+7t10-t11)/(1-t)8(-30240+13728t+11494t2-4431t3-1295t4+777t5-119t6+6t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:DgG?A_Qpicture of the graph :DgG?A_Q
00131
00001
10011
30100
11100
[5, 4, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
10491011(4t+t2-4t3)/(1-t)27+t
2000944(9t3+8t4-18t5+8t6-t7)/(1-t)4(24-60t+6t2+6t3)/3!
300000(3t5+34t6-38t7+15t8-2t9)/(1-t)6(-1080-862t+755t2+70t3-95t4+12t5)/5!
400000(18t8-18t9+7t10-t11)/(1-t)8(-30240+13728t+11494t2-4431t3-1295t4+777t5-119t6+6t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Dg?_A_Qpicture of the graph :Dg?_A_Q
00221
00001
20011
20100
11100
[5, 4, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
10491011(4t+t2-4t3)/(1-t)27+t
2000944(9t3+8t4-17t5+7t6-t7)/(1-t)4(60-81t+9t2+6t3)/3!
300000(4t5+31t6-35t7+14t8-2t9)/(1-t)6(-360-1282t+815t2+70t3-95t4+12t5)/5!
400000(18t8-18t9+7t10-t11)/(1-t)8(-30240+13728t+11494t2-4431t3-1295t4+777t5-119t6+6t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:DgGI?Cbpicture of the graph :DgGI?Cb
00112
00001
10011
10101
21110
[5, 4, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
10491215(4t+t2-2t3)/(1-t)23+3t
20001148(11t3+4t4-18t5+11t6-2t7)/(1-t)4(-12-33t+3t2+6t3)/3!
300000(t5+41t6-47t7+20t8-3t9)/(1-t)6(-1320-562t+695t2+70t3-95t4+12t5)/5!
400000(18t8-18t9+7t10-t11)/(1-t)8(-30240+13728t+11494t2-4431t3-1295t4+777t5-119t6+6t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Dg?_gCbpicture of the graph :Dg?_gCb
00211
00001
20011
10101
11110
[4, 4, 4, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
10481012(4t-2t3)/(1-t)24+2t
20001247(12t3+11t4-11t5+2t6)/(1-t)3(-2-32t+14t2)/2!
300000(3t5+44t6-60t7+24t8-3t9)/(1-t)6(-2400-2248t+2760t2-640t3+8t5)/5!
400000(27t8-27t9+9t10-t11)/(1-t)8(-75600-9780t+65170t2-28588t3+3010t4+560t5-140t6+8t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Eo?E@Cbpicture of the graph :Eo?E@Cb
000021
000012
000001
000001
210000
121100
[5, 3, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031018(3t+t2-3t3+2t4)/(1-t)3(6+t+3t2)/2!
20019(t2+4t3+3t4-9t5+5t6-t7)/(1-t)5(24+10t-51t2+14t3+3t4)/4!
30000(7t5+6t6-6t7+2t8)/(1-t)6(-1440+1056t-570t2+315t3-90t4+9t5)/5!
40000(6t8-4t9+t10)/(1-t)8(-50400+42480t-17290t2+7287t3-2800t4+630t5-70t6+3t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Eo?CWCbpicture of the graph :Eo?CWCb
000021
000021
000001
000001
220000
111100
[4, 4, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
103813(3t-t2-2t3+2t4)/(1-t)3(8+2t2)/2!
20008(8t3+5t4-6t5+t6)/(1-t)4(54-38t-12t2+8t3)/3!
30000(6t5+10t6-10t7+2t8)/(1-t)6(960-2048t+900t2-60t4+8t5)/5!
40000(9t8-6t9+t10)/(1-t)8(15120-56844t+41034t2-9254t3-630t4+574t5-84t6+4t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Eo?CgCRpicture of the graph :Eo?CgCR
000021
000012
000010
000001
211000
120100
[4, 4, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
103913(3t+3t2-2t3)/(1-t)21+4t
20018(t2+4t3+8t4-6t5+t6)/(1-t)4(36-14t-18t2+8t3)/3!
30000(6t5+10t6-10t7+2t8)/(1-t)6(960-2048t+900t2-60t4+8t5)/5!
40000(9t8-6t9+t10)/(1-t)8(15120-56844t+41034t2-9254t3-630t4+574t5-84t6+4t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Eo?CQ_Rpicture of the graph :Eo?CQ_R
000021
000021
000010
000001
221000
110100
[5, 3, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
103913(3t+3t2-2t3)/(1-t)21+4t
20004(4t3+10t4-6t5+t6)/(1-t)4(24+9t-30t2+9t3)/3!
30000(2t5+13t6-8t7+2t8)/(1-t)6(-840+766t-735t2+425t3-105t4+9t5)/5!
40000(6t8-4t9+t10)/(1-t)8(-50400+42480t-17290t2+7287t3-2800t4+630t5-70t6+3t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Ek?e@Cbpicture of the graph :Ek?e@Cb
000201
000012
000001
200001
010000
121100
[5, 3, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031019(3t+t2-2t3+t4)/(1-t)3(2+3t+3t2)/2!
200110(t2+5t3-6t5+4t6-t7)/(1-t)5(-24+34t-51t2+14t3+3t4)/4!
30000(7t5+6t6-6t7+2t8)/(1-t)6(-1440+1056t-570t2+315t3-90t4+9t5)/5!
40000(6t8-4t9+t10)/(1-t)8(-50400+42480t-17290t2+7287t3-2800t4+630t5-70t6+3t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:EkGCP_Qpicture of the graph :EkGCP_Q
000111
000031
000001
100000
130000
111000
[4, 4, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
103810(3t+2t2-3t3)/(1-t)24+2t
20005(5t3+9t4-11t5+2t6)/(1-t)4(90-83t+6t2+5t3)/3!
30000(2t5+19t6-16t7+3t8)/(1-t)6(1680-3188t+1380t2-60t3-60t4+8t5)/5!
40000(9t8-6t9+t10)/(1-t)8(15120-56844t+41034t2-9254t3-630t4+574t5-84t6+4t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:EkGCW?Qpicture of the graph :EkGCW?Q
000112
000021
000001
100000
120000
211000
[4, 4, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
103913(3t+3t2-2t3)/(1-t)21+4t
20018(t2+3t3+4t4-10t5+7t6-t7)/(1-t)5(240-256t+68t2-8t3+4t4)/4!
30000(10t5+6t6-10t7+2t8)/(1-t)6(1440-3048t+1600t2-200t3-40t4+8t5)/5!
40000(9t8-6t9+t10)/(1-t)8(15120-56844t+41034t2-9254t3-630t4+574t5-84t6+4t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:EkG?WCQpicture of the graph :EkG?WCQ
000121
000012
000001
100000
210000
121000
[4, 4, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
103913(3t+3t2-2t3)/(1-t)21+4t
20018(t2+4t3+8t4-6t5+t6)/(1-t)4(36-14t-18t2+8t3)/3!
30000(6t5+10t6-10t7+2t8)/(1-t)6(960-2048t+900t2-60t4+8t5)/5!
40000(9t8-6t9+t10)/(1-t)8(15120-56844t+41034t2-9254t3-630t4+574t5-84t6+4t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:EkG?P_Qpicture of the graph :EkG?P_Q
000121
000021
000001
100000
220000
111000
[4, 4, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
103811(3t+2t2-2t3)/(1-t)22+3t
20006(6t3+7t4-8t5+t6)/(1-t)4(90-72t+6t3)/3!
30000(4t5+14t6-12t7+2t8)/(1-t)6(1920-3088t+1260t2-40t3-60t4+8t5)/5!
40000(9t8-6t9+t10)/(1-t)8(15120-56844t+41034t2-9254t3-630t4+574t5-84t6+4t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Ek?A@_cpicture of the graph :Ek?A@_c
000311
000010
000001
300000
110001
101010
[5, 3, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
103914(3t+3t2-t3)/(1-t)2-1+5t
20005(5t3+8t4-5t5+2t6)/(1-t)4(-48+62t-42t2+10t3)/3!
30000(2t5+14t6-10t7+3t8)/(1-t)6(-2040+1706t-975t2+445t3-105t4+9t5)/5!
40000(6t8-4t9+t10)/(1-t)8(-50400+42480t-17290t2+7287t3-2800t4+630t5-70t6+3t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:EkGE@Ccpicture of the graph :EkGE@Cc
000111
000012
000001
100000
110001
121010
[5, 3, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
103913(3t+3t2-2t3)/(1-t)21+4t
20004(4t3+10t4-7t5+2t6)/(1-t)4(-12+30t-33t2+9t3)/3!
30000(t5+16t6-11t7+3t8)/(1-t)6(-1560+1186t-795t2+425t3-105t4+9t5)/5!
40000(6t8-4t9+t10)/(1-t)8(-50400+42480t-17290t2+7287t3-2800t4+630t5-70t6+3t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:EkGCWCcpicture of the graph :EkGCWCc
000111
000021
000001
100000
120001
111010
[4, 4, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
103811(3t+2t2-2t3)/(1-t)22+3t
20006(6t3+7t4-9t5+2t6)/(1-t)4(54-51t-3t2+6t3)/3!
30000(3t5+17t6-15t7+3t8)/(1-t)6(1200-2668t+1200t2-40t3-60t4+8t5)/5!
40000(9t8-6t9+t10)/(1-t)8(15120-56844t+41034t2-9254t3-630t4+574t5-84t6+4t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:EkHCg?Ppicture of the graph :EkHCg?P
000102
000022
000010
100000
021000
220000
[4, 4, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
103915(3t+3t2)/(1-t)2-3+6t
200110(t2+6t3+4t4-3t5)/(1-t)4(48-23t-15t2+8t3)/3!
30000(7t5+7t6-7t7+t8)/(1-t)6(1680-2468t+960t2-60t4+8t5)/5!
40000(9t8-6t9+t10)/(1-t)8(15120-56844t+41034t2-9254t3-630t4+574t5-84t6+4t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:EkHI?CSpicture of the graph :EkHI?CS
000102
000012
000010
100000
011001
220010
[5, 3, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
103914(3t+3t2-t3)/(1-t)2-1+5t
20005(5t3+8t4-5t5+t6)/(1-t)4(12+15t-30t2+9t3)/3!
30000(2t5+13t6-8t7+2t8)/(1-t)6(-840+766t-735t2+425t3-105t4+9t5)/5!
40000(6t8-4t9+t10)/(1-t)8(-50400+42480t-17290t2+7287t3-2800t4+630t5-70t6+3t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:EkHCg?Spicture of the graph :EkHCg?S
000102
000021
000010
100000
021001
210010
[4, 4, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
103914(3t+3t2-t3)/(1-t)2-1+5t
20019(t2+5t3+6t4-5t5+t6)/(1-t)4(24-8t-18t2+8t3)/3!
30000(6t5+10t6-10t7+2t8)/(1-t)6(960-2048t+900t2-60t4+8t5)/5!
40000(9t8-6t9+t10)/(1-t)8(15120-56844t+41034t2-9254t3-630t4+574t5-84t6+4t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Ek?cgLCpicture of the graph :Ek?cgLC
000201
000010
000010
200001
011002
100120
[4, 4, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
103916(3t-2t3+t4)/(1-t)3(2+4t+2t2)/2!
200111(t2+6t3-3t4-5t5+6t6-t7)/(1-t)5(240-304t+92t2-8t3+4t4)/4!
30000(10t5+6t6-10t7+2t8)/(1-t)6(1440-3048t+1600t2-200t3-40t4+8t5)/5!
40000(9t8-6t9+t10)/(1-t)8(15120-56844t+41034t2-9254t3-630t4+574t5-84t6+4t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:EkG?wCbpicture of the graph :EkG?wCb
000121
000001
000001
100011
200100
111100
[4, 4, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
103813(3t-t2-2t3+2t4)/(1-t)3(8+2t2)/2!
20008(8t3+5t4-9t5+2t6)/(1-t)4(66-69t+3t2+6t3)/3!
30000(3t5+17t6-15t7+3t8)/(1-t)6(1200-2668t+1200t2-40t3-60t4+8t5)/5!
40000(9t8-6t9+t10)/(1-t)8(15120-56844t+41034t2-9254t3-630t4+574t5-84t6+4t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:EkGM@Gspicture of the graph :EkGM@Gs
000111
000001
000001
100011
100101
111110
[5, 3, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
103917(3t-t3+t4)/(1-t)3(4+t+3t2)/2!
20008(8t3+5t4-7t5+3t6)/(1-t)4(-42+30t-27t2+9t3)/3!
30000(19t6-14t7+4t8)/(1-t)6(-2280+1606t-855t2+425t3-105t4+9t5)/5!
40000(6t8-4t9+t10)/(1-t)8(-50400+42480t-17290t2+7287t3-2800t4+630t5-70t6+3t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:EkGCwGspicture of the graph :EkGCwGs
000111
000010
000001
100011
110101
101110
[4, 4, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
103812(3t+2t2-t3)/(1-t)24t
20007(7t3+5t4-11t5+3t6)/(1-t)4(54-76t+12t2+4t3)/3!
30000(24t6-20t7+4t8)/(1-t)6(1440-3288t+1500t2-80t3-60t4+8t5)/5!
40000(9t8-6t9+t10)/(1-t)8(15120-56844t+41034t2-9254t3-630t4+574t5-84t6+4t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Ek@_g?spicture of the graph :Ek@_g?s
000112
000100
000010
110001
101001
200110
[4, 4, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
103810(3t+2t2-3t3)/(1-t)24+2t
20005(5t3+9t4-12t5+2t6)/(1-t)4(114-109t+15t2+4t3)/3!
30000(t5+21t6-17t7+3t8)/(1-t)6(2160-3708t+1560t2-80t3-60t4+8t5)/5!
40000(9t8-6t9+t10)/(1-t)8(15120-56844t+41034t2-9254t3-630t4+574t5-84t6+4t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Ek?EA_spicture of the graph :Ek?EA_s
000211
000100
000010
210001
101001
100110
[4, 4, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
103811(3t+2t2-2t3)/(1-t)22+3t
20006(6t3+7t4-11t5+2t6)/(1-t)4(102-103t+15t2+4t3)/3!
30000(t5+21t6-17t7+3t8)/(1-t)6(2160-3708t+1560t2-80t3-60t4+8t5)/5!
40000(9t8-6t9+t10)/(1-t)8(15120-56844t+41034t2-9254t3-630t4+574t5-84t6+4t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:FoGCWCbpicture of the graph :FoGCWCb
0000111
0000021
0000001
0000001
1000000
1200000
1111000
[4, 3, 3, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
1027(2t+t2-2t3+t4)/(1-t)3(2+2t+2t2)/2!
2000(4t3+2t4-7t5+3t6)/(1-t)5(192-116t-14t2+8t3+2t4)/4!
3000(3t5+6t6-3t7)/(1-t)6(1440-1416t+240t2+150t3-60t4+6t5)/5!
4000(3t8-t9)/(1-t)8(25200-30060t+9464t2+1883t3-1855t4+455t5-49t6+2t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:FoGDGGspicture of the graph :FoGDGGs
0000111
0000010
0000001
0000001
1000011
1100100
1011100
[4, 3, 3, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
1027(2t+t2-2t3+t4)/(1-t)3(2+2t+2t2)/2!
2000(4t3+6t4-4t5)/(1-t)4(60-30t-12t2+6t3)/3!
3000(10t6-4t7)/(1-t)6(1680-1436t+70t2+230t3-70t4+6t5)/5!
4000(3t8-t9)/(1-t)8(25200-30060t+9464t2+1883t3-1855t4+455t5-49t6+2t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Fo?EAlDpicture of the graph :Fo?EAlD
0000210
0000100
0000010
0000001
2100001
1010001
0001110
[4, 3, 3, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
1027(2t+3t2-t3)/(1-t)2-1+4t
2000(2t3+8t4-3t5)/(1-t)4(24+14t-27t2+7t3)/3!
3000(t5+8t6-3t7)/(1-t)6(1200-916t-110t2+250t3-70t4+6t5)/5!
4000(3t8-t9)/(1-t)8(25200-30060t+9464t2+1883t3-1855t4+455t5-49t6+2t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Fo@_gLDpicture of the graph :Fo@_gLD
0000111
0000100
0000010
0000001
1100001
1010001
1001110
[4, 3, 3, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
1027(2t+3t2-t3)/(1-t)2-1+4t
2000(2t3+8t4-4t5)/(1-t)4(48-12t-18t2+6t3)/3!
3000(10t6-4t7)/(1-t)6(1680-1436t+70t2+230t3-70t4+6t5)/5!
4000(3t8-t9)/(1-t)8(25200-30060t+9464t2+1883t3-1855t4+455t5-49t6+2t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:FkH_gCTpicture of the graph :FkH_gCT
0001011
0000102
0000010
1000000
0100000
1010001
1200010
[4, 3, 3, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
1027(2t+3t2)/(1-t)2-3+5t
2000(3t3+6t4-2t5)/(1-t)4(12+20t-27t2+7t3)/3!
3000(t5+8t6-3t7)/(1-t)6(1200-916t-110t2+250t3-70t4+6t5)/5!
4000(3t8-t9)/(1-t)8(25200-30060t+9464t2+1883t3-1855t4+455t5-49t6+2t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:GoH_Q_Rpicture of the graph :GoH_Q_R
00001011
00000111
00000010
00000001
10000000
01000000
11100000
11010000
[3, 3, 3, 3, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01Poincaré seriesstable polynomial value
0111/(1-t)1
101(t+3t2)/(1-t)2-3+4t
2006t4/(1-t)4(-36+66t-36t2+6t3)/3!
3004t6/(1-t)6(-480+1096t-900t2+340t3-60t4+4t5)/5!
400t8/(1-t)8(-5040+13068t-13132t2+6769t3-1960t4+322t5-28t6+t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Cw?HIQpicture of the graph :Cw?HIQ
0003
0003
0003
3330
[9, 3, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k0123456Poincaré seriesstable polynomial value
011111111/(1-t)1
106224269103144(6t+4t2-6t3+3t4)/(1-t)3(6+5t+7t2)/2!
20001281261636(12t3+21t4-24t5+21t6-12t7+3t8)/(1-t)5(144+54t-21t2-54t3+21t4)/4!
300000688(6t5+46t6-66t7+60t8-38t9+18t10-6t11+t12)/(1-t)7(2880+612t-636t2-405t3+615t4-207t5+21t6)/6!
40000000(28t8-56t9+70t10-56t11+28t12-8t13+t14)/(1-t)9(40320+6000t-8540t2-1372t3+7343t4-4480t5+1190t6-148t7+7t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Co?_@Hpicture of the graph :Co?_@H
0033
0003
3000
3300
[6, 6, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k0123456Poincaré seriesstable polynomial value
011111111/(1-t)1
1061725334149(6t+5t2-3t3)/(1-t)21+8t
200440162424909(4t2+20t3+2t4-26t5+29t6-16t7+3t8)/(1-t)5(-384+412t-220t2+32t3+16t4)/4!
30000042321(42t5+27t6-104t7+121t8-78t9+31t10-8t11+t12)/(1-t)7(-39600+36072t-12892t2+3000t3-100t4-192t5+32t6)/6!
40000000(100t8-200t9+200t10-120t11+45t12-10t13+t14)/(1-t)9(-1532160+1591776t-519136t2+62216t3-6216t4-616t5+1176t6-256t7+16t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Co?C@Hpicture of the graph :Co?C@H
0042
0003
4000
2300
[6, 5, 4, 3]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10617243138(6t+5t2-4t3)/(1-t)23+7t
200643146346(6t2+13t3-9t4-14t5+25t6-16t7+3t8)/(1-t)5(-576+476t-200t2+52t3+8t4)/4!
30000287(2t4+73t5-36t6-95t7+144t8-85t9+24t10-3t11)/(1-t)7(-58320+42912t-7944t2+1740t3-720t4-12t5+24t6)/6!
4000000(6t7+146t8-279t9+235t10-108t11+27t12-3t13)/(1-t)9(-2177280+1819296t-281088t2-34216t3-21504t4+9464t5+168t6-304t7+24t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Co_HHQpicture of the graph :Co_HHQ
0012
0004
1002
2420
[8, 4, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10617232935(6t+5t2-5t3)/(1-t)25+6t
200018106303(18t3+16t4-47t5+44t6-25t7+6t8)/(1-t)5(192+236t-264t2+40t3+12t4)/4!
30000011(11t5+82t6-145t7+125t8-67t9+21t10-3t11)/(1-t)7(-8640+6732t-7134t2+3840t3-450t4-132t5+24t6)/6!
4000000(t7+56t8-105t9+105t10-63t11+21t12-3t13)/(1-t)9(-604800+172800t-115008t2+88088t3-27132t4+1400t5+1008t6-208t7+12t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Co_@HQpicture of the graph :Co_@HQ
0013
0003
1002
3320
[8, 4, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k0123456Poincaré seriesstable polynomial value
011111111/(1-t)1
1061723293541(6t+5t2-5t3)/(1-t)25+6t
200018106304681(18t3+16t4-46t5+41t6-22t7+5t8)/(1-t)5(96+260t-264t2+40t3+12t4)/4!
30000012161(12t5+77t6-136t7+120t8-72t9+30t10-8t11+t12)/(1-t)7(-7200+6732t-7134t2+3840t3-450t4-132t5+24t6)/6!
40000000(63t8-126t9+140t10-98t11+42t12-10t13+t14)/(1-t)9(-362880+132480t-115008t2+88088t3-27132t4+1400t5+1008t6-208t7+12t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:CoCHHIpicture of the graph :CoCHHI
0021
0005
2001
1510
[7, 5, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
106182328(6t+6t2-7t3)/(1-t)28+5t
200433148(4t2+9t3+10t4-19t5+31t6-38t7+24t8-6t9)/(1-t)6(3480-1250t+265t2-145t3+35t4+15t5)/5!
300004(4t4+73t5-50t6-46t7+91t8-54t9+12t10)/(1-t)7(62640-38484t+12750t2-1380t3-180t4-96t5+30t6)/6!
400000(4t7+65t8-114t9+90t10-36t11+6t12)/(1-t)9(2661120-1589904t+460116t2-82516t3+2415t4-616t5+1134t6-244t7+15t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:CoC@HQpicture of the graph :CoC@HQ
0022
0003
2002
2320
[7, 4, 4, 3]

Betti numbers βi(Bk(Γ)):

i\k0123456Poincaré seriesstable polynomial value
011111111/(1-t)1
1061520253035(6t+3t2-4t3)/(1-t)25+5t
200231126301585(2t2+23t3+14t4-25t5+15t6-4t7)/(1-t)4(96-43t-48t2+25t3)/3!
30000038311(38t5+45t6-151t7+157t8-103t9+43t10-10t11+t12)/(1-t)7(27360-25356t+1550t2+5160t3-1570t4+36t5+20t6)/6!
40000000(135t8-270t9+270t10-164t11+60t12-12t13+t14)/(1-t)9(1088640-990144t+241536t2+71512t3-60340t4+11704t5+224t6-272t7+20t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:CoC@HIpicture of the graph :CoC@HI
0022
0004
2001
2410
[7, 4, 4, 3]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10616212631(6t+4t2-5t3)/(1-t)26+5t
200332128324(3t2+17t3-2t4-26t5+34t6-22t7+6t8)/(1-t)5(576-200t-82t2+32t3+10t4)/4!
30000160(t4+53t5+5t6-120t7+145t8-88t9+27t10-3t11)/(1-t)7(49680-33396t+5570t2+3120t3-1270t4+36t5+20t6)/6!
4000000(3t7+116t8-219t9+195t10-99t11+27t12-3t13)/(1-t)9(2056320-1393344t+281856t2+71512t3-60340t4+11704t5+224t6-272t7+20t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:CoC?HIpicture of the graph :CoC?HI
0023
0003
2001
3310
[7, 5, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k0123456Poincaré seriesstable polynomial value
011111111/(1-t)1
1061621263136(6t+4t2-5t3)/(1-t)26+5t
200231142381825(2t2+21t3+7t4-39t5+40t6-21t7+5t8)/(1-t)5(504-222t-75t2+18t3+15t4)/4!
30000030265(30t5+55t6-133t7+135t8-83t9+33t10-8t11+t12)/(1-t)7(30240-26484t+7830t2+30t3+60t4-186t5+30t6)/6!
40000000(90t8-180t9+185t10-116t11+45t12-10t13+t14)/(1-t)9(1088640-964944t+399636t2-82516t3+2415t4-616t5+1134t6-244t7+15t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Co?`HIpicture of the graph :Co?`HI
0031
0004
3001
1410
[6, 4, 4, 4]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10616202428(6t+4t2-6t3)/(1-t)28+4t
200640127284(6t2+10t3-13t4-11t5+38t6-31t7+9t8)/(1-t)5(696-356t+76t2+8t3+8t4)/4!
30000295(2t4+83t5+17t6-130t7+106t8-33t9+3t10)/(1-t)6(840+512t+1220t2-80t3-260t4+48t5)/5!
4000000(9t7+219t8-419t9+340t10-147t11+33t12-3t13)/(1-t)9(-564480+860256t+106928t2-79520t3-65072t4+25984t5-1568t6-320t7+32t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Co?_HIpicture of the graph :Co?_HI
0032
0003
3001
2310
[6, 5, 4, 3]

Betti numbers βi(Bk(Γ)):

i\k0123456Poincaré seriesstable polynomial value
011111111/(1-t)1
1061519232731(6t+3t2-5t3)/(1-t)27+4t
200438136308581(4t2+22t3+8t4-24t5+17t6-5t7)/(1-t)4(108-67t-27t2+22t3)/3!
30000060431(60t5+11t6-154t7+195t8-126t9+47t10-10t11+t12)/(1-t)7(-5040+3312t-504t2+2460t3-960t4-12t5+24t6)/6!
40000000(180t8-360t9+340t10-188t11+63t12-12t13+t14)/(1-t)9(-725760+730656t-19008t2-54376t3-21504t4+9464t5+168t6-304t7+24t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Co?CHIpicture of the graph :Co?CHI
0041
0003
4001
1310
[5, 5, 5, 3]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10616192225(6t+4t2-7t3)/(1-t)210+3t
200641136312(6t2+11t3-9t4-18t5+37t6-24t7+6t8)/(1-t)5(408-354t+99t2+6t3+9t4)/4!
30000299(2t4+85t5-46t6-125t7+197t8-113t9+30t10-3t11)/(1-t)7(-14400-2004t+17928t2-6195t3+405t4-81t5+27t6)/6!
4000000(6t7+182t8-351t9+291t10-128t11+30t12-3t13)/(1-t)9(-1088640+533808t+662964t2-398076t3+42483t4+5712t5+126t6-324t7+27t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Co?K@Hpicture of the graph :Co?K@H
0032
0013
3100
2300
[5, 5, 4, 4]

Betti numbers βi(Bk(Γ)):

i\k0123456Poincaré seriesstable polynomial value
011111111/(1-t)1
1061313131313(6t+7t2)/(1-t)13
200436114232409(4t2+20t3-6t4-24t5+25t6-7t7)/(1-t)4(-48+3t-3t2+12t3)/3!
30000082517(82t5+25t6-171t7+146t8-56t9+11t10-t11)/(1-t)6(-7560+4004t+2250t2-920t3-90t4+36t5)/5!
40000000(324t8-648t9+576t10-288t11+85t12-14t13+t14)/(1-t)9(-1693440+1250592t+598352t2-425544t3+8204t4+22008t5-1792t6-336t7+36t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Co?H_Hpicture of the graph :Co?H_H
0032
0022
3200
2200
[5, 5, 4, 4]

Betti numbers βi(Bk(Γ)):

i\k0123456Poincaré seriesstable polynomial value
011111111/(1-t)1
1061212121212(6t+6t2)/(1-t)12
200335115238416(3t2+23t3-7t4-24t5+17t6-3t7)/(1-t)4(-42-81t+30t2+9t3)/3!
30000289525(2t4+77t5+21t6-152t7+130t8-52t9+11t10-t11)/(1-t)6(-7320+2324t+2910t2-980t3-90t4+36t5)/5!
40000000(324t8-648t9+576t10-288t11+85t12-14t13+t14)/(1-t)9(-1693440+1250592t+598352t2-425544t3+8204t4+22008t5-1792t6-336t7+36t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Co?H_@picture of the graph :Co?H_@
0033
0021
3200
3100
[6, 5, 4, 3]

Betti numbers βi(Bk(Γ)):

i\k0123456Poincaré seriesstable polynomial value
011111111/(1-t)1
1061313131313(6t+7t2)/(1-t)13
200232126283530(2t2+24t3+10t4-37t5+28t6-7t7)/(1-t)4(-12-8t-30t2+20t3)/3!
30000049398(49t5+55t6-222t7+245t8-143t9+49t10-10t11+t12)/(1-t)7(-23760+13272t-864t2+2220t3-960t4-12t5+24t6)/6!
40000000(180t8-360t9+340t10-188t11+63t12-12t13+t14)/(1-t)9(-725760+730656t-19008t2-54376t3-21504t4+9464t5+168t6-304t7+24t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Co?@`Hpicture of the graph :Co?@`H
0041
0013
4100
1300
[5, 5, 4, 4]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10615151515(6t+9t2)/(1-t)15
200638118259(6t2+8t3-12t4-11t5+51t6-45t7+12t8)/(1-t)5(-264+506t-117t2+10t3+9t4)/4!
300002107(2t4+95t5+10t6-175t7+140t8-39t9+3t10)/(1-t)6(-11280+9874t+765t2-1030t3-45t4+36t5)/5!
4000000(9t7+273t8-527t9+421t10-173t11+36t12-3t13)/(1-t)9(-2741760+2392992t+275792t2-398664t3+8204t4+22008t5-1792t6-336t7+36t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Co?@_Hpicture of the graph :Co?@_H
0042
0012
4100
2200
[6, 5, 4, 3]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10614141414(6t+8t2)/(1-t)14
200333128313(3t2+18t3-7t4-27t5+47t6-28t7+6t8)/(1-t)5(-48-68t+36t2-4t3+12t4)/4!
30000178(t4+71t5-11t6-150t7+198t8-112t9+30t10-3t11)/(1-t)7(-7200+4992t+4536t2-300t3-600t4-12t5+24t6)/6!
4000000(3t7+161t8-309t9+265t10-123t11+30t12-3t13)/(1-t)9(241920+327456t+21312t2-54376t3-21504t4+9464t5+168t6-304t7+24t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Co?@K@picture of the graph :Co?@K@
0042
0021
4200
2100
[6, 6, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10614141414(6t+8t2)/(1-t)14
200129143380(t2+24t3+8t4-55t5+63t6-31t7+6t8)/(1-t)5(120-180t-4t2+16t4)/4!
30000025(25t5+90t6-193t7+178t8-89t9+24t10-3t11)/(1-t)7(-38160+24792t-6412t2+2040t3-100t4-192t5+32t6)/6!
4000000(t7+93t8-179t9+165t10-85t11+24t12-3t13)/(1-t)9(-1774080+1632096t-519136t2+62216t3-6216t4-616t5+1176t6-256t7+16t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Co??KHpicture of the graph :Co??KH
0051
0012
5100
1200
[6, 6, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
106171717(6t+11t2)/(1-t)17
200432150(4t2+8t3+18t4-31t5+44t6-49t7+28t8-6t9)/(1-t)6(-240+1504t-340t2-140t3+40t4+16t5)/5!
300004(4t4+83t5-61t6-53t7+109t8-62t9+12t10)/(1-t)7(-12960+27336t-7252t2+1200t3-340t4-96t5+32t6)/6!
400000(4t7+75t8-134t9+105t10-40t11+6t12)/(1-t)9(40320+966816t-458656t2+62216t3-6216t4-616t5+1176t6-256t7+16t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Co@`IQpicture of the graph :Co@`IQ
0021
0012
2103
1230
[6, 6, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k0123456Poincaré seriesstable polynomial value
011111111/(1-t)1
1061414141414(6t+8t2)/(1-t)14
200129143379816(t2+24t3+8t4-56t5+66t6-34t7+7t8)/(1-t)5(216-204t-4t2+16t4)/4!
30000024263(24t5+95t6-204t7+193t8-104t9+35t10-8t11+t12)/(1-t)7(-30960+23352t-6412t2+2040t3-100t4-192t5+32t6)/6!
40000000(100t8-200t9+200t10-120t11+45t12-10t13+t14)/(1-t)9(-1532160+1591776t-519136t2+62216t3-6216t4-616t5+1176t6-256t7+16t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Co@KIQpicture of the graph :Co@KIQ
0021
0021
2203
1130
[7, 5, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k0123456Poincaré seriesstable polynomial value
011111111/(1-t)1
1061414141414(6t+8t2)/(1-t)14
200024130350758(24t3+10t4-60t5+68t6-34t7+7t8)/(1-t)5(360-322t+21t2-2t3+15t4)/4!
30000016220(16t5+108t6-210t7+188t8-100t9+35t10-8t11+t12)/(1-t)7(20160-25884t+10710t2-570t3+60t4-186t5+30t6)/6!
40000000(90t8-180t9+185t10-116t11+45t12-10t13+t14)/(1-t)9(1088640-964944t+399636t2-82516t3+2415t4-616t5+1134t6-244t7+15t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Co@K@Qpicture of the graph :Co@K@Q
0022
0021
2202
2120
[6, 5, 4, 3]

Betti numbers βi(Bk(Γ)):

i\k0123456Poincaré seriesstable polynomial value
011111111/(1-t)1
1061212121212(6t+6t2)/(1-t)12
200131125270486(t2+27t3+7t4-48t5+33t6-8t7)/(1-t)4(90-159t+33t2+12t3)/3!
30000037355(37t5+96t6-274t7+275t8-151t9+50t10-10t11+t12)/(1-t)7(-10800-4848t+6696t2+1260t3-960t4-12t5+24t6)/6!
40000000(180t8-360t9+340t10-188t11+63t12-12t13+t14)/(1-t)9(-725760+730656t-19008t2-54376t3-21504t4+9464t5+168t6-304t7+24t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Co@K@Ipicture of the graph :Co@K@I
0022
0022
2201
2210
[5, 5, 4, 4]

Betti numbers βi(Bk(Γ)):

i\k0123456Poincaré seriesstable polynomial value
011111111/(1-t)1
1061111111111(6t+5t2)/(1-t)11
200234113219358(2t2+28t3+17t4-20t5+6t6)/(1-t)3(38-85t+33t2)/2!
30000171468(t4+65t5+57t6-187t7+145t8-55t9+11t10-t11)/(1-t)6(-4080-1156t+4290t2-1160t3-90t4+36t5)/5!
40000000(324t8-648t9+576t10-288t11+85t12-14t13+t14)/(1-t)9(-1693440+1250592t+598352t2-425544t3+8204t4+22008t5-1792t6-336t7+36t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Co?KHQpicture of the graph :Co?KHQ
0031
0012
3102
1220
[6, 5, 4, 3]

Betti numbers βi(Bk(Γ)):

i\k0123456Poincaré seriesstable polynomial value
011111111/(1-t)1
1061313131313(6t+7t2)/(1-t)13
200232126281526(2t2+24t3+10t4-39t5+32t6-9t7)/(1-t)4(36-20t-30t2+20t3)/3!
30000047394(47t5+65t6-242t7+265t8-153t9+51t10-10t11+t12)/(1-t)7(-18000+11832t-864t2+2220t3-960t4-12t5+24t6)/6!
40000000(180t8-360t9+340t10-188t11+63t12-12t13+t14)/(1-t)9(-725760+730656t-19008t2-54376t3-21504t4+9464t5+168t6-304t7+24t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Co?KHIpicture of the graph :Co?KHI
0031
0013
3101
1310
[5, 5, 4, 4]

Betti numbers βi(Bk(Γ)):

i\k0123456Poincaré seriesstable polynomial value
011111111/(1-t)1
1061313131313(6t+7t2)/(1-t)13
200436114228401(4t2+20t3-6t4-28t5+33t6-11t7)/(1-t)4(48-21t-3t2+12t3)/3!
30000078509(78t5+41t6-195t7+162t8-60t9+11t10-t11)/(1-t)6(-5640+3524t+2250t2-920t3-90t4+36t5)/5!
40000000(324t8-648t9+576t10-288t11+85t12-14t13+t14)/(1-t)9(-1693440+1250592t+598352t2-425544t3+8204t4+22008t5-1792t6-336t7+36t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Co?H`Qpicture of the graph :Co?H`Q
0031
0021
3202
1120
[7, 4, 4, 3]

Betti numbers βi(Bk(Γ)):

i\k0123456Poincaré seriesstable polynomial value
011111111/(1-t)1
1061313131313(6t+7t2)/(1-t)13
200024114266509(24t3+18t4-46t5+33t6-9t7)/(1-t)4(96-65t-27t2+20t3)/3!
30000020257(20t5+117t6-264t7+244t8-136t9+48t10-10t11+t12)/(1-t)7(21600-24396t+4070t2+4560t3-1570t4+36t5+20t6)/6!
40000000(135t8-270t9+270t10-164t11+60t12-12t13+t14)/(1-t)9(1088640-990144t+241536t2+71512t3-60340t4+11704t5+224t6-272t7+20t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Co?H`Ipicture of the graph :Co?H`I
0031
0022
3201
1210
[6, 4, 4, 4]

Betti numbers βi(Bk(Γ)):

i\k0123456Poincaré seriesstable polynomial value
011111111/(1-t)1
1061212121212(6t+6t2)/(1-t)12
200232113232405(2t2+24t3-3t4-36t5+29t6-8t7)/(1-t)4(102-152t+42t2+8t3)/3!
30000059424(59t5+70t6-172t7+135t8-54t9+11t10-t11)/(1-t)6(2040-3668t+2640t2-40t3-300t4+48t5)/5!
40000000(270t8-540t9+495t10-262t11+82t12-14t13+t14)/(1-t)9(483840-282144t+429488t2-106400t3-65072t4+25984t5-1568t6-320t7+32t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Co?HKIpicture of the graph :Co?HKI
0031
0031
3301
1110
[7, 4, 4, 3]

Betti numbers βi(Bk(Γ)):

i\k0123456Poincaré seriesstable polynomial value
011111111/(1-t)1
1061313131313(6t+7t2)/(1-t)13
200024114264505(24t3+18t4-48t5+37t6-11t7)/(1-t)4(144-77t-27t2+20t3)/3!
30000018253(18t5+127t6-284t7+264t8-146t9+50t10-10t11+t12)/(1-t)7(27360-25836t+4070t2+4560t3-1570t4+36t5+20t6)/6!
40000000(135t8-270t9+270t10-164t11+60t12-12t13+t14)/(1-t)9(1088640-990144t+241536t2+71512t3-60340t4+11704t5+224t6-272t7+20t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Co?K@Ipicture of the graph :Co?K@I
0032
0012
3101
2210
[5, 5, 5, 3]

Betti numbers βi(Bk(Γ)):

i\k0123456Poincaré seriesstable polynomial value
011111111/(1-t)1
1061212121212(6t+6t2)/(1-t)12
200234124256448(2t2+26t3-44t5+34t6-9t7)/(1-t)4(96-162t+45t2+9t3)/3!
30000056452(56t5+60t6-267t7+302t8-169t9+54t10-10t11+t12)/(1-t)7(9360-28104t+25038t2-5655t3+135t4-81t5+27t6)/6!
40000000(216t8-432t9+396t10-208t11+66t12-12t13+t14)/(1-t)9(362880-554832t+925044t2-418236t3+42483t4+5712t5+126t6-324t7+27t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Co?H_Ipicture of the graph :Co?H_I
0032
0021
3201
2110
[6, 5, 4, 3]

Betti numbers βi(Bk(Γ)):

i\k0123456Poincaré seriesstable polynomial value
011111111/(1-t)1
1061212121212(6t+6t2)/(1-t)12
200131125269484(t2+27t3+7t4-49t5+35t6-9t7)/(1-t)4(114-165t+33t2+12t3)/3!
30000036353(36t5+101t6-284t7+285t8-156t9+51t10-10t11+t12)/(1-t)7(-7920-5568t+6696t2+1260t3-960t4-12t5+24t6)/6!
40000000(180t8-360t9+340t10-188t11+63t12-12t13+t14)/(1-t)9(-725760+730656t-19008t2-54376t3-21504t4+9464t5+168t6-304t7+24t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Co?@`Ipicture of the graph :Co?@`I
0041
0012
4101
1210
[6, 5, 4, 3]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10614141414(6t+8t2)/(1-t)14
200333128310(3t2+18t3-7t4-30t5+56t6-37t7+9t8)/(1-t)5(240-140t+36t2-4t3+12t4)/4!
30000175(t4+68t5+4t6-180t7+228t8-127t9+33t10-3t11)/(1-t)7(1440+2832t+4536t2-300t3-600t4-12t5+24t6)/6!
4000000(3t7+161t8-309t9+265t10-123t11+30t12-3t13)/(1-t)9(241920+327456t+21312t2-54376t3-21504t4+9464t5+168t6-304t7+24t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Co?@KIpicture of the graph :Co?@KI
0041
0021
4201
1110
[7, 5, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10614141414(6t+8t2)/(1-t)14
200024130348(24t3+10t4-62t5+74t6-40t7+9t8)/(1-t)5(552-370t+21t2-2t3+15t4)/4!
30000014(14t5+118t6-229t7+203t8-100t9+27t10-3t11)/(1-t)7(21600-26604t+10710t2-570t3+60t4-186t5+30t6)/6!
4000000(t7+83t8-159t9+150t10-81t11+24t12-3t13)/(1-t)9(846720-924624t+399636t2-82516t3+2415t4-616t5+1134t6-244t7+15t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:C__KHVpicture of the graph :C__KHV
0221
2012
2101
1210
[5, 5, 4, 4]

Betti numbers βi(Bk(Γ)):

i\k0123456Poincaré seriesstable polynomial value
011111111/(1-t)1
1061010101010(6t+4t2)/(1-t)10
200133111195300(t2+30t3+15t4-40t5+15t6)/(1-t)3(-30-21t+21t2)/2!
30000048411(48t5+123t6-273t7+192t8-64t9+11t10-t11)/(1-t)6(-8040+2684t+3570t2-1160t3-90t4+36t5)/5!
40000000(324t8-648t9+576t10-288t11+85t12-14t13+t14)/(1-t)9(-1693440+1250592t+598352t2-425544t3+8204t4+22008t5-1792t6-336t7+36t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:C__H`Vpicture of the graph :C__H`V
0221
2021
2201
1110
[5, 5, 5, 3]

Betti numbers βi(Bk(Γ)):

i\k0123456Poincaré seriesstable polynomial value
011111111/(1-t)1
1061010101010(6t+4t2)/(1-t)10
200032122221347(32t3+26t4-49t5+18t6)/(1-t)3(-8-45t+27t2)/2!
30000023353(23t5+192t6-474t7+461t8-229t9+63t10-10t11+t12)/(1-t)7(-3600-24864t+29358t2-6735t3+135t4-81t5+27t6)/6!
40000000(216t8-432t9+396t10-208t11+66t12-12t13+t14)/(1-t)9(362880-554832t+925044t2-418236t3+42483t4+5712t5+126t6-324t7+27t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:C__K@Vpicture of the graph :C__K@V
0222
2011
2101
2110
[6, 4, 4, 4]

Betti numbers βi(Bk(Γ)):

i\k0123456Poincaré seriesstable polynomial value
011111111/(1-t)1
1061010101010(6t+4t2)/(1-t)10
200030111201315(30t3+21t4-42t5+15t6)/(1-t)3(-18-36t+24t2)/2!
30000030336(30t5+156t6-264t7+177t8-61t9+11t10-t11)/(1-t)6(-840-2788t+3240t2-200t3-300t4+48t5)/5!
40000000(270t8-540t9+495t10-262t11+82t12-14t13+t14)/(1-t)9(483840-282144t+429488t2-106400t3-65072t4+25984t5-1568t6-320t7+32t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:C_CKIVpicture of the graph :C_CKIV
0311
3011
1102
1120
[5, 5, 4, 4]

Betti numbers βi(Bk(Γ)):

i\k0123456Poincaré seriesstable polynomial value
011111111/(1-t)1
1061111111111(6t+5t2)/(1-t)11
200234112209349(2t2+26t3-12t4-43t5+51t6-15t7)/(1-t)4(-156+87t-6t2+9t3)/3!
30000061459(61t5+93t6-252t7+188t8-64t9+11t10-t11)/(1-t)6(-9480+5684t+2190t2-980t3-90t4+36t5)/5!
40000000(324t8-648t9+576t10-288t11+85t12-14t13+t14)/(1-t)9(-1693440+1250592t+598352t2-425544t3+8204t4+22008t5-1792t6-336t7+36t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:C_C@`Vpicture of the graph :C_C@`V
0321
3011
2101
1110
[6, 5, 4, 3]

Betti numbers βi(Bk(Γ)):

i\k0123456Poincaré seriesstable polynomial value
011111111/(1-t)1
1061111111111(6t+5t2)/(1-t)11
200030124251439(30t3+4t4-65t5+59t6-16t7)/(1-t)4(-84+3t+3t2+12t3)/3!
30000019309(19t5+176t6-414t7+395t8-201t9+58t10-10t11+t12)/(1-t)7(-30960+14592t+3096t2+1260t3-960t4-12t5+24t6)/6!
40000000(180t8-360t9+340t10-188t11+63t12-12t13+t14)/(1-t)9(-725760+730656t-19008t2-54376t3-21504t4+9464t5+168t6-304t7+24t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:C_?``Vpicture of the graph :C_?``V
0411
4011
1101
1110
[6, 6, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10613131313(6t+7t2)/(1-t)13
200028142365(28t3+2t4-65t5+96t6-57t7+12t8)/(1-t)5(-480+348t-100t2+16t4)/4!
30000011(11t5+152t6-301t7+270t8-127t9+30t10-3t11)/(1-t)7(-55440+40632t-9292t2+2040t3-100t4-192t5+32t6)/6!
4000000(t7+93t8-179t9+165t10-85t11+24t12-3t13)/(1-t)9(-1774080+1632096t-519136t2+62216t3-6216t4-616t5+1176t6-256t7+16t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:DkG?PCaJpicture of the graph :DkG?PCaJ
00012
00003
00003
10000
23300
[8, 3, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10519376191(5t+4t2-5t3+2t4)/(1-t)3(2+6t+6t2)/2!
20001068221(10t3+18t4-19t5+14t6-6t7+t8)/(1-t)5(-96+120t-18t2-48t3+18t4)/4!
3000005(5t5+36t6-45t7+35t8-18t9+6t10-t11)/(1-t)7(-7200+2700t-558t2-360t3+540t4-180t5+18t6)/6!
4000000(21t8-35t9+35t10-21t11+7t12-t13)/(1-t)9(-201600+45600t-7496t2-1232t3+6454t4-3920t5+1036t6-128t7+6t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dk?A?CPJpicture of the graph :Dk?A?CPJ
00032
00003
00001
30000
23100
[6, 5, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10517314971(5t+2t2-5t3+2t4)/(1-t)3(2+8t+4t2)/2!
200434134355(4t2+14t3+4t4-15t5+14t6-6t7+t8)/(1-t)5(4t-40t2-4t3+16t4)/4!
30000033(33t5+10t6-53t7+56t8-29t9+8t10-t11)/(1-t)7(-7920+1656t+1236t2-60t3+180t4-156t5+24t6)/6!
4000000(60t8-100t9+80t10-36t11+9t12-t13)/(1-t)9(-403200+208800t+77968t2-46760t3+1708t4-560t5+952t6-200t7+12t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:DkG?PCbNpicture of the graph :DkG?PCbN
00012
00003
00001
10002
23120
[8, 3, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10519365988(5t+4t2-6t3+3t4)/(1-t)3(6+4t+6t2)/2!
2000966217(9t3+21t4-23t5+18t6-9t7+2t8)/(1-t)5(48+72t-18t2-48t3+18t4)/4!
3000004(4t5+41t6-55t7+45t8-23t9+7t10-t11)/(1-t)7(-4320+1980t-558t2-360t3+540t4-180t5+18t6)/6!
4000000(21t8-35t9+35t10-21t11+7t12-t13)/(1-t)9(-201600+45600t-7496t2-1232t3+6454t4-3920t5+1036t6-128t7+6t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dk?_PCQNpicture of the graph :Dk?_PCQN
00021
00004
00001
20001
14110
[7, 4, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
105183251(5t+3t2-7t3+4t4)/(1-t)3(10+3t+5t2)/2!
200325111(3t2+7t3+6t4-17t5+22t6-20t7+12t8-3t9)/(1-t)6(1680-70t-375t2+60t3+15t4+10t5)/5!
300001(t4+43t5-18t6-31t7+46t8-27t9+6t10)/(1-t)7(28080-9816t-2320t2+2670t3-580t4-54t5+20t6)/6!
400000(t7+39t8-60t9+45t10-18t11+3t12)/(1-t)9(1209600-499680t-38328t2+75376t3-23030t4+1120t5+868t6-176t7+10t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dk?_@CQNpicture of the graph :Dk?_@CQN
00022
00003
00001
20001
23110
[7, 4, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10517315074(5t+2t2-5t3+3t4)/(1-t)3(8+3t+5t2)/2!
200224109305(2t2+14t3+9t4-20t5+16t6-8t7+2t8)/(1-t)5(240-34t-75t2-2t3+15t4)/4!
30000022(22t5+23t6-56t7+53t8-30t9+9t10-t11)/(1-t)7(15120-6456t-2680t2+2250t3-220t4-114t5+20t6)/6!
4000000(45t8-75t9+65t10-33t11+9t12-t13)/(1-t)9(604800-277920t-58488t2+75376t3-23030t4+1120t5+868t6-176t7+10t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dk?A@CQNpicture of the graph :Dk?A@CQN
00031
00003
00001
30001
13110
[6, 4, 4, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10516274261(5t+t2-6t3+4t4)/(1-t)3(12+2t+4t2)/2!
200432119291(4t2+12t3-t4-24t5+21t6-11t7+3t8)/(1-t)5(504-164t-148t2+68t3+4t4)/4!
30000039(39t5+8t6-83t7+88t8-47t9+12t10-t11)/(1-t)7(10800-864t-5336t2+4440t3-1160t4+24t5+16t6)/6!
4000000(90t8-150t9+115t10-49t11+11t12-t13)/(1-t)9(225120t-111344t2+88144t3-50176t4+9520t5+224t6-224t7+16t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dk?E@CPJpicture of the graph :Dk?E@CPJ
00021
00014
00001
21000
14100
[6, 5, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
105162024(5t+6t2-7t3)/(1-t)28+4t
200323110(3t2+5t3+17t4-31t5+38t6-32t7+15t8-3t9)/(1-t)6(840-362t+215t2-130t3+25t4+12t5)/5!
300001(t4+58t5-30t6-45t7+67t8-33t9+6t10)/(1-t)7(2880-4596t+5526t2-720t3-150t4-84t5+24t6)/6!
400000(t7+54t8-85t9+60t10-21t11+3t12)/(1-t)9(201600-12960t+98128t2-46760t3+1708t4-560t5+952t6-200t7+12t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dk?E?CPJpicture of the graph :Dk?E?CPJ
00022
00013
00001
21000
23100
[6, 4, 4, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10514182226(5t+4t2-5t3)/(1-t)26+4t
20022399256(2t2+13t3+4t4-29t5+28t6-12t7+2t8)/(1-t)5(24-36t-68t2+24t3+8t4)/4!
30000039(39t5+14t6-96t7+95t8-46t9+11t10-t11)/(1-t)7(-3600+816t-1496t2+3120t3-1040t4+24t5+16t6)/6!
4000000(90t8-150t9+115t10-49t11+11t12-t13)/(1-t)9(225120t-111344t2+88144t3-50176t4+9520t5+224t6-224t7+16t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dk?CW?PJpicture of the graph :Dk?CW?PJ
00022
00022
00001
22000
22100
[5, 4, 4, 4, 1]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10512151821(5t+2t2-4t3)/(1-t)26+3t
20022696218(2t2+18t3+4t4-18t5+6t6)/(1-t)4(48-108t+12t2+12t3)/3!
30000154(t4+48t5+30t6-76t7+42t8-10t9+t10)/(1-t)6(-2640-2476t+2960t2-320t3-200t4+36t5)/5!
4000000(162t8-270t9+189t10-69t11+13t12-t13)/(1-t)9(-967680-34464t+767120t2-227584t3-40264t4+20384t5-1120t6-256t7+24t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dk?E??PJpicture of the graph :Dk?E??PJ
00023
00012
00001
21000
32100
[6, 5, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10514182226(5t+4t2-5t3)/(1-t)26+4t
200121107295(t2+16t3+12t4-40t5+34t6-13t7+2t8)/(1-t)5(120-108t-60t2+12t3+12t4)/4!
30000018(18t5+57t6-109t7+88t8-38t9+9t10-t11)/(1-t)7(-7920-1704t+2076t2+420t3+60t4-156t5+24t6)/6!
4000000(60t8-100t9+80t10-36t11+9t12-t13)/(1-t)9(-403200+208800t+77968t2-46760t3+1708t4-560t5+952t6-200t7+12t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dk?CW?@Jpicture of the graph :Dk?CW?@J
00023
00021
00001
22000
31100
[5, 5, 4, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10513161922(5t+3t2-5t3)/(1-t)27+3t
200225102255(2t2+15t3-3t4-25t5+30t6-12t7+2t8)/(1-t)5(360-498t+135t2-6t3+9t4)/4!
30000048(48t5+3t6-102t7+108t8-49t9+11t10-t11)/(1-t)7(-2880-17772t+15402t2-2370t3-300t4-18t5+18t6)/6!
4000000(108t8-180t9+132t10-52t11+11t12-t13)/(1-t)9(-483840-82752t+491704t2-166320t3-8078t4+7392t5+196t6-240t7+18t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dk??WCPJpicture of the graph :Dk??WCPJ
00031
00013
00001
31000
13100
[5, 4, 4, 4, 1]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10514172023(5t+4t2-6t3)/(1-t)28+3t
20042897221(4t2+8t3-3t4-24t5+39t6-23t7+5t8)/(1-t)5(24-104t+42t2+8t3+6t4)/4!
30000055(55t5+37t6-106t7+64t8-15t9+t10)/(1-t)6(-3720-836t+2930t2-520t3-170t4+36t5)/5!
4000000(162t8-270t9+189t10-69t11+13t12-t13)/(1-t)9(-967680-34464t+767120t2-227584t3-40264t4+20384t5-1120t6-256t7+24t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dk??P_PJpicture of the graph :Dk??P_PJ
00031
00022
00001
32000
12100
[5, 4, 4, 4, 1]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10512141618(5t+2t2-5t3)/(1-t)28+2t
20022593206(2t2+17t3+5t4-24t5+12t6-2t7)/(1-t)4(66-121t+21t2+10t3)/3!
30000045(45t5+45t6-95t7+52t8-12t9+t10)/(1-t)6(-2520-2616t+3140t2-360t3-200t4+36t5)/5!
4000000(162t8-270t9+189t10-69t11+13t12-t13)/(1-t)9(-967680-34464t+767120t2-227584t3-40264t4+20384t5-1120t6-256t7+24t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dk??PE@Jpicture of the graph :Dk??PE@J
00031
00031
00001
33000
11100
[6, 4, 4, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10512131415(5t+2t2-6t3)/(1-t)210+t
20001891219(18t3+19t4-37t5+21t6-5t7)/(1-t)4(114-100t-12t2+16t3)/3!
30000013(13t5+95t6-194t7+155t8-66t9+14t10-t11)/(1-t)7(6480-7944t-896t2+4320t3-1280t4+24t5+16t6)/6!
4000000(90t8-150t9+115t10-49t11+11t12-t13)/(1-t)9(225120t-111344t2+88144t3-50176t4+9520t5+224t6-224t7+16t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dk??W?PJpicture of the graph :Dk??W?PJ
00032
00012
00001
31000
22100
[5, 5, 4, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10513161922(5t+3t2-5t3)/(1-t)27+3t
200225102240(2t2+17t3+14t4-26t5+13t6-2t7)/(1-t)4(-27t-27t2+18t3)/3!
30000033(33t5+42t6-138t7+123t8-52t9+11t10-t11)/(1-t)7(-13680-6072t+8112t2-30t3-570t4-18t5+18t6)/6!
4000000(108t8-180t9+132t10-52t11+11t12-t13)/(1-t)9(-483840-82752t+491704t2-166320t3-8078t4+7392t5+196t6-240t7+18t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dk??P_@Jpicture of the graph :Dk??P_@J
00032
00021
00001
32000
21100
[5, 5, 4, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10512141618(5t+2t2-5t3)/(1-t)28+2t
20012399233(t2+19t3+13t4-29t5+13t6-2t7)/(1-t)4(78-111t+15t3)/3!
30000030(30t5+51t6-147t7+126t8-52t9+11t10-t11)/(1-t)7(-5040-15432t+11352t2-390t3-570t4-18t5+18t6)/6!
4000000(108t8-180t9+132t10-52t11+11t12-t13)/(1-t)9(-483840-82752t+491704t2-166320t3-8078t4+7392t5+196t6-240t7+18t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dk??@_PJpicture of the graph :Dk??@_PJ
00041
00012
00001
41000
12100
[5, 5, 4, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
105141618(5t+4t2-7t3)/(1-t)210+2t
200325102(3t2+10t3+7t4-36t5+40t6-18t7+3t8)/(1-t)5(-24-146t+39t2+2t3+9t4)/4!
300001(t4+42t5+20t6-125t7+119t8-45t9+6t10)/(1-t)7(-34560+7308t+9282t2-1890t3-300t4-18t5+18t6)/6!
400000(3t7+92t8-145t9+92t10-27t11+3t12)/(1-t)9(-1491840+690048t+310264t2-152880t3-8078t4+7392t5+196t6-240t7+18t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dk??@E@Jpicture of the graph :Dk??@E@J
00041
00021
00001
42000
11100
[6, 5, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
105131415(5t+3t2-7t3)/(1-t)211+t
200017100(17t3+15t4-52t5+47t6-18t7+3t8)/(1-t)5(432-452t+60t2-4t3+12t4)/4!
300000(11t5+82t6-142t7+106t8-39t9+6t10)/(1-t)7(8640-13824t+6036t2-60t3+60t4-156t5+24t6)/6!
400000(t7+54t8-85t9+60t10-21t11+3t12)/(1-t)9(201600-12960t+98128t2-46760t3+1708t4-560t5+952t6-200t7+12t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dk?EAGbNpicture of the graph :Dk?EAGbN
00021
00010
00003
21002
10320
[6, 5, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10515222936(5t+5t2-3t3)/(1-t)21+7t
200225114310(2t2+15t3+9t4-30t5+25t6-11t7+2t8)/(1-t)5(108t-144t2+24t3+12t4)/4!
30000023(23t5+40t6-88t7+77t8-36t9+9t10-t11)/(1-t)7(-7920+2616t-444t2+780t3+60t4-156t5+24t6)/6!
4000000(60t8-100t9+80t10-36t11+9t12-t13)/(1-t)9(-403200+208800t+77968t2-46760t3+1708t4-560t5+952t6-200t7+12t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dk?EAGaNpicture of the graph :Dk?EAGaN
00021
00010
00004
21001
10410
[6, 4, 4, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
105152127(5t+5t2-4t3)/(1-t)23+6t
200326105(3t2+11t3+5t4-28t5+29t6-15t7+3t8)/(1-t)5(-72+136t-128t2+32t3+8t4)/4!
300001(t4+36t5+19t6-101t7+94t8-39t9+6t10)/(1-t)7(-22320+18336t-6536t2+3600t3-1040t4+24t5+16t6)/6!
400000(3t7+74t8-115t9+75t10-24t11+3t12)/(1-t)9(-1008000+997920t-292784t2+101584t3-50176t4+9520t5+224t6-224t7+16t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dk?CP_bNpicture of the graph :Dk?CP_bN
00021
00030
00001
23002
10120
[7, 4, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10515222936(5t+5t2-3t3)/(1-t)21+7t
20001588255(15t3+13t4-35t5+26t6-11t7+2t8)/(1-t)5(184t-202t2+32t3+10t4)/4!
30000010(10t5+57t6-91t7+69t8-33t9+9t10-t11)/(1-t)7(10080-3876t-4690t2+3270t3-370t4-114t5+20t6)/6!
4000000(45t8-75t9+65t10-33t11+9t12-t13)/(1-t)9(604800-277920t-58488t2+75376t3-23030t4+1120t5+868t6-176t7+10t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dk?CPEANpicture of the graph :Dk?CPEAN
00021
00040
00001
24001
10110
[7, 4, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
105152127(5t+5t2-4t3)/(1-t)23+6t
20001486(14t3+16t4-40t5+32t6-15t7+3t8)/(1-t)5(220t-214t2+32t3+10t4)/4!
300000(8t5+66t6-106t7+79t8-33t9+6t10)/(1-t)7(19440-6036t-4690t2+3270t3-370t4-114t5+20t6)/6!
400000(t7+39t8-60t9+45t10-18t11+3t12)/(1-t)9(1209600-499680t-38328t2+75376t3-23030t4+1120t5+868t6-176t7+10t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dk?CP_ANpicture of the graph :Dk?CP_AN
00022
00030
00001
23001
20110
[6, 4, 4, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10514202632(5t+4t2-3t3)/(1-t)22+6t
200225103254(2t2+17t3+15t4-16t5+8t6-2t7)/(1-t)4(54+9t-63t2+24t3)/3!
30000031(31t5+28t6-98t7+89t8-44t9+11t10-t11)/(1-t)7(5040+1536t-7016t2+5280t3-1280t4+24t5+16t6)/6!
4000000(90t8-150t9+115t10-49t11+11t12-t13)/(1-t)9(225120t-111344t2+88144t3-50176t4+9520t5+224t6-224t7+16t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dk??WGaNpicture of the graph :Dk??WGaN
00031
00010
00003
31001
10310
[5, 5, 4, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10515212733(5t+5t2-4t3)/(1-t)23+6t
200430110267(4t2+10t3-23t5+26t6-14t7+3t8)/(1-t)5(48+32t-102t2+40t3+6t4)/4!
30000049(49t5-2t6-97t7+110t8-53t9+12t10-t11)/(1-t)7(-9360-4032t+8292t2-990t3-390t4-18t5+18t6)/6!
4000000(108t8-180t9+132t10-52t11+11t12-t13)/(1-t)9(-483840-82752t+491704t2-166320t3-8078t4+7392t5+196t6-240t7+18t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dk??PEANpicture of the graph :Dk??PEAN
00031
00030
00001
33001
10110
[7, 4, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10515212733(5t+5t2-4t3)/(1-t)23+6t
20001486251(14t3+16t4-39t5+30t6-14t7+3t8)/(1-t)5(144+136t-202t2+32t3+10t4)/4!
3000009(9t5+62t6-101t7+79t8-38t9+10t10-t11)/(1-t)7(12960-4596t-4690t2+3270t3-370t4-114t5+20t6)/6!
4000000(45t8-75t9+65t10-33t11+9t12-t13)/(1-t)9(604800-277920t-58488t2+75376t3-23030t4+1120t5+868t6-176t7+10t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dk@_@CbNpicture of the graph :Dk@_@CbN
00012
00012
00001
11002
22120
[7, 4, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10515202530(5t+5t2-5t3)/(1-t)25+5t
20001384246(13t3+19t4-44t5+35t6-16t7+3t8)/(1-t)5(-96+280t-226t2+32t3+10t4)/4!
3000007(7t5+70t6-113t7+87t8-40t9+10t10-t11)/(1-t)7(4320+444t-5410t2+3270t3-370t4-114t5+20t6)/6!
4000000(45t8-75t9+65t10-33t11+9t12-t13)/(1-t)9(604800-277920t-58488t2+75376t3-23030t4+1120t5+868t6-176t7+10t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dk@_?CQNpicture of the graph :Dk@_?CQN
00013
00012
00001
11001
32110
[7, 4, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10515202530(5t+5t2-5t3)/(1-t)25+5t
20001384245(13t3+19t4-45t5+38t6-19t7+4t8)/(1-t)5(256t-226t2+32t3+10t4)/4!
3000006(6t5+75t6-123t7+97t8-45t9+11t10-t11)/(1-t)7(7200-276t-5410t2+3270t3-370t4-114t5+20t6)/6!
4000000(45t8-75t9+65t10-33t11+9t12-t13)/(1-t)9(604800-277920t-58488t2+75376t3-23030t4+1120t5+868t6-176t7+10t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dk?E@CbNpicture of the graph :Dk?E@CbN
00021
00012
00001
21002
12120
[6, 5, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10514182226(5t+4t2-5t3)/(1-t)26+4t
200121107294(t2+16t3+12t4-41t5+37t6-16t7+3t8)/(1-t)5(216-132t-60t2+12t3+12t4)/4!
30000017(17t5+62t6-119t7+98t8-43t9+10t10-t11)/(1-t)7(-5040-2424t+2076t2+420t3+60t4-156t5+24t6)/6!
4000000(60t8-100t9+80t10-36t11+9t12-t13)/(1-t)9(-403200+208800t+77968t2-46760t3+1708t4-560t5+952t6-200t7+12t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dk?E@CQNpicture of the graph :Dk?E@CQN
00021
00013
00001
21001
13110
[6, 4, 4, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10514182226(5t+4t2-5t3)/(1-t)26+4t
20022399254(2t2+13t3+4t4-31t5+34t6-18t7+4t8)/(1-t)5(216-84t-68t2+24t3+8t4)/4!
30000037(37t5+24t6-116t7+115t8-56t9+13t10-t11)/(1-t)7(2160-624t-1496t2+3120t3-1040t4+24t5+16t6)/6!
4000000(90t8-150t9+115t10-49t11+11t12-t13)/(1-t)9(225120t-111344t2+88144t3-50176t4+9520t5+224t6-224t7+16t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dk?CWCbNpicture of the graph :Dk?CWCbN
00021
00021
00001
22002
11120
[6, 5, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10513161922(5t+3t2-5t3)/(1-t)27+3t
200019104286(19t3+9t4-44t5+41t6-16t7+3t8)/(1-t)5(624-572t+84t2-4t3+12t4)/4!
30000013(13t5+74t6-131t7+102t8-43t9+10t10-t11)/(1-t)7(6480-14904t+6396t2-60t3+60t4-156t5+24t6)/6!
4000000(60t8-100t9+80t10-36t11+9t12-t13)/(1-t)9(-403200+208800t+77968t2-46760t3+1708t4-560t5+952t6-200t7+12t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dk?E?CQNpicture of the graph :Dk?E?CQN
00022
00012
00001
21001
22110
[6, 4, 4, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10513172125(5t+3t2-4t3)/(1-t)25+4t
20012298238(t2+18t3+16t4-26t5+14t6-3t7)/(1-t)4(48-29t-39t2+20t3)/3!
30000022(22t5+61t6-144t7+119t8-53t9+12t10-t11)/(1-t)7(2160-1584t-4136t2+4800t3-1280t4+24t5+16t6)/6!
4000000(90t8-150t9+115t10-49t11+11t12-t13)/(1-t)9(225120t-111344t2+88144t3-50176t4+9520t5+224t6-224t7+16t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dk?CW?QNpicture of the graph :Dk?CW?QN
00022
00021
00001
22001
21110
[5, 5, 4, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10512151821(5t+2t2-4t3)/(1-t)26+3t
200124101236(t2+20t3+11t4-28t5+14t6-3t7)/(1-t)4(126-132t+3t2+15t3)/3!
30000030(30t5+52t6-151t7+132t8-56t9+12t10-t11)/(1-t)7(2160-18672t+11712t2-390t3-570t4-18t5+18t6)/6!
4000000(108t8-180t9+132t10-52t11+11t12-t13)/(1-t)9(-483840-82752t+491704t2-166320t3-8078t4+7392t5+196t6-240t7+18t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dk??WCQNpicture of the graph :Dk??WCQN
00031
00012
00001
31001
12110
[5, 5, 4, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10513161922(5t+3t2-5t3)/(1-t)27+3t
200225102238(2t2+17t3+14t4-28t5+17t6-4t7)/(1-t)4(48-39t-27t2+18t3)/3!
30000031(31t5+52t6-158t7+143t8-62t9+13t10-t11)/(1-t)7(-7920-7512t+8112t2-30t3-570t4-18t5+18t6)/6!
4000000(108t8-180t9+132t10-52t11+11t12-t13)/(1-t)9(-483840-82752t+491704t2-166320t3-8078t4+7392t5+196t6-240t7+18t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dk??P_QNpicture of the graph :Dk??P_QN
00031
00021
00001
32001
11110
[6, 4, 4, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10512141618(5t+2t2-5t3)/(1-t)28+2t
20001993225(19t3+17t4-33t5+17t6-4t7)/(1-t)4(150-130t-6t2+16t3)/3!
30000016(16t5+82t6-172t7+137t8-59t9+13t10-t11)/(1-t)7(12240-12264t-176t2+4320t3-1280t4+24t5+16t6)/6!
4000000(90t8-150t9+115t10-49t11+11t12-t13)/(1-t)9(225120t-111344t2+88144t3-50176t4+9520t5+224t6-224t7+16t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dg?AW?PFpicture of the graph :Dg?AW?PF
00302
00013
30000
01000
23000
[5, 5, 4, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10515233139(5t+5t2-2t3)/(1-t)2-1+8t
200432114275(4t2+12t3-6t4-15t5+18t6-8t7+t8)/(1-t)5(-240+128t-102t2+40t3+6t4)/4!
30000051(51t5-12t6-77t7+90t8-43t9+10t10-t11)/(1-t)7(-15120-2592t+8292t2-990t3-390t4-18t5+18t6)/6!
4000000(108t8-180t9+132t10-52t11+11t12-t13)/(1-t)9(-483840-82752t+491704t2-166320t3-8078t4+7392t5+196t6-240t7+18t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dg?AW?@Fpicture of the graph :Dg?AW?@F
00303
00012
30000
01000
32000
[6, 5, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10515233139(5t+5t2-2t3)/(1-t)2-1+8t
200226116314(2t2+16t3+6t4-26t5+21t6-8t7+t8)/(1-t)5(-144+156t-144t2+24t3+12t4)/4!
30000024(24t5+35t6-78t7+67t8-31t9+8t10-t11)/(1-t)7(-10800+3336t-444t2+780t3+60t4-156t5+24t6)/6!
4000000(60t8-100t9+80t10-36t11+9t12-t13)/(1-t)9(-403200+208800t+77968t2-46760t3+1708t4-560t5+952t6-200t7+12t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dg??H_@Fpicture of the graph :Dg??H_@F
00402
00012
40000
01000
22000
[6, 4, 4, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
105152229(5t+5t2-3t3)/(1-t)21+7t
200327107(3t2+12t3+2t4-22t5+19t6-6t7)/(1-t)5(-408+232t-128t2+32t3+8t4)/4!
300001(t4+39t5+4t6-71t7+64t8-24t9+3t10)/(1-t)7(-30960+20496t-6536t2+3600t3-1040t4+24t5+16t6)/6!
400000(3t7+74t8-115t9+75t10-24t11+3t12)/(1-t)9(-1008000+997920t-292784t2+101584t3-50176t4+9520t5+224t6-224t7+16t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:DgH_@CQJpicture of the graph :DgH_@CQJ
00102
00013
10002
01000
23200
[7, 4, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10515222936(5t+5t2-3t3)/(1-t)21+7t
20001588253(15t3+13t4-37t5+30t6-13t7+2t8)/(1-t)5(-288+352t-226t2+32t3+10t4)/4!
3000008(8t5+65t6-103t7+77t8-35t9+9t10-t11)/(1-t)7(1440+1164t-5410t2+3270t3-370t4-114t5+20t6)/6!
4000000(45t8-75t9+65t10-33t11+9t12-t13)/(1-t)9(604800-277920t-58488t2+75376t3-23030t4+1120t5+868t6-176t7+10t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:DgH_?CQJpicture of the graph :DgH_?CQJ
00103
00012
10002
01000
32200
[7, 4, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10515212733(5t+5t2-4t3)/(1-t)23+6t
20001486251(14t3+16t4-39t5+28t6-10t7+t8)/(1-t)5(-336+352t-226t2+32t3+10t4)/4!
3000009(9t5+60t6-93t7+67t8-30t9+8t10-t11)/(1-t)7(-1440+1884t-5410t2+3270t3-370t4-114t5+20t6)/6!
4000000(45t8-75t9+65t10-33t11+9t12-t13)/(1-t)9(604800-277920t-58488t2+75376t3-23030t4+1120t5+868t6-176t7+10t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dg?e@CPJpicture of the graph :Dg?e@CPJ
00201
00014
20001
01000
14100
[6, 5, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
105162330(5t+6t2-4t3)/(1-t)22+7t
200326116(3t2+8t3+5t4-13t5+26t6-29t7+15t8-3t9)/(1-t)6(120-2t+215t2-130t3+25t4+12t5)/5!
300001(t4+58t5-30t6-45t7+67t8-33t9+6t10)/(1-t)7(2880-4596t+5526t2-720t3-150t4-84t5+24t6)/6!
400000(t7+54t8-85t9+60t10-21t11+3t12)/(1-t)9(201600-12960t+98128t2-46760t3+1708t4-560t5+952t6-200t7+12t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dg?e?CQJpicture of the graph :Dg?e?CQJ
00202
00012
20002
01000
22200
[6, 4, 4, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10513182328(5t+3t2-3t3)/(1-t)23+5t
200123100243(t2+19t3+14t4-23t5+10t6-t7)/(1-t)4(-12-11t-39t2+20t3)/3!
30000024(24t5+51t6-124t7+99t8-43t9+10t10-t11)/(1-t)7(-3600-144t-4136t2+4800t3-1280t4+24t5+16t6)/6!
4000000(90t8-150t9+115t10-49t11+11t12-t13)/(1-t)9(225120t-111344t2+88144t3-50176t4+9520t5+224t6-224t7+16t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dg?e?CPJpicture of the graph :Dg?e?CPJ
00202
00013
20001
01000
23100
[6, 4, 4, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10514202632(5t+4t2-3t3)/(1-t)22+6t
200225103262(2t2+15t3-2t4-23t5+26t6-12t7+2t8)/(1-t)5(-72+12t-68t2+24t3+8t4)/4!
30000039(39t5+14t6-96t7+95t8-46t9+11t10-t11)/(1-t)7(-3600+816t-1496t2+3120t3-1040t4+24t5+16t6)/6!
4000000(90t8-150t9+115t10-49t11+11t12-t13)/(1-t)9(225120t-111344t2+88144t3-50176t4+9520t5+224t6-224t7+16t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dg?e??PJpicture of the graph :Dg?e??PJ
00203
00012
20001
01000
32100
[6, 5, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10514192429(5t+4t2-4t3)/(1-t)24+5t
200122109299(t2+17t3+9t4-36t5+30t6-10t7+t8)/(1-t)5(-24-60t-60t2+12t3+12t4)/4!
30000019(19t5+52t6-99t7+78t8-33t9+8t10-t11)/(1-t)7(-10800-984t+2076t2+420t3+60t4-156t5+24t6)/6!
4000000(60t8-100t9+80t10-36t11+9t12-t13)/(1-t)9(-403200+208800t+77968t2-46760t3+1708t4-560t5+952t6-200t7+12t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dg?AWCPJpicture of the graph :Dg?AWCPJ
00301
00013
30001
01000
13100
[5, 4, 4, 4, 1]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10514192429(5t+4t2-4t3)/(1-t)24+5t
200430101229(4t2+10t3-9t4-16t5+31t6-17t7+3t8)/(1-t)5(-264-8t+42t2+8t3+6t4)/4!
30000057(57t5+29t6-94t7+56t8-13t9+t10)/(1-t)6(-4680-596t+2930t2-520t3-170t4+36t5)/5!
4000000(162t8-270t9+189t10-69t11+13t12-t13)/(1-t)9(-967680-34464t+767120t2-227584t3-40264t4+20384t5-1120t6-256t7+24t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dg?AW?PJpicture of the graph :Dg?AW?PJ
00302
00012
30001
01000
22100
[5, 5, 4, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10513172125(5t+3t2-4t3)/(1-t)25+4t
200226104244(2t2+18t3+12t4-24t5+11t6-t7)/(1-t)4(-36-15t-27t2+18t3)/3!
30000034(34t5+37t6-128t7+113t8-47t9+10t10-t11)/(1-t)7(-16560-5352t+8112t2-30t3-570t4-18t5+18t6)/6!
4000000(108t8-180t9+132t10-52t11+11t12-t13)/(1-t)9(-483840-82752t+491704t2-166320t3-8078t4+7392t5+196t6-240t7+18t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dg??H_PJpicture of the graph :Dg??H_PJ
00401
00012
40001
01000
12100
[5, 5, 4, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
105141720(5t+4t2-6t3)/(1-t)28+3t
200326104(3t2+11t3+4t4-30t5+30t6-9t7)/(1-t)5(-360-50t+39t2+2t3+9t4)/4!
300001(t4+45t5+5t6-95t7+89t8-30t9+3t10)/(1-t)7(-43200+9468t+9282t2-1890t3-300t4-18t5+18t6)/6!
400000(3t7+92t8-145t9+92t10-27t11+3t12)/(1-t)9(-1491840+690048t+310264t2-152880t3-8078t4+7392t5+196t6-240t7+18t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:DgG?gCaJpicture of the graph :DgG?gCaJ
00121
00001
10013
20100
11300
[5, 5, 4, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10513161922(5t+3t2-5t3)/(1-t)27+3t
200225102250(2t2+15t3-3t4-30t5+42t6-21t7+4t8)/(1-t)5(120-294t+99t2-6t3+9t4)/4!
30000043(43t5+25t6-140t7+140t8-62t9+13t10-t11)/(1-t)7(-10080-11652t+14322t2-2370t3-300t4-18t5+18t6)/6!
4000000(108t8-180t9+132t10-52t11+11t12-t13)/(1-t)9(-483840-82752t+491704t2-166320t3-8078t4+7392t5+196t6-240t7+18t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:DgG?g?QJpicture of the graph :DgG?g?QJ
00122
00001
10012
20100
21200
[5, 5, 4, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10512151821(5t+2t2-4t3)/(1-t)26+3t
200124101233(t2+20t3+11t4-31t5+17t6-3t7)/(1-t)4(18-69t-6t2+15t3)/3!
30000027(27t5+64t6-169t7+144t8-59t9+12t10-t11)/(1-t)7(-10800-11112t+10632t2-390t3-570t4-18t5+18t6)/6!
4000000(108t8-180t9+132t10-52t11+11t12-t13)/(1-t)9(-483840-82752t+491704t2-166320t3-8078t4+7392t5+196t6-240t7+18t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:DgG?a_@Jpicture of the graph :DgG?a_@J
00122
00001
10021
20200
21100
[5, 4, 4, 4, 1]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10511131517(5t+t2-4t3)/(1-t)27+2t
20012492196(t2+20t3+2t4-32t5+18t6-3t7)/(1-t)4(36-147t+45t2+6t3)/3!
30000036(36t5+69t6-117t7+60t8-13t9+t10)/(1-t)6(-3000-3136t+3620t2-440t3-200t4+36t5)/5!
4000000(162t8-270t9+189t10-69t11+13t12-t13)/(1-t)9(-967680-34464t+767120t2-227584t3-40264t4+20384t5-1120t6-256t7+24t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:DgG?g?@Jpicture of the graph :DgG?g?@J
00123
00001
10011
20100
31100
[6, 5, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10513161922(5t+3t2-5t3)/(1-t)27+3t
200019104282(19t3+9t4-48t5+50t6-22t7+4t8)/(1-t)5(288-344t+48t2-4t3+12t4)/4!
3000009(9t5+91t6-159t7+124t8-51t9+11t10-t11)/(1-t)7(-3600-8064t+5316t2-60t3+60t4-156t5+24t6)/6!
4000000(60t8-100t9+80t10-36t11+9t12-t13)/(1-t)9(-403200+208800t+77968t2-46760t3+1708t4-560t5+952t6-200t7+12t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:DgG?A_QJpicture of the graph :DgG?A_QJ
00131
00001
10012
30100
11200
[5, 4, 4, 4, 1]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10512141618(5t+2t2-5t3)/(1-t)28+2t
20022593200(2t2+17t3+5t4-30t5+20t6-4t7)/(1-t)4(-30-49t+9t2+10t3)/3!
30000039(39t5+65t6-119t7+64t8-14t9+t10)/(1-t)6(-4440-1176t+2900t2-360t3-200t4+36t5)/5!
4000000(162t8-270t9+189t10-69t11+13t12-t13)/(1-t)9(-967680-34464t+767120t2-227584t3-40264t4+20384t5-1120t6-256t7+24t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:DgG?AI@Jpicture of the graph :DgG?AI@J
00131
00001
10021
30200
11100
[5, 5, 4, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10511121314(5t+t2-5t3)/(1-t)29+t
20002196213(21t3+12t4-45t5+26t6-5t7)/(1-t)4(48-144t+33t2+9t3)/3!
30000014(14t5+112t6-237t7+190t8-74t9+14t10-t11)/(1-t)7(-9360-18672t+15312t2-1110t3-570t4-18t5+18t6)/6!
4000000(108t8-180t9+132t10-52t11+11t12-t13)/(1-t)9(-483840-82752t+491704t2-166320t3-8078t4+7392t5+196t6-240t7+18t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:DgG?A_@Jpicture of the graph :DgG?A_@J
00132
00001
10011
30100
21100
[6, 4, 4, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10512141618(5t+2t2-5t3)/(1-t)28+2t
20001993221(19t3+17t4-37t5+21t6-4t7)/(1-t)4(6-46t-18t2+16t3)/3!
30000012(12t5+98t6-196t7+153t8-63t9+13t10-t11)/(1-t)7(-5040-2184t-1616t2+4320t3-1280t4+24t5+16t6)/6!
4000000(90t8-150t9+115t10-49t11+11t12-t13)/(1-t)9(225120t-111344t2+88144t3-50176t4+9520t5+224t6-224t7+16t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:DgG??I@Jpicture of the graph :DgG??I@J
00141
00001
10011
40100
11100
[6, 5, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
105131415(5t+3t2-7t3)/(1-t)211+t
200017100(17t3+15t4-55t5+53t6-21t7+3t8)/(1-t)5(-200t+24t2-4t3+12t4)/4!
300000(8t5+94t6-160t7+118t8-42t9+6t10)/(1-t)7(-4320-6264t+4956t2-60t3+60t4-156t5+24t6)/6!
400000(t7+54t8-85t9+60t10-21t11+3t12)/(1-t)9(201600-12960t+98128t2-46760t3+1708t4-560t5+952t6-200t7+12t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dg?_A_QJpicture of the graph :Dg?_A_QJ
00221
00001
20012
20100
11200
[5, 5, 4, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10512141618(5t+2t2-5t3)/(1-t)28+2t
20012399230(t2+19t3+13t4-32t5+17t6-3t7)/(1-t)4(30-75t-6t2+15t3)/3!
30000027(27t5+64t6-169t7+144t8-59t9+12t10-t11)/(1-t)7(-10800-11112t+10632t2-390t3-570t4-18t5+18t6)/6!
4000000(108t8-180t9+132t10-52t11+11t12-t13)/(1-t)9(-483840-82752t+491704t2-166320t3-8078t4+7392t5+196t6-240t7+18t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dg?_AI@Jpicture of the graph :Dg?_AI@J
00221
00001
20021
20200
11100
[5, 5, 4, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10511121314(5t+t2-5t3)/(1-t)29+t
20002196214(21t3+12t4-44t5+25t6-5t7)/(1-t)4(84-165t+36t2+9t3)/3!
30000015(15t5+108t6-231t7+186t8-73t9+14t10-t11)/(1-t)7(-5040-21192t+15672t2-1110t3-570t4-18t5+18t6)/6!
4000000(108t8-180t9+132t10-52t11+11t12-t13)/(1-t)9(-483840-82752t+491704t2-166320t3-8078t4+7392t5+196t6-240t7+18t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dg?_A_@Jpicture of the graph :Dg?_A_@J
00222
00001
20011
20100
21100
[6, 4, 4, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10512141618(5t+2t2-5t3)/(1-t)28+2t
20001993224(19t3+17t4-34t5+17t6-3t7)/(1-t)4(54-82t-12t2+16t3)/3!
30000015(15t5+85t6-174t7+135t8-56t9+12t10-t11)/(1-t)7(720-6504t-896t2+4320t3-1280t4+24t5+16t6)/6!
4000000(90t8-150t9+115t10-49t11+11t12-t13)/(1-t)9(225120t-111344t2+88144t3-50176t4+9520t5+224t6-224t7+16t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dg?_?I@Jpicture of the graph :Dg?_?I@J
00231
00001
20011
30100
11100
[6, 4, 4, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10512131415(5t+2t2-6t3)/(1-t)210+t
20001891217(18t3+19t4-39t5+23t6-5t7)/(1-t)4(42-58t-18t2+16t3)/3!
30000011(11t5+103t6-206t7+163t8-68t9+14t10-t11)/(1-t)7(-2160-2904t-1616t2+4320t3-1280t4+24t5+16t6)/6!
4000000(90t8-150t9+115t10-49t11+11t12-t13)/(1-t)9(225120t-111344t2+88144t3-50176t4+9520t5+224t6-224t7+16t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dg?A?I@Jpicture of the graph :Dg?A?I@J
00321
00001
30011
20100
11100
[6, 5, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10513141516(5t+3t2-7t3)/(1-t)211+t
200017100277(17t3+15t4-53t5+49t6-19t7+3t8)/(1-t)5(288-368t+48t2-4t3+12t4)/4!
30000010(10t5+86t6-149t7+114t8-46t9+10t10-t11)/(1-t)7(-6480-7344t+5316t2-60t3+60t4-156t5+24t6)/6!
4000000(60t8-100t9+80t10-36t11+9t12-t13)/(1-t)9(-403200+208800t+77968t2-46760t3+1708t4-560t5+952t6-200t7+12t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:DgGI?CaNpicture of the graph :DgGI?CaN
00112
00001
10012
10101
21210
[6, 4, 4, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10512162024(5t+2t2-3t3)/(1-t)24+4t
20002197222(21t3+13t4-40t5+29t6-7t7)/(1-t)4(-18-10t-24t2+16t3)/3!
3000007(7t5+121t6-238t7+191t8-80t9+16t10-t11)/(1-t)7(-5040+696t-2336t2+4320t3-1280t4+24t5+16t6)/6!
4000000(90t8-150t9+115t10-49t11+11t12-t13)/(1-t)9(225120t-111344t2+88144t3-50176t4+9520t5+224t6-224t7+16t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:DgGI??QNpicture of the graph :DgGI??QN
00113
00001
10011
10101
31110
[6, 5, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10513172125(5t+3t2-4t3)/(1-t)25+4t
200020106280(20t3+6t4-50t5+61t6-31t7+6t8)/(1-t)5(-116t+12t2-4t3+12t4)/4!
3000004(4t5+113t6-197t7+156t8-64t9+13t10-t11)/(1-t)7(-10800-1944t+4236t2-60t3+60t4-156t5+24t6)/6!
4000000(60t8-100t9+80t10-36t11+9t12-t13)/(1-t)9(-403200+208800t+77968t2-46760t3+1708t4-560t5+952t6-200t7+12t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dg?_gCbNpicture of the graph :Dg?_gCbN
00211
00001
20011
10102
11120
[5, 4, 4, 4, 1]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10511141720(5t+t2-3t3)/(1-t)25+3t
20012594191(t2+21t3-39t5+30t6-7t7)/(1-t)4(-24-81t+33t2+6t3)/3!
30000028(28t5+97t6-153t7+80t8-17t9+t10)/(1-t)6(-3960-1936t+3380t2-440t3-200t4+36t5)/5!
4000000(162t8-270t9+189t10-69t11+13t12-t13)/(1-t)9(-967680-34464t+767120t2-227584t3-40264t4+20384t5-1120t6-256t7+24t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dg?_g?QNpicture of the graph :Dg?_g?QN
00212
00001
20011
10101
21110
[5, 5, 4, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10511141720(5t+t2-3t3)/(1-t)25+3t
200023100215(23t3+8t4-47t5+32t6-7t7)/(1-t)4(-102t+27t2+9t3)/3!
30000010(10t5+130t6-269t7+218t8-86t9+16t10-t11)/(1-t)7(-12240-15072t+14592t2-1110t3-570t4-18t5+18t6)/6!
4000000(108t8-180t9+132t10-52t11+11t12-t13)/(1-t)9(-483840-82752t+491704t2-166320t3-8078t4+7392t5+196t6-240t7+18t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dg?_A_QNpicture of the graph :Dg?_A_QN
00221
00001
20011
20101
11110
[5, 4, 4, 4, 1]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10510121416(5t-3t3)/(1-t)26+2t
20002391178(23t3+22t4-26t5+7t6)/(1-t)3(6-60t+26t2)/2!
30000019(19t5+118t6-168t7+83t8-17t9+t10)/(1-t)6(-3240-3796t+4280t2-560t3-200t4+36t5)/5!
4000000(162t8-270t9+189t10-69t11+13t12-t13)/(1-t)9(-967680-34464t+767120t2-227584t3-40264t4+20384t5-1120t6-256t7+24t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dg?AA_QNpicture of the graph :Dg?AA_QN
00311
00001
30011
10101
11110
[5, 5, 4, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10511131517(5t+t2-4t3)/(1-t)27+2t
20002298212(22t3+10t4-48t5+31t6-6t7)/(1-t)4(-48-81t+24t2+9t3)/3!
30000010(10t5+129t6-265t7+212t8-82t9+15t10-t11)/(1-t)7(-19440-11832t+14232t2-1110t3-570t4-18t5+18t6)/6!
4000000(108t8-180t9+132t10-52t11+11t12-t13)/(1-t)9(-483840-82752t+491704t2-166320t3-8078t4+7392t5+196t6-240t7+18t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Eo?_PCbRpicture of the graph :Eo?_PCbR
000021
000003
000001
000001
200001
131110
[7, 3, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104184489(4t+2t2-4t3+5t4-2t5)/(1-t)4(18+t+12t2+5t3)/3!
20022091(2t2+8t3+t4-13t5+12t6-8t7+4t8-t9)/(1-t)6(960-290t-45t2-75t3+45t4+5t5)/5!
300000(17t5+2t6-13t7+16t8-9t9+2t10)/(1-t)7(10800-4812t+420t2-105t3+285t4-123t5+15t6)/6!
400000(15t8-20t9+15t10-6t11+t12)/(1-t)9(403200-176880t+13708t2-1092t3+5565t4-3360t5+882t6-108t7+5t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Eo?E?GaNpicture of the graph :Eo?E?GaN
000022
000010
000003
000001
210000
203100
[6, 4, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104152947(4t+3t2-4t3+t4)/(1-t)3(-2+8t+4t2)/2!
20022088(2t2+10t3+8t4-13t5+7t6-2t7)/(1-t)5(-192+224t-120t2+4t3+12t4)/4!
300000(17t5+15t6-31t7+22t8-8t9+t10)/(1-t)7(-12240+12876t-7046t2+2340t3-170t4-96t5+16t6)/6!
400000(30t8-40t9+25t10-8t11+t12)/(1-t)9(-403200+487680t-223728t2+76104t3-18928t4+840t5+728t6-144t7+8t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Eo?CP_ANpicture of the graph :Eo?CP_AN
000022
000030
000001
000001
230000
201100
[5, 4, 4, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104132335(4t+t2-4t3+t4)/(1-t)3(-2+10t+2t2)/2!
20022288(2t2+12t3-2t4-15t5+9t6-2t7)/(1-t)5(80t-160t2+52t3+4t4)/4!
300000(27t5+7t6-47t7+34t8-10t9+t10)/(1-t)7(-3600-4932t+1458t2+2040t3-750t4+12t5+12t6)/6!
400000(54t8-72t9+39t10-10t11+t12)/(1-t)9(-241920-232896t+274976t2-16184t3-33292t4+7336t5+224t6-176t7+12t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Eo?E@CQNpicture of the graph :Eo?E@CQN
000021
000013
000001
000001
210000
131100
[6, 4, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104152641(4t+3t2-7t3+4t4)/(1-t)3(10+2t+4t2)/2!
20021782(2t2+5t3+10t4-24t5+26t6-16t7+6t8-t9)/(1-t)6(372t-310t2+40t3+10t4+8t5)/5!
300000(32t5-6t6-29t7+30t8-13t9+2t10)/(1-t)7(-10800+10548t-5306t2+2460t3-470t4-48t5+16t6)/6!
400000(30t8-40t9+25t10-8t11+t12)/(1-t)9(-403200+487680t-223728t2+76104t3-18928t4+840t5+728t6-144t7+8t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Eo?E?CQNpicture of the graph :Eo?E?CQN
000022
000012
000001
000001
210000
221100
[6, 4, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104142540(4t+2t2-5t3+3t4)/(1-t)3(8+2t+4t2)/2!
20011681(t2+11t3+11t4-21t5+13t6-3t7)/(1-t)5(-24+28t-60t2-4t3+12t4)/4!
300000(14t5+25t6-43t7+28t8-9t9+t10)/(1-t)7(-10800+9156t-5246t2+2100t3-170t4-96t5+16t6)/6!
400000(30t8-40t9+25t10-8t11+t12)/(1-t)9(-403200+487680t-223728t2+76104t3-18928t4+840t5+728t6-144t7+8t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Eo?CW?QNpicture of the graph :Eo?CW?QN
000022
000021
000001
000001
220000
211100
[5, 4, 4, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104122031(4t-4t3+3t4)/(1-t)3(10+t+3t2)/2!
20011984(t2+14t3-t4-19t5+14t6-3t7)/(1-t)5(144-148t-54t2+28t3+6t4)/4!
300000(27t5+10t6-54t7+39t8-11t9+t10)/(1-t)7(-3600-8532t+4278t2+1320t3-690t4+12t5+12t6)/6!
400000(54t8-72t9+39t10-10t11+t12)/(1-t)9(-241920-232896t+274976t2-16184t3-33292t4+7336t5+224t6-176t7+12t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Eo??WCQNpicture of the graph :Eo??WCQN
000031
000012
000001
000001
310000
121100
[5, 4, 4, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104132132(4t+t2-6t3+4t4)/(1-t)3(12+t+3t2)/2!
20022085(2t2+10t3+5t4-29t5+21t6-7t7+t8)/(1-t)5(144-42t-135t2+54t3+3t4)/4!
300000(21t5+28t6-76t7+54t8-17t9+2t10)/(1-t)7(-4320-5352t+1848t2+2100t3-780t4+12t5+12t6)/6!
400000(54t8-72t9+39t10-10t11+t12)/(1-t)9(-241920-232896t+274976t2-16184t3-33292t4+7336t5+224t6-176t7+12t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Eo??P_QNpicture of the graph :Eo??P_QN
000031
000021
000001
000001
320000
111100
[5, 4, 4, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104111623(4t-t2-5t3+4t4)/(1-t)3(14+2t2)/2!
20001576(15t3+16t4-18t5+6t6-t7)/(1-t)4(96-54t-36t2+18t3)/3!
300000(15t5+43t6-88t7+57t8-17t9+2t10)/(1-t)7(2160-10212t+1938t2+2640t3-870t4+12t5+12t6)/6!
400000(54t8-72t9+39t10-10t11+t12)/(1-t)9(-241920-232896t+274976t2-16184t3-33292t4+7336t5+224t6-176t7+12t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Eo@_AGbRpicture of the graph :Eo@_AGbR
000012
000010
000003
000001
110001
203110
[7, 3, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104163151(4t+4t2-5t3+2t4)/(1-t)3(2+5t+5t2)/2!
2000753(7t3+18t4-18t5+12t6-5t7+t8)/(1-t)5(48+30t-3t2-42t3+15t4)/4!
300000(3t5+32t6-38t7+27t8-11t9+2t10)/(1-t)7(7920-3852t+240t2-315t3+465t4-153t5+15t6)/6!
400000(15t8-20t9+15t10-6t11+t12)/(1-t)9(403200-176880t+13708t2-1092t3+5565t4-3360t5+882t6-108t7+5t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Eo@CW?bRpicture of the graph :Eo@CW?bR
000012
000030
000001
000001
130001
201110
[5, 5, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104142539(4t+2t2-5t3+2t4)/(1-t)3(2+7t+3t2)/2!
20022193(2t2+11t3+8t4-19t5+14t6-5t7+t8)/(1-t)5(264-164t-12t2-4t3+12t4)/4!
300000(18t5+24t6-51t7+38t8-13t9+2t10)/(1-t)7(13680-18804t+8382t2-1230t3+240t4-126t5+18t6)/6!
400000(36t8-48t9+28t10-8t11+t12)/(1-t)9(362880-656976t+436700t2-108444t3+6041t4-504t5+770t6-156t7+9t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Eo?EAGbRpicture of the graph :Eo?EAGbR
000021
000010
000003
000001
210001
103110
[6, 4, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104152845(4t+3t2-5t3+2t4)/(1-t)3(2+6t+4t2)/2!
20021986(2t2+9t3+11t4-17t5+11t6-5t7+t8)/(1-t)5(-48+176t-120t2+4t3+12t4)/4!
300000(16t5+20t6-41t7+32t8-13t9+2t10)/(1-t)7(-9360+12156t-7046t2+2340t3-170t4-96t5+16t6)/6!
400000(30t8-40t9+25t10-8t11+t12)/(1-t)9(-403200+487680t-223728t2+76104t3-18928t4+840t5+728t6-144t7+8t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Eo?CP_bRpicture of the graph :Eo?CP_bR
000021
000030
000001
000001
230001
101110
[6, 4, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104132233(4t+t2-5t3+2t4)/(1-t)3(2+8t+2t2)/2!
20001374(13t3+9t4-24t5+14t6-5t7+t8)/(1-t)5(144+88t-176t2+32t3+8t4)/4!
300000(9t5+37t6-54t7+35t8-13t9+2t10)/(1-t)7(-3600+8796t-8006t2+3180t3-290t4-96t5+16t6)/6!
400000(30t8-40t9+25t10-8t11+t12)/(1-t)9(-403200+487680t-223728t2+76104t3-18928t4+840t5+728t6-144t7+8t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Eo@_@CbRpicture of the graph :Eo@_@CbR
000012
000012
000001
000001
110001
221110
[7, 3, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104163049(4t+4t2-6t3+3t4)/(1-t)3(6+3t+5t2)/2!
2000651(6t3+21t4-22t5+15t6-6t7+t8)/(1-t)5(-48+90t-15t2-42t3+15t4)/4!
300000(2t5+36t6-44t7+31t8-12t9+2t10)/(1-t)7(3600-1332t-120t2-315t3+465t4-153t5+15t6)/6!
400000(15t8-20t9+15t10-6t11+t12)/(1-t)9(403200-176880t+13708t2-1092t3+5565t4-3360t5+882t6-108t7+5t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Eo?E@CbRpicture of the graph :Eo?E@CbR
000021
000012
000001
000001
210001
121110
[6, 4, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104142540(4t+2t2-5t3+3t4)/(1-t)3(8+2t+4t2)/2!
20011681(t2+11t3+11t4-22t5+16t6-6t7+t8)/(1-t)5(72+4t-60t2-4t3+12t4)/4!
300000(13t5+30t6-53t7+38t8-14t9+2t10)/(1-t)7(-7920+8436t-5246t2+2100t3-170t4-96t5+16t6)/6!
400000(30t8-40t9+25t10-8t11+t12)/(1-t)9(-403200+487680t-223728t2+76104t3-18928t4+840t5+728t6-144t7+8t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Eo?CWCbRpicture of the graph :Eo?CWCbR
000021
000021
000001
000001
220001
111110
[5, 5, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104122031(4t-4t3+3t4)/(1-t)3(10+t+3t2)/2!
20001685(16t3+5t4-26t5+19t6-6t7+t8)/(1-t)5(336-210t-57t2+18t3+9t4)/4!
300000(12t5+40t6-66t7+44t8-14t9+2t10)/(1-t)7(12960-18024t+7032t2-570t3+150t4-126t5+18t6)/6!
400000(36t8-48t9+28t10-8t11+t12)/(1-t)9(362880-656976t+436700t2-108444t3+6041t4-504t5+770t6-156t7+9t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Eo?CQ_@Npicture of the graph :Eo?CQ_@N
000022
000021
000010
000001
221000
210100
[5, 4, 4, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104121722(4t+4t2-3t3)/(1-t)22+5t
20011675(t2+12t3+17t4-14t5+3t6)/(1-t)4(54-13t-48t2+19t3)/3!
300000(18t5+31t6-69t7+42t8-11t9+t10)/(1-t)7(720-8892t+1218t2+2760t3-870t4+12t5+12t6)/6!
400000(54t8-72t9+39t10-10t11+t12)/(1-t)9(-241920-232896t+274976t2-16184t3-33292t4+7336t5+224t6-176t7+12t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Eo??Q_PNpicture of the graph :Eo??Q_PN
000031
000012
000010
000001
311000
120100
[5, 4, 4, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104131823(4t+5t2-4t3)/(1-t)23+5t
20021776(2t2+7t3+11t4-29t5+21t6-7t7+t8)/(1-t)5(144-84t-66t2+24t3+6t4)/4!
300000(24t5+22t6-73t7+54t8-17t9+2t10)/(1-t)7(-2160-9852t+4998t2+1200t3-690t4+12t5+12t6)/6!
400000(54t8-72t9+39t10-10t11+t12)/(1-t)9(-241920-232896t+274976t2-16184t3-33292t4+7336t5+224t6-176t7+12t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Eo??PI@Npicture of the graph :Eo??PI@N
000031
000021
000010
000001
321000
110100
[6, 4, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104131823(4t+5t2-4t3)/(1-t)23+5t
2000964(9t3+19t4-36t5+22t6-7t7+t8)/(1-t)5(96+72t-152t2+24t3+8t4)/4!
300000(5t5+51t6-72t7+45t8-15t9+2t10)/(1-t)7(-6480+7596t-6566t2+2940t3-290t4-96t5+16t6)/6!
400000(30t8-40t9+25t10-8t11+t12)/(1-t)9(-403200+487680t-223728t2+76104t3-18928t4+840t5+728t6-144t7+8t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Eo?CgCRRpicture of the graph :Eo?CgCRR
000021
000012
000010
000001
211001
120110
[5, 5, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104131925(4t+5t2-3t3)/(1-t)21+6t
20011579(t2+10t3+14t4-30t5+19t6-6t7+t8)/(1-t)5(240-78t-93t2+18t3+9t4)/4!
300000(12t5+40t6-66t7+44t8-14t9+2t10)/(1-t)7(12960-18024t+7032t2-570t3+150t4-126t5+18t6)/6!
400000(36t8-48t9+28t10-8t11+t12)/(1-t)9(362880-656976t+436700t2-108444t3+6041t4-504t5+770t6-156t7+9t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Eo?CQ_RRpicture of the graph :Eo?CQ_RR
000021
000021
000010
000001
221001
110110
[6, 4, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104131925(4t+5t2-3t3)/(1-t)21+6t
20001066(10t3+16t4-32t5+19t6-6t7+t8)/(1-t)5(192+12t-140t2+24t3+8t4)/4!
300000(6t5+47t6-66t7+41t8-14t9+2t10)/(1-t)7(-2160+5076t-6206t2+2940t3-290t4-96t5+16t6)/6!
400000(30t8-40t9+25t10-8t11+t12)/(1-t)9(-403200+487680t-223728t2+76104t3-18928t4+840t5+728t6-144t7+8t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:EkH_@CaJpicture of the graph :EkH_@CaJ
000102
000012
000003
100000
010000
223000
[7, 3, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104163253(4t+4t2-4t3+t4)/(1-t)3(-2+7t+5t2)/2!
2000855(8t3+15t4-14t5+8t6-2t7)/(1-t)5(-96+78t-3t2-42t3+15t4)/4!
300000(4t5+27t6-28t7+17t8-6t9+t10)/(1-t)7(5040-3132t+240t2-315t3+465t4-153t5+15t6)/6!
400000(15t8-20t9+15t10-6t11+t12)/(1-t)9(403200-176880t+13708t2-1092t3+5565t4-3360t5+882t6-108t7+5t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Ek?AW?PJpicture of the graph :Ek?AW?PJ
000302
000012
000001
300000
010000
221000
[5, 5, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104142641(4t+2t2-4t3+t4)/(1-t)3(-2+9t+3t2)/2!
20022295(2t2+12t3+5t4-15t5+10t6-2t7)/(1-t)5(120-116t-12t2-4t3+12t4)/4!
300000(19t5+19t6-41t7+28t8-8t9+t10)/(1-t)7(10800-18084t+8382t2-1230t3+240t4-126t5+18t6)/6!
400000(36t8-48t9+28t10-8t11+t12)/(1-t)9(362880-656976t+436700t2-108444t3+6041t4-504t5+770t6-156t7+9t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:EkH_@CbNpicture of the graph :EkH_@CbN
000102
000012
000001
100002
010000
221200
[7, 3, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104163151(4t+4t2-5t3+2t4)/(1-t)3(2+5t+5t2)/2!
2000753(7t3+18t4-18t5+11t6-3t7)/(1-t)5(-192+138t-15t2-42t3+15t4)/4!
300000(3t5+31t6-34t7+21t8-7t9+t10)/(1-t)7(720-612t-120t2-315t3+465t4-153t5+15t6)/6!
400000(15t8-20t9+15t10-6t11+t12)/(1-t)9(403200-176880t+13708t2-1092t3+5565t4-3360t5+882t6-108t7+5t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Ek?e@CQNpicture of the graph :Ek?e@CQN
000201
000013
000001
200001
010000
131100
[6, 4, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104152845(4t+3t2-5t3+2t4)/(1-t)3(2+6t+4t2)/2!
20021986(2t2+7t3+2t4-12t5+18t6-14t7+6t8-t9)/(1-t)6(-480+612t-310t2+40t3+10t4+8t5)/5!
300000(32t5-6t6-29t7+30t8-13t9+2t10)/(1-t)7(-10800+10548t-5306t2+2460t3-470t4-48t5+16t6)/6!
400000(30t8-40t9+25t10-8t11+t12)/(1-t)9(-403200+487680t-223728t2+76104t3-18928t4+840t5+728t6-144t7+8t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Ek?e?CQNpicture of the graph :Ek?e?CQN
000202
000012
000001
200001
010000
221100
[6, 4, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104142642(4t+2t2-4t3+2t4)/(1-t)3(4+4t+4t2)/2!
20011783(t2+12t3+8t4-18t5+12t6-3t7)/(1-t)5(-72+52t-60t2-4t3+12t4)/4!
300000(14t5+25t6-43t7+28t8-9t9+t10)/(1-t)7(-10800+9156t-5246t2+2100t3-170t4-96t5+16t6)/6!
400000(30t8-40t9+25t10-8t11+t12)/(1-t)9(-403200+487680t-223728t2+76104t3-18928t4+840t5+728t6-144t7+8t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Ek?AWCQNpicture of the graph :Ek?AWCQN
000301
000012
000001
300001
010000
121100
[5, 4, 4, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104132234(4t+t2-5t3+3t4)/(1-t)3(8+3t+3t2)/2!
20022187(2t2+11t3+2t4-25t5+17t6-4t7)/(1-t)5(6t-135t2+54t3+3t4)/4!
300000(22t5+23t6-66t7+44t8-12t9+t10)/(1-t)7(-7200-4632t+1848t2+2100t3-780t4+12t5+12t6)/6!
400000(54t8-72t9+39t10-10t11+t12)/(1-t)9(-241920-232896t+274976t2-16184t3-33292t4+7336t5+224t6-176t7+12t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:EkGCPE@Jpicture of the graph :EkGCPE@J
000111
000041
000001
100000
140000
111000
[5, 5, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1041214(4t+4t2-6t3)/(1-t)28+2t
200010(10t3+20t4-45t5+30t6-6t7)/(1-t)5(360-418t+51t2-2t3+9t4)/4!
30000(5t5+62t6-88t7+48t8-9t9)/(1-t)7(-2880-16464t+9552t2-1050t3+150t4-126t5+18t6)/6!
40000(t7+31t8-38t9+18t10-3t11)/(1-t)9(-443520-159696t+335900t2-101724t3+6041t4-504t5+770t6-156t7+9t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:EkGCP_@Jpicture of the graph :EkGCP_@J
000112
000031
000001
100000
130000
211000
[4, 4, 4, 4, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104121620(4t+4t2-4t3)/(1-t)24+4t
20021873(2t2+8t3+3t4-29t5+28t6-9t7+t8)/(1-t)5(264-428t+104t2+8t3+4t4)/4!
300000(27t5+45t6-57t7+19t8-2t9)/(1-t)6(1200-6092t+3400t2-120t3-220t4+32t5)/5!
400000(81t8-108t9+54t10-12t11+t12)/(1-t)9(120960-1193952t+849392t2-93408t3-62496t4+17472t5-672t6-192t7+16t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:EkGCW?@Jpicture of the graph :EkGCW?@J
000113
000021
000001
100000
120000
311000
[5, 5, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104142026(4t+6t2-4t3)/(1-t)22+6t
20021680(2t2+4t3+14t4-28t5+31t6-19t7+6t8-t9)/(1-t)6(1560-1514t+525t2-115t3+15t4+9t5)/5!
300000(38t5-9t6-36t7+36t8-13t9+2t10)/(1-t)7(14400-24768t+12972t2-1800t3-30t4-72t5+18t6)/6!
400000(36t8-48t9+28t10-8t11+t12)/(1-t)9(362880-656976t+436700t2-108444t3+6041t4-504t5+770t6-156t7+9t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:EkG?P_PJpicture of the graph :EkG?P_PJ
000121
000022
000001
100000
220000
121000
[4, 4, 4, 4, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104111519(4t+3t2-3t3)/(1-t)23+4t
20011772(t2+13t3+10t4-15t5+3t6)/(1-t)4(120-114t+12t3)/3!
300000(27t5+36t6-42t7+12t8-t9)/(1-t)6(2400-6232t+2880t2+80t3-240t4+32t5)/5!
400000(81t8-108t9+54t10-12t11+t12)/(1-t)9(120960-1193952t+849392t2-93408t3-62496t4+17472t5-672t6-192t7+16t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:EkG?PE@Jpicture of the graph :EkG?PE@J
000121
000031
000001
100000
230000
111000
[5, 4, 4, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104111417(4t+3t2-4t3)/(1-t)25+3t
20001370(13t3+18t4-24t5+8t6-t7)/(1-t)4(108-98t-12t2+14t3)/3!
300000(9t5+63t6-112t7+69t8-19t9+2t10)/(1-t)7(5040-17652t+5538t2+2160t3-870t4+12t5+12t6)/6!
400000(54t8-72t9+39t10-10t11+t12)/(1-t)9(-241920-232896t+274976t2-16184t3-33292t4+7336t5+224t6-176t7+12t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:EkG?W?PJpicture of the graph :EkG?W?PJ
000122
000012
000001
100000
210000
221000
[5, 5, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104131925(4t+5t2-3t3)/(1-t)21+6t
20011579(t2+10t3+14t4-29t5+16t6-3t7)/(1-t)5(144-54t-93t2+18t3+9t4)/4!
300000(13t5+35t6-56t7+34t8-9t9+t10)/(1-t)7(10080-17304t+7032t2-570t3+150t4-126t5+18t6)/6!
400000(36t8-48t9+28t10-8t11+t12)/(1-t)9(362880-656976t+436700t2-108444t3+6041t4-504t5+770t6-156t7+9t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:EkG?P_@Jpicture of the graph :EkG?P_@J
000122
000021
000001
100000
220000
211000
[5, 4, 4, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104121722(4t+4t2-3t3)/(1-t)22+5t
20011675(t2+11t3+5t4-25t5+17t6-3t7)/(1-t)5(360-352t+18t2+16t3+6t4)/4!
300000(24t5+19t6-63t7+42t8-11t9+t10)/(1-t)7(5040-17892t+7518t2+960t3-690t4+12t5+12t6)/6!
400000(54t8-72t9+39t10-10t11+t12)/(1-t)9(-241920-232896t+274976t2-16184t3-33292t4+7336t5+224t6-176t7+12t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:EkG?@_PJpicture of the graph :EkG?@_PJ
000131
000012
000001
100000
310000
121000
[5, 4, 4, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104131823(4t+5t2-4t3)/(1-t)23+5t
20021776(2t2+7t3+11t4-29t5+21t6-7t7+t8)/(1-t)5(144-84t-66t2+24t3+6t4)/4!
300000(24t5+22t6-73t7+54t8-17t9+2t10)/(1-t)7(-2160-9852t+4998t2+1200t3-690t4+12t5+12t6)/6!
400000(54t8-72t9+39t10-10t11+t12)/(1-t)9(-241920-232896t+274976t2-16184t3-33292t4+7336t5+224t6-176t7+12t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:EkG?@E@Jpicture of the graph :EkG?@E@J
000131
000021
000001
100000
320000
111000
[5, 5, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104121620(4t+4t2-4t3)/(1-t)24+4t
20001274(12t3+14t4-36t5+25t6-7t7+t8)/(1-t)5(456-354t+3t2+6t3+9t4)/4!
300000(8t5+53t6-81t7+51t8-15t9+2t10)/(1-t)7(17280-24864t+9912t2-930t3+150t4-126t5+18t6)/6!
400000(36t8-48t9+28t10-8t11+t12)/(1-t)9(362880-656976t+436700t2-108444t3+6041t4-504t5+770t6-156t7+9t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Ek?A@_cRpicture of the graph :Ek?A@_cR
000311
000010
000001
300000
110002
101020
[5, 4, 4, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104132027(4t+5t2-2t3)/(1-t)2-1+7t
20021980(2t2+9t3+5t4-23t5+17t6-7t7+t8)/(1-t)5(-192+272t-208t2+52t3+4t4)/4!
300000(24t5+20t6-69t7+52t8-17t9+2t10)/(1-t)7(-9360-612t+738t2+2040t3-750t4+12t5+12t6)/6!
400000(54t8-72t9+39t10-10t11+t12)/(1-t)9(-241920-232896t+274976t2-16184t3-33292t4+7336t5+224t6-176t7+12t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Ek?A?EARpicture of the graph :Ek?A?EAR
000321
000010
000001
300000
210001
101010
[6, 4, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104132027(4t+5t2-2t3)/(1-t)2-1+7t
20001168(11t3+13t4-28t5+18t6-7t7+t8)/(1-t)5(-192+328t-224t2+32t3+8t4)/4!
300000(7t5+45t6-66t7+43t8-15t9+2t10)/(1-t)7(-12240+13836t-8726t2+3180t3-290t4-96t5+16t6)/6!
400000(30t8-40t9+25t10-8t11+t12)/(1-t)9(-403200+487680t-223728t2+76104t3-18928t4+840t5+728t6-144t7+8t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Ek??GEARpicture of the graph :Ek??GEAR
000411
000010
000001
400000
110001
101010
[6, 4, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1041319(4t+5t2-3t3)/(1-t)21+6t
200010(10t3+16t4-33t5+21t6-6t7)/(1-t)5(-432+392t-212t2+28t3+8t4)/4!
30000(5t5+51t6-70t7+39t8-9t9)/(1-t)7(-35280+25356t-10166t2+3180t3-290t4-96t5+16t6)/6!
40000(t7+25t8-30t9+15t10-3t11)/(1-t)9(-1209600+984960t-324528t2+82824t3-18928t4+840t5+728t6-144t7+8t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:EkGE@CcRpicture of the graph :EkGE@CcR
000111
000012
000001
100000
110002
121020
[6, 4, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104131823(4t+5t2-4t3)/(1-t)23+5t
2000964(9t3+19t4-37t5+24t6-8t7+t8)/(1-t)5(-48+156t-164t2+24t3+8t4)/4!
300000(4t5+55t6-78t7+49t8-16t9+2t10)/(1-t)7(-10800+10116t-6926t2+2940t3-290t4-96t5+16t6)/6!
400000(30t8-40t9+25t10-8t11+t12)/(1-t)9(-403200+487680t-223728t2+76104t3-18928t4+840t5+728t6-144t7+8t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:EkGE@CQRpicture of the graph :EkGE@CQR
000111
000013
000001
100000
110001
131010
[6, 4, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104131823(4t+5t2-4t3)/(1-t)23+5t
2000964(9t3+19t4-38t5+26t6-9t7+t8)/(1-t)5(-192+240t-176t2+24t3+8t4)/4!
300000(3t5+59t6-84t7+53t8-17t9+2t10)/(1-t)7(-15120+12636t-7286t2+2940t3-290t4-96t5+16t6)/6!
400000(30t8-40t9+25t10-8t11+t12)/(1-t)9(-403200+487680t-223728t2+76104t3-18928t4+840t5+728t6-144t7+8t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:EkGCWCcRpicture of the graph :EkGCWCcR
000111
000021
000001
100000
120002
111020
[5, 5, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104121620(4t+4t2-4t3)/(1-t)24+4t
20001274(12t3+14t4-37t5+27t6-8t7+t8)/(1-t)5(312-270t-9t2+6t3+9t4)/4!
300000(7t5+57t6-87t7+55t8-16t9+2t10)/(1-t)7(12960-22344t+9552t2-930t3+150t4-126t5+18t6)/6!
400000(36t8-48t9+28t10-8t11+t12)/(1-t)9(362880-656976t+436700t2-108444t3+6041t4-504t5+770t6-156t7+9t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:EkGCWCQRpicture of the graph :EkGCWCQR
000111
000022
000001
100000
120001
121010
[5, 4, 4, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104111519(4t+3t2-3t3)/(1-t)23+4t
20001472(14t3+16t4-23t5+9t6-t7)/(1-t)4(36-45t-24t2+15t3)/3!
300000(9t5+64t6-115t7+72t8-20t9+2t10)/(1-t)7(-2160-12012t+4098t2+2280t3-870t4+12t5+12t6)/6!
400000(54t8-72t9+39t10-10t11+t12)/(1-t)9(-241920-232896t+274976t2-16184t3-33292t4+7336t5+224t6-176t7+12t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:EkGCP_QRpicture of the graph :EkGCP_QR
000111
000031
000001
100000
130001
111010
[5, 4, 4, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104111417(4t+3t2-4t3)/(1-t)25+3t
20001370(13t3+18t4-26t5+10t6-t7)/(1-t)4(36-56t-18t2+14t3)/3!
300000(7t5+71t6-124t7+77t8-21t9+2t10)/(1-t)7(-3600-12612t+4818t2+2160t3-870t4+12t5+12t6)/6!
400000(54t8-72t9+39t10-10t11+t12)/(1-t)9(-241920-232896t+274976t2-16184t3-33292t4+7336t5+224t6-176t7+12t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:EkGE?CQRpicture of the graph :EkGE?CQR
000112
000012
000001
100000
110001
221010
[6, 4, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104131925(4t+5t2-3t3)/(1-t)21+6t
20001066(10t3+16t4-34t5+23t6-8t7+t8)/(1-t)5(-96+180t-164t2+24t3+8t4)/4!
300000(4t5+55t6-78t7+49t8-16t9+2t10)/(1-t)7(-10800+10116t-6926t2+2940t3-290t4-96t5+16t6)/6!
400000(30t8-40t9+25t10-8t11+t12)/(1-t)9(-403200+487680t-223728t2+76104t3-18928t4+840t5+728t6-144t7+8t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:EkGCW?QRpicture of the graph :EkGCW?QR
000112
000021
000001
100000
120001
211010
[5, 4, 4, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104121722(4t+4t2-3t3)/(1-t)22+5t
20011675(t2+11t3+5t4-28t5+24t6-8t7+t8)/(1-t)5(168-208t-6t2+16t3+6t4)/4!
300000(21t5+32t6-85t7+60t8-18t9+2t10)/(1-t)7(-720-13572t+6798t2+960t3-690t4+12t5+12t6)/6!
400000(54t8-72t9+39t10-10t11+t12)/(1-t)9(-241920-232896t+274976t2-16184t3-33292t4+7336t5+224t6-176t7+12t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:EkG?WCQRpicture of the graph :EkG?WCQR
000121
000012
000001
100000
210001
121010
[5, 4, 4, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104121722(4t+4t2-3t3)/(1-t)22+5t
20011675(t2+12t3+17t4-17t5+7t6-t7)/(1-t)4(6+23t-54t2+19t3)/3!
300000(15t5+44t6-91t7+60t8-18t9+2t10)/(1-t)7(-5040-4572t+498t2+2760t3-870t4+12t5+12t6)/6!
400000(54t8-72t9+39t10-10t11+t12)/(1-t)9(-241920-232896t+274976t2-16184t3-33292t4+7336t5+224t6-176t7+12t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:EkG?P_QRpicture of the graph :EkG?P_QR
000121
000021
000001
100000
220001
111010
[5, 4, 4, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104111519(4t+3t2-3t3)/(1-t)23+4t
20001472(14t3+16t4-20t5+7t6-t7)/(1-t)4(84-61t-27t2+16t3)/3!
300000(12t5+53t6-100t7+63t8-18t9+2t10)/(1-t)7(3600-13932t+3738t2+2400t3-870t4+12t5+12t6)/6!
400000(54t8-72t9+39t10-10t11+t12)/(1-t)9(-241920-232896t+274976t2-16184t3-33292t4+7336t5+224t6-176t7+12t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:EkHCg?PFpicture of the graph :EkHCg?PF
000102
000023
000010
100000
021000
230000
[5, 5, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104132129(4t+5t2-t3)/(1-t)2-3+8t
20011783(t2+12t3+8t4-22t5+12t6-2t7)/(1-t)5(192-90t-81t2+18t3+9t4)/4!
300000(14t5+31t6-50t7+30t8-8t9+t10)/(1-t)7(14400-19824t+7392t2-570t3+150t4-126t5+18t6)/6!
400000(36t8-48t9+28t10-8t11+t12)/(1-t)9(362880-656976t+436700t2-108444t3+6041t4-504t5+770t6-156t7+9t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:EkHCg?@Fpicture of the graph :EkHCg?@F
000103
000022
000010
100000
021000
320000
[5, 4, 4, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104132129(4t+5t2-t3)/(1-t)2-3+8t
20022082(2t2+10t3+2t4-17t5+11t6-2t7)/(1-t)5(192-156t-42t2+24t3+6t4)/4!
300000(27t5+9t6-51t7+36t8-10t9+t10)/(1-t)7(3600-14172t+5718t2+1200t3-690t4+12t5+12t6)/6!
400000(54t8-72t9+39t10-10t11+t12)/(1-t)9(-241920-232896t+274976t2-16184t3-33292t4+7336t5+224t6-176t7+12t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:EkHI?CSRpicture of the graph :EkHI?CSR
000102
000012
000010
100000
011002
220020
[6, 4, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104132027(4t+5t2-2t3)/(1-t)2-1+7t
20001168(11t3+13t4-28t5+15t6-3t7)/(1-t)5(48+60t-140t2+24t3+8t4)/4!
300000(7t5+42t6-56t7+31t8-9t9+t10)/(1-t)7(-5040+5796t-6206t2+2940t3-290t4-96t5+16t6)/6!
400000(30t8-40t9+25t10-8t11+t12)/(1-t)9(-403200+487680t-223728t2+76104t3-18928t4+840t5+728t6-144t7+8t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:EkHI?CPRpicture of the graph :EkHI?CPR
000102
000013
000010
100000
011001
230010
[6, 4, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104131925(4t+5t2-3t3)/(1-t)21+6t
20001066(10t3+16t4-32t5+18t6-4t7)/(1-t)5(-48+120t-152t2+24t3+8t4)/4!
300000(6t5+46t6-62t7+35t8-10t9+t10)/(1-t)7(-9360+8316t-6566t2+2940t3-290t4-96t5+16t6)/6!
400000(30t8-40t9+25t10-8t11+t12)/(1-t)9(-403200+487680t-223728t2+76104t3-18928t4+840t5+728t6-144t7+8t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:EkHCg?SRpicture of the graph :EkHCg?SR
000102
000021
000010
100000
021002
210020
[5, 5, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104132027(4t+5t2-2t3)/(1-t)2-1+7t
20011681(t2+11t3+11t4-26t5+15t6-3t7)/(1-t)5(96-30t-93t2+18t3+9t4)/4!
300000(13t5+35t6-56t7+34t8-9t9+t10)/(1-t)7(10080-17304t+7032t2-570t3+150t4-126t5+18t6)/6!
400000(36t8-48t9+28t10-8t11+t12)/(1-t)9(362880-656976t+436700t2-108444t3+6041t4-504t5+770t6-156t7+9t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:EkHCg?PRpicture of the graph :EkHCg?PR
000102
000022
000010
100000
021001
220010
[5, 4, 4, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104121824(4t+4t2-2t3)/(1-t)26t
20011777(t2+13t3+15t4-13t5+3t6)/(1-t)4(42-7t-48t2+19t3)/3!
300000(18t5+31t6-69t7+42t8-11t9+t10)/(1-t)7(720-8892t+1218t2+2760t3-870t4+12t5+12t6)/6!
400000(54t8-72t9+39t10-10t11+t12)/(1-t)9(-241920-232896t+274976t2-16184t3-33292t4+7336t5+224t6-176t7+12t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:EkHCQ_@Rpicture of the graph :EkHCQ_@R
000102
000031
000010
100000
031001
210010
[5, 4, 4, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104131925(4t+5t2-3t3)/(1-t)21+6t
20021878(2t2+8t3+8t4-25t5+17t6-4t7)/(1-t)5(-36t-66t2+24t3+6t4)/4!
300000(25t5+17t6-63t7+44t8-12t9+t10)/(1-t)7(-5040-9132t+4998t2+1200t3-690t4+12t5+12t6)/6!
400000(54t8-72t9+39t10-10t11+t12)/(1-t)9(-241920-232896t+274976t2-16184t3-33292t4+7336t5+224t6-176t7+12t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:EkHI??PRpicture of the graph :EkHI??PR
000103
000012
000010
100000
011001
320010
[6, 4, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104132027(4t+5t2-2t3)/(1-t)2-1+7t
20001168(11t3+13t4-30t5+20t6-7t7+t8)/(1-t)5(120t-152t2+24t3+8t4)/4!
300000(5t5+51t6-72t7+45t8-15t9+2t10)/(1-t)7(-6480+7596t-6566t2+2940t3-290t4-96t5+16t6)/6!
400000(30t8-40t9+25t10-8t11+t12)/(1-t)9(-403200+487680t-223728t2+76104t3-18928t4+840t5+728t6-144t7+8t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:EkHCg?@Rpicture of the graph :EkHCg?@R
000103
000021
000010
100000
021001
310010
[5, 4, 4, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104132027(4t+5t2-2t3)/(1-t)2-1+7t
20021980(2t2+9t3+5t4-23t5+19t6-7t7+t8)/(1-t)5(48-36t-66t2+24t3+6t4)/4!
300000(24t5+22t6-73t7+54t8-17t9+2t10)/(1-t)7(-2160-9852t+4998t2+1200t3-690t4+12t5+12t6)/6!
400000(54t8-72t9+39t10-10t11+t12)/(1-t)9(-241920-232896t+274976t2-16184t3-33292t4+7336t5+224t6-176t7+12t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:EkHI?KsRpicture of the graph :EkHI?KsR
000102
000010
000010
100002
011002
200220
[6, 4, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104132233(4t+t2-5t3+2t4)/(1-t)3(2+8t+2t2)/2!
20001374(13t3+9t4-26t5+15t6-3t7)/(1-t)5(96-12t-116t2+24t3+8t4)/4!
300000(7t5+42t6-56t7+31t8-9t9+t10)/(1-t)7(-5040+5796t-6206t2+2940t3-290t4-96t5+16t6)/6!
400000(30t8-40t9+25t10-8t11+t12)/(1-t)9(-403200+487680t-223728t2+76104t3-18928t4+840t5+728t6-144t7+8t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Ek?cgLCRpicture of the graph :Ek?cgLCR
000201
000010
000010
200001
011003
100130
[5, 5, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104142539(4t+2t2-5t3+2t4)/(1-t)3(2+7t+3t2)/2!
20022193(2t2+9t3-3t4-7t5+20t6-17t7+6t8-t9)/(1-t)6(1440-1814t+705t2-115t3+15t4+9t5)/5!
300000(38t5-9t6-36t7+36t8-13t9+2t10)/(1-t)7(14400-24768t+12972t2-1800t3-30t4-72t5+18t6)/6!
400000(36t8-48t9+28t10-8t11+t12)/(1-t)9(362880-656976t+436700t2-108444t3+6041t4-504t5+770t6-156t7+9t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Ek?cg?sRpicture of the graph :Ek?cg?sR
000202
000010
000010
200001
011002
200120
[5, 4, 4, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104122030(4t-4t3+2t4)/(1-t)3(4+6t+2t2)/2!
20011983(t2+14t3-2t4-20t5+16t6-3t7)/(1-t)5(360-400t+42t2+16t3+6t4)/4!
300000(24t5+19t6-63t7+42t8-11t9+t10)/(1-t)7(5040-17892t+7518t2+960t3-690t4+12t5+12t6)/6!
400000(54t8-72t9+39t10-10t11+t12)/(1-t)9(-241920-232896t+274976t2-16184t3-33292t4+7336t5+224t6-176t7+12t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Ek?AQ_sRpicture of the graph :Ek?AQ_sR
000301
000010
000010
300001
011002
100120
[4, 4, 4, 4, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104121928(4t-5t3+3t4)/(1-t)3(8+4t+2t2)/2!
20022181(2t2+11t3-4t4-21t5+20t6-4t7)/(1-t)5(456-620t+152t2+8t3+4t4)/4!
300000(30t5+35t6-45t7+13t8-t9)/(1-t)6(2160-6812t+3520t2-120t3-220t4+32t5)/5!
400000(81t8-108t9+54t10-12t11+t12)/(1-t)9(120960-1193952t+849392t2-93408t3-62496t4+17472t5-672t6-192t7+16t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:EkG?wCbNpicture of the graph :EkG?wCbN
000121
000001
000001
100012
200100
111200
[5, 4, 4, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104122031(4t-4t3+3t4)/(1-t)3(10+t+3t2)/2!
20011984(t2+14t3-t4-25t5+24t6-8t7+t8)/(1-t)5(240-316t+30t2+16t3+6t4)/4!
300000(21t5+32t6-85t7+60t8-18t9+2t10)/(1-t)7(-720-13572t+6798t2+960t3-690t4+12t5+12t6)/6!
400000(54t8-72t9+39t10-10t11+t12)/(1-t)9(-241920-232896t+274976t2-16184t3-33292t4+7336t5+224t6-176t7+12t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:EkG?r_QNpicture of the graph :EkG?r_QN
000121
000001
000001
100021
200200
111100
[4, 4, 4, 4, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104101522(4t-2t2-3t3+3t4)/(1-t)3(12+2t2)/2!
20001775(17t3+7t4-24t5+9t6-t7)/(1-t)4(114-164t+30t2+8t3)/3!
300000(18t5+60t6-64t7+20t8-2t9)/(1-t)6(1920-6752t+3360t2-240t4+32t5)/5!
400000(81t8-108t9+54t10-12t11+t12)/(1-t)9(120960-1193952t+849392t2-93408t3-62496t4+17472t5-672t6-192t7+16t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:EkG?w?QNpicture of the graph :EkG?w?QN
000122
000001
000001
100011
200100
211100
[5, 5, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104122031(4t-4t3+3t4)/(1-t)3(10+t+3t2)/2!
20001685(16t3+5t4-31t5+26t6-8t7+t8)/(1-t)5(336-354t+27t2+6t3+9t4)/4!
300000(7t5+57t6-87t7+55t8-16t9+2t10)/(1-t)7(12960-22344t+9552t2-930t3+150t4-126t5+18t6)/6!
400000(36t8-48t9+28t10-8t11+t12)/(1-t)9(362880-656976t+436700t2-108444t3+6041t4-504t5+770t6-156t7+9t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:EkG?B_QNpicture of the graph :EkG?B_QN
000131
000001
000001
100011
300100
111100
[5, 4, 4, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104111623(4t-t2-5t3+4t4)/(1-t)3(14+2t2)/2!
20001576(15t3+16t4-24t5+8t6-t7)/(1-t)4(120-116t-6t2+14t3)/3!
300000(9t5+63t6-112t7+69t8-19t9+2t10)/(1-t)7(5040-17652t+5538t2+2160t3-870t4+12t5+12t6)/6!
400000(54t8-72t9+39t10-10t11+t12)/(1-t)9(-241920-232896t+274976t2-16184t3-33292t4+7336t5+224t6-176t7+12t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Ek?_B_QNpicture of the graph :Ek?_B_QN
000221
000001
000001
200011
200100
111100
[5, 4, 4, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104111623(4t-t2-5t3+4t4)/(1-t)3(14+2t2)/2!
20001576(15t3+16t4-21t5+7t6-t7)/(1-t)4(108-85t-21t2+16t3)/3!
300000(12t5+53t6-100t7+63t8-18t9+2t10)/(1-t)7(3600-13932t+3738t2+2400t3-870t4+12t5+12t6)/6!
400000(54t8-72t9+39t10-10t11+t12)/(1-t)9(-241920-232896t+274976t2-16184t3-33292t4+7336t5+224t6-176t7+12t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:EkGM?CbRpicture of the graph :EkGM?CbR
000112
000001
000001
100011
100101
211110
[6, 4, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104132439(4t+t2-3t3+2t4)/(1-t)3(6+2t+4t2)/2!
20001580(15t3+5t4-30t5+29t6-13t7+2t8)/(1-t)5(-240+204t-140t2+24t3+8t4)/4!
300000(t5+68t6-100t7+67t8-23t9+3t10)/(1-t)7(-16560+14436t-7646t2+2940t3-290t4-96t5+16t6)/6!
400000(30t8-40t9+25t10-8t11+t12)/(1-t)9(-403200+487680t-223728t2+76104t3-18928t4+840t5+728t6-144t7+8t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Ek?_wCbRpicture of the graph :Ek?_wCbR
000211
000001
000001
200011
100101
111110
[5, 4, 4, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104111930(4t-t2-2t3+2t4)/(1-t)3(8+t+3t2)/2!
20001883(18t3+11t4-25t5+13t6-2t7)/(1-t)4(-6-30t-21t2+15t3)/3!
300000(6t5+77t6-137t7+90t8-27t9+3t10)/(1-t)7(-7920-7692t+3378t2+2280t3-870t4+12t5+12t6)/6!
400000(54t8-72t9+39t10-10t11+t12)/(1-t)9(-241920-232896t+274976t2-16184t3-33292t4+7336t5+224t6-176t7+12t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:EkGCwGsRpicture of the graph :EkGCwGsR
000111
000010
000001
100011
110102
101120
[5, 5, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104121824(4t+4t2-2t3)/(1-t)26t
20001478(14t3+8t4-37t5+35t6-13t7+2t8)/(1-t)5(312-390t+75t2-6t3+9t4)/4!
300000(t5+79t6-118t7+76t8-23t9+3t10)/(1-t)7(15840-27384t+12072t2-1290t3+150t4-126t5+18t6)/6!
400000(36t8-48t9+28t10-8t11+t12)/(1-t)9(362880-656976t+436700t2-108444t3+6041t4-504t5+770t6-156t7+9t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:EkG?R_bRpicture of the graph :EkG?R_bR
000121
000010
000001
100011
210101
101110
[5, 4, 4, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104111621(4t+3t2-2t3)/(1-t)21+5t
20001574(15t3+14t4-28t5+13t6-2t7)/(1-t)4(48-81t-3t2+12t3)/3!
300000(3t5+86t6-146t7+93t8-27t9+3t10)/(1-t)7(720-17052t+6618t2+1920t3-870t4+12t5+12t6)/6!
400000(54t8-72t9+39t10-10t11+t12)/(1-t)9(-241920-232896t+274976t2-16184t3-33292t4+7336t5+224t6-176t7+12t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Ek?_R_bRpicture of the graph :Ek?_R_bR
000211
000010
000001
200011
110101
101110
[4, 4, 4, 4, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104101418(4t+2t2-2t3)/(1-t)22+4t
20001671(16t3+7t4-32t5+15t6-2t7)/(1-t)4(66-166t+48t2+4t3)/3!
300000(9t5+84t6-86t7+28t8-3t9)/(1-t)6(1440-7272t+3840t2-80t3-240t4+32t5)/5!
400000(81t8-108t9+54t10-12t11+t12)/(1-t)9(120960-1193952t+849392t2-93408t3-62496t4+17472t5-672t6-192t7+16t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Ek@_g?BRpicture of the graph :Ek@_g?BR
000113
000100
000010
110001
101001
300110
[5, 5, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104121416(4t+4t2-6t3)/(1-t)28+2t
20001070(10t3+20t4-46t5+31t6-6t7)/(1-t)5(456-522t+87t2-6t3+9t4)/4!
300000(4t5+65t6-92t7+52t8-12t9+t10)/(1-t)7(14400-28464t+12432t2-1290t3+150t4-126t5+18t6)/6!
400000(36t8-48t9+28t10-8t11+t12)/(1-t)9(362880-656976t+436700t2-108444t3+6041t4-504t5+770t6-156t7+9t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Ek?EA_sRpicture of the graph :Ek?EA_sR
000211
000100
000010
210001
101002
100120
[4, 4, 4, 4, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104111519(4t+3t2-3t3)/(1-t)23+4t
20011772(t2+13t3+10t4-24t5+9t6-t7)/(1-t)4(96-140t+24t2+8t3)/3!
300000(18t5+60t6-64t7+20t8-2t9)/(1-t)6(1920-6752t+3360t2-240t4+32t5)/5!
400000(81t8-108t9+54t10-12t11+t12)/(1-t)9(120960-1193952t+849392t2-93408t3-62496t4+17472t5-672t6-192t7+16t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Ek?EA_rRpicture of the graph :Ek?EA_rR
000211
000100
000010
210002
101001
100210
[5, 4, 4, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104111519(4t+3t2-3t3)/(1-t)23+4t
20001472(14t3+16t4-26t5+9t6-t7)/(1-t)4(108-123t+3t2+12t3)/3!
300000(6t5+73t6-124t7+75t8-20t9+2t10)/(1-t)7(6480-21372t+7338t2+1920t3-870t4+12t5+12t6)/6!
400000(54t8-72t9+39t10-10t11+t12)/(1-t)9(-241920-232896t+274976t2-16184t3-33292t4+7336t5+224t6-176t7+12t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Ek?EA_BRpicture of the graph :Ek?EA_BR
000212
000100
000010
210001
101001
200110
[5, 4, 4, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104111417(4t+3t2-4t3)/(1-t)25+3t
20001370(13t3+18t4-27t5+9t6-t7)/(1-t)4(120-129t+3t2+12t3)/3!
300000(6t5+73t6-124t7+75t8-20t9+2t10)/(1-t)7(6480-21372t+7338t2+1920t3-870t4+12t5+12t6)/6!
400000(54t8-72t9+39t10-10t11+t12)/(1-t)9(-241920-232896t+274976t2-16184t3-33292t4+7336t5+224t6-176t7+12t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Ek?E?IBRpicture of the graph :Ek?E?IBR
000221
000100
000010
210001
201001
100110
[5, 4, 4, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104111519(4t+3t2-3t3)/(1-t)23+4t
20001472(14t3+16t4-26t5+9t6-t7)/(1-t)4(108-123t+3t2+12t3)/3!
300000(6t5+73t6-124t7+75t8-20t9+2t10)/(1-t)7(6480-21372t+7338t2+1920t3-870t4+12t5+12t6)/6!
400000(54t8-72t9+39t10-10t11+t12)/(1-t)9(-241920-232896t+274976t2-16184t3-33292t4+7336t5+224t6-176t7+12t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Ek??WIBRpicture of the graph :Ek??WIBR
000311
000100
000010
310001
101001
100110
[5, 5, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104121620(4t+4t2-4t3)/(1-t)24+4t
20001274(12t3+14t4-41t5+32t6-9t7+t8)/(1-t)5(456-498t+87t2-6t3+9t4)/4!
300000(3t5+70t6-102t7+62t8-17t9+2t10)/(1-t)7(17280-29184t+12432t2-1290t3+150t4-126t5+18t6)/6!
400000(36t8-48t9+28t10-8t11+t12)/(1-t)9(362880-656976t+436700t2-108444t3+6041t4-504t5+770t6-156t7+9t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Fs?E@CbRpicture of the graph :Fs?E@CbR
0000021
0000012
0000001
0000001
0000001
2100000
1211100
[6, 3, 3, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031434(3t+2t2-4t3+5t4-2t5)/(1-t)4(18-t+9t2+4t3)/3!
200113(t2+7t3+3t4-16t5+14t6-6t7+t8)/(1-t)6(120-54t-35t2-70t3+35t4+4t5)/5!
30000(11t5+7t6-12t7+8t8-2t9)/(1-t)7(-8640+5472t-1332t2+30t3+240t4-102t5+12t6)/6!
40000(10t8-10t9+5t10-t11)/(1-t)9(-403200+319680t-86048t2+5768t3+4676t4-2800t5+728t6-88t7+4t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Fs?CWCbRpicture of the graph :Fs?CWCbR
0000021
0000021
0000001
0000001
0000001
2200000
1111100
[5, 4, 3, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031125(3t-t2-t3+4t4-2t5)/(1-t)4(24-3t+6t2+3t3)/3!
200014(14t3+3t4-11t5+7t6-t7)/(1-t)5(216-176t+12t2-16t3+12t4)/4!
30000(12t5+13t6-23t7+12t8-2t9)/(1-t)7(3600-7932t+2838t2+90t3+30t4-78t5+12t6)/6!
40000(18t8-18t9+7t10-t11)/(1-t)9(-171360t+91512t2+9632t3-11466t4+560t5+588t6-112t7+6t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Fs@I?CRRpicture of the graph :Fs@I?CRR
0000012
0000012
0000010
0000001
0000001
1110000
2201100
[6, 3, 3, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031325(3t+4t2-5t3+2t4)/(1-t)3(2+4t+4t2)/2!
20004(4t3+18t4-16t5+7t6-t7)/(1-t)5(96-36t+12t2-36t3+12t4)/4!
30000(2t5+23t6-21t7+10t8-2t9)/(1-t)7(-5040+3156t-1122t2-150t3+390t4-126t5+12t6)/6!
40000(10t8-10t9+5t10-t11)/(1-t)9(-403200+319680t-86048t2+5768t3+4676t4-2800t5+728t6-88t7+4t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Fs?CgCRRpicture of the graph :Fs?CgCRR
0000021
0000012
0000010
0000001
0000001
2110000
1201100
[5, 4, 3, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031222(3t+3t2-5t3+2t4)/(1-t)3(2+5t+3t2)/2!
200111(t2+6t3+13t4-17t5+7t6-t7)/(1-t)5(72+46t-81t2+2t3+9t4)/4!
30000(9t5+19t6-26t7+12t8-2t9)/(1-t)7(1440-3432t-312t2+990t3-60t4-78t5+12t6)/6!
40000(18t8-18t9+7t10-t11)/(1-t)9(-171360t+91512t2+9632t3-11466t4+560t5+588t6-112t7+6t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Fs?CQ_RRpicture of the graph :Fs?CQ_RR
0000021
0000021
0000010
0000001
0000001
2210000
1101100
[5, 4, 3, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031119(3t+2t2-5t3+2t4)/(1-t)3(2+6t+2t2)/2!
20008(8t3+12t4-20t5+7t6-t7)/(1-t)5(208t-198t2+32t3+6t4)/4!
30000(6t5+25t6-29t7+12t8-2t9)/(1-t)7(-720+1068t-3462t2+1890t3-150t4-78t5+12t6)/6!
40000(18t8-18t9+7t10-t11)/(1-t)9(-171360t+91512t2+9632t3-11466t4+560t5+588t6-112t7+6t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Fo?e@CbRpicture of the graph :Fo?e@CbR
0000201
0000012
0000001
0000001
2000001
0100000
1211100
[6, 3, 3, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031435(3t+2t2-3t3+3t4-t5)/(1-t)4(6+5t+9t2+4t3)/3!
200114(t2+8t3-t4-10t5+10t6-5t7+t8)/(1-t)6(-120+66t-35t2-70t3+35t4+4t5)/5!
30000(11t5+7t6-12t7+8t8-2t9)/(1-t)7(-8640+5472t-1332t2+30t3+240t4-102t5+12t6)/6!
40000(10t8-10t9+5t10-t11)/(1-t)9(-403200+319680t-86048t2+5768t3+4676t4-2800t5+728t6-88t7+4t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:FoG?PcQNpicture of the graph :FoG?PcQN
0000120
0000022
0000001
0000001
1000000
2200000
0211000
[4, 4, 4, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031121(3t+2t2-3t3)/(1-t)3(-6+10t+2t2)/2!
200114(t2+9t3+2t4-11t5+3t6)/(1-t)5(96+92t-160t2+40t3+4t4)/4!
30000(15t5+10t6-26t7+10t8-t9)/(1-t)7(11520-10704t-988t2+3120t3-820t4+24t5+8t6)/6!
40000(27t8-27t9+9t10-t11)/(1-t)9(362880-557856t+164016t2+67648t3-43288t4+6496t5+224t6-128t7+8t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:FoGCWCQNpicture of the graph :FoGCWCQN
0000111
0000022
0000001
0000001
1000000
1200000
1211000
[5, 4, 3, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031120(3t+2t2-4t3+2t4)/(1-t)3(4+3t+3t2)/2!
20009(9t3+10t4-18t5+9t6-t7)/(1-t)5(288-186t-9t2-6t3+9t4)/4!
30000(7t5+25t6-32t7+14t8-2t9)/(1-t)7(7200-9672t+1848t2+750t3-60t4-78t5+12t6)/6!
40000(18t8-18t9+7t10-t11)/(1-t)9(-171360t+91512t2+9632t3-11466t4+560t5+588t6-112t7+6t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:FoGCP_QNpicture of the graph :FoGCP_QN
0000111
0000031
0000001
0000001
1000000
1300000
1111000
[4, 4, 4, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031016(3t+t2-5t3+3t4)/(1-t)3(8+2t+2t2)/2!
20009(9t3+8t4-28t5+15t6-2t7)/(1-t)5(408-256t-74t2+40t3+2t4)/4!
30000(6t5+37t6-55t7+23t8-3t9)/(1-t)7(15840-18264t+1592t2+3120t3-880t4+24t5+8t6)/6!
40000(27t8-27t9+9t10-t11)/(1-t)9(362880-557856t+164016t2+67648t3-43288t4+6496t5+224t6-128t7+8t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:FoGCW?QNpicture of the graph :FoGCW?QN
0000112
0000021
0000001
0000001
1000000
1200000
2111000
[5, 4, 3, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031222(3t+3t2-5t3+2t4)/(1-t)3(2+5t+3t2)/2!
200111(t2+5t3+7t4-20t5+20t6-8t7+t8)/(1-t)6(840-626t-5t2+20t3+5t4+6t5)/5!
30000(19t5+5t6-22t7+12t8-2t9)/(1-t)7(4320-8568t+2088t2+1050t3-300t4-42t5+12t6)/6!
40000(18t8-18t9+7t10-t11)/(1-t)9(-171360t+91512t2+9632t3-11466t4+560t5+588t6-112t7+6t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:FoG?WCQNpicture of the graph :FoG?WCQN
0000121
0000012
0000001
0000001
1000000
2100000
1211000
[5, 4, 3, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031222(3t+3t2-5t3+2t4)/(1-t)3(2+5t+3t2)/2!
200111(t2+6t3+13t4-17t5+7t6-t7)/(1-t)5(72+46t-81t2+2t3+9t4)/4!
30000(9t5+19t6-26t7+12t8-2t9)/(1-t)7(1440-3432t-312t2+990t3-60t4-78t5+12t6)/6!
40000(18t8-18t9+7t10-t11)/(1-t)9(-171360t+91512t2+9632t3-11466t4+560t5+588t6-112t7+6t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:FoG?P_QNpicture of the graph :FoG?P_QN
0000121
0000021
0000001
0000001
1000000
2200000
1111000
[4, 4, 4, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031017(3t+t2-4t3+2t4)/(1-t)3(4+4t+2t2)/2!
200010(10t3+5t4-19t5+9t6-t7)/(1-t)5(264-104t-100t2+32t3+4t4)/4!
30000(12t5+20t6-38t7+16t8-2t9)/(1-t)7(12960-14424t+812t2+2880t3-820t4+24t5+8t6)/6!
40000(27t8-27t9+9t10-t11)/(1-t)9(362880-557856t+164016t2+67648t3-43288t4+6496t5+224t6-128t7+8t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:FoG?WGsRpicture of the graph :FoG?WGsR
0000121
0000010
0000001
0000001
1000002
2100000
1011200
[5, 4, 3, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031223(3t+3t2-4t3+t4)/(1-t)3(-2+7t+3t2)/2!
200112(t2+7t3+10t4-14t5+6t6-t7)/(1-t)5(24+70t-81t2+2t3+9t4)/4!
30000(9t5+19t6-26t7+12t8-2t9)/(1-t)7(1440-3432t-312t2+990t3-60t4-78t5+12t6)/6!
40000(18t8-18t9+7t10-t11)/(1-t)9(-171360t+91512t2+9632t3-11466t4+560t5+588t6-112t7+6t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Fo?_@_bRpicture of the graph :Fo?_@_bR
0000221
0000010
0000001
0000001
2000001
2100000
1011100
[5, 4, 3, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031120(3t+2t2-4t3+t4)/(1-t)3(-2+8t+2t2)/2!
20009(9t3+9t4-17t5+6t6-t7)/(1-t)5(-48+232t-198t2+32t3+6t4)/4!
30000(6t5+25t6-29t7+12t8-2t9)/(1-t)7(-720+1068t-3462t2+1890t3-150t4-78t5+12t6)/6!
40000(18t8-18t9+7t10-t11)/(1-t)9(-171360t+91512t2+9632t3-11466t4+560t5+588t6-112t7+6t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:FoGEAGbVpicture of the graph :FoGEAGbV
0000111
0000010
0000003
0000001
1000000
1100001
1031010
[6, 3, 3, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031326(3t+4t2-4t3+t4)/(1-t)3(-2+6t+4t2)/2!
20005(5t3+15t4-13t5+7t6-2t7)/(1-t)5(-192+176t-36t2-32t3+12t4)/4!
30000(2t5+24t6-24t7+13t8-3t9)/(1-t)7(-12240+8796t-2562t2-30t3+390t4-126t5+12t6)/6!
40000(10t8-10t9+5t10-t11)/(1-t)9(-403200+319680t-86048t2+5768t3+4676t4-2800t5+728t6-88t7+4t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Fo?A@_bVpicture of the graph :Fo?A@_bV
0000311
0000010
0000001
0000001
3000000
1100001
1011010
[5, 4, 3, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031120(3t+2t2-4t3+t4)/(1-t)3(-2+8t+2t2)/2!
20009(9t3+9t4-17t5+9t6-2t7)/(1-t)5(-48+112t-104t2+8t3+8t4)/4!
30000(6t5+28t6-36t7+17t8-3t9)/(1-t)7(-720-2532t-642t2+1170t3-90t4-78t5+12t6)/6!
40000(18t8-18t9+7t10-t11)/(1-t)9(-171360t+91512t2+9632t3-11466t4+560t5+588t6-112t7+6t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:FoGE@CbVpicture of the graph :FoGE@CbV
0000111
0000012
0000001
0000001
1000000
1100001
1211010
[6, 3, 3, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031325(3t+4t2-5t3+2t4)/(1-t)3(2+4t+4t2)/2!
20004(4t3+18t4-17t5+9t6-2t7)/(1-t)5(-48+48t-36t3+12t4)/4!
30000(t5+27t6-27t7+14t8-3t9)/(1-t)7(-9360+5676t-1482t2-150t3+390t4-126t5+12t6)/6!
40000(10t8-10t9+5t10-t11)/(1-t)9(-403200+319680t-86048t2+5768t3+4676t4-2800t5+728t6-88t7+4t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:FoGCWCbVpicture of the graph :FoGCWCbV
0000111
0000021
0000001
0000001
1000000
1200001
1111010
[5, 4, 3, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031120(3t+2t2-4t3+2t4)/(1-t)3(4+3t+3t2)/2!
20009(9t3+10t4-19t5+11t6-2t7)/(1-t)5(144-102t-21t2-6t3+9t4)/4!
30000(6t5+29t6-38t7+18t8-3t9)/(1-t)7(2880-7152t+1488t2+750t3-60t4-78t5+12t6)/6!
40000(18t8-18t9+7t10-t11)/(1-t)9(-171360t+91512t2+9632t3-11466t4+560t5+588t6-112t7+6t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:FoHCg?PNpicture of the graph :FoHCg?PN
0000102
0000022
0000010
0000001
1000000
0210000
2201000
[5, 4, 3, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031224(3t+3t2-3t3)/(1-t)3(-6+9t+3t2)/2!
200113(t2+8t3+7t4-10t5+3t6)/(1-t)5(120+10t-69t2+2t3+9t4)/4!
30000(10t5+15t6-20t7+8t8-t9)/(1-t)7(5760-5952t+48t2+990t3-60t4-78t5+12t6)/6!
40000(18t8-18t9+7t10-t11)/(1-t)9(-171360t+91512t2+9632t3-11466t4+560t5+588t6-112t7+6t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:FoHI?CRVpicture of the graph :FoHI?CRV
0000102
0000012
0000010
0000001
1000000
0110001
2201010
[6, 3, 3, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031326(3t+4t2-4t3+t4)/(1-t)3(-2+6t+4t2)/2!
20005(5t3+15t4-13t5+6t6-t7)/(1-t)5(48-12t+12t2-36t3+12t4)/4!
30000(2t5+23t6-21t7+10t8-2t9)/(1-t)7(-5040+3156t-1122t2-150t3+390t4-126t5+12t6)/6!
40000(10t8-10t9+5t10-t11)/(1-t)9(-403200+319680t-86048t2+5768t3+4676t4-2800t5+728t6-88t7+4t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:FoHCg?RVpicture of the graph :FoHCg?RV
0000102
0000021
0000010
0000001
1000000
0210001
2101010
[5, 4, 3, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031223(3t+3t2-4t3+t4)/(1-t)3(-2+7t+3t2)/2!
200112(t2+7t3+10t4-14t5+6t6-t7)/(1-t)5(24+70t-81t2+2t3+9t4)/4!
30000(9t5+19t6-26t7+12t8-2t9)/(1-t)7(1440-3432t-312t2+990t3-60t4-78t5+12t6)/6!
40000(18t8-18t9+7t10-t11)/(1-t)9(-171360t+91512t2+9632t3-11466t4+560t5+588t6-112t7+6t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Fo?cgLDVpicture of the graph :Fo?cgLDV
0000201
0000010
0000010
0000001
2000001
0110002
1001120
[5, 4, 3, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031225(3t+3t2-2t3+t4)/(1-t)3(2+t+5t2)/2!
200114(t2+8t3-3t4-8t5+14t6-7t7+t8)/(1-t)6(840-866t+115t2+20t3+5t4+6t5)/5!
30000(19t5+5t6-22t7+12t8-2t9)/(1-t)7(4320-8568t+2088t2+1050t3-300t4-42t5+12t6)/6!
40000(18t8-18t9+7t10-t11)/(1-t)9(-171360t+91512t2+9632t3-11466t4+560t5+588t6-112t7+6t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:FoGPG?QNpicture of the graph :FoGPG?QN
0000112
0000001
0000001
0000001
1000020
1000200
2111000
[5, 4, 3, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031228(3t-2t3+3t4-t5)/(1-t)4(6+9t+6t2+3t3)/3!
200117(t2+11t3-9t4-5t5+14t6-7t7+t8)/(1-t)6(840-746t-65t2+80t3+5t4+6t5)/5!
30000(19t5+5t6-22t7+12t8-2t9)/(1-t)7(4320-8568t+2088t2+1050t3-300t4-42t5+12t6)/6!
40000(18t8-18t9+7t10-t11)/(1-t)9(-171360t+91512t2+9632t3-11466t4+560t5+588t6-112t7+6t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:FoG@GCbRpicture of the graph :FoG@GCbR
0000121
0000001
0000001
0000001
1000011
2000100
1111100
[5, 4, 3, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031125(3t-t2-t3+4t4-2t5)/(1-t)4(24-3t+6t2+3t3)/3!
200014(14t3+3t4-17t5+11t6-2t7)/(1-t)5(192-150t-33t2+6t3+9t4)/4!
30000(6t5+29t6-38t7+18t8-3t9)/(1-t)7(2880-7152t+1488t2+750t3-60t4-78t5+12t6)/6!
40000(18t8-18t9+7t10-t11)/(1-t)9(-171360t+91512t2+9632t3-11466t4+560t5+588t6-112t7+6t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:FoGQ@GsVpicture of the graph :FoGQ@GsV
0000111
0000001
0000001
0000001
1000011
1000101
1111110
[6, 3, 3, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031333(3t+t2-t3+2t4-t5)/(1-t)4(12-t+9t2+4t3)/3!
200012(12t3+5t4-12t5+10t6-3t7)/(1-t)5(-168+80t-24t2-20t3+12t4)/4!
30000(31t6-33t7+18t8-4t9)/(1-t)7(-13680+8196t-1842t2-150t3+390t4-126t5+12t6)/6!
40000(10t8-10t9+5t10-t11)/(1-t)9(-403200+319680t-86048t2+5768t3+4676t4-2800t5+728t6-88t7+4t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:FoGCQ_RVpicture of the graph :FoGCQ_RV
0000111
0000021
0000010
0000001
1000000
1210001
1101010
[5, 4, 3, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031117(3t+5t2-2t3)/(1-t)2-1+6t
20006(6t3+16t4-25t5+11t6-2t7)/(1-t)5(156t-162t2+24t3+6t4)/4!
30000(3t5+35t6-41t7+18t8-3t9)/(1-t)7(720-2652t-1662t2+1650t3-150t4-78t5+12t6)/6!
40000(18t8-18t9+7t10-t11)/(1-t)9(-171360t+91512t2+9632t3-11466t4+560t5+588t6-112t7+6t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:FoGCgLCVpicture of the graph :FoGCgLCV
0000111
0000010
0000010
0000001
1000002
1110001
1001210
[5, 4, 3, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031119(3t+2t2-5t3+2t4)/(1-t)3(2+6t+2t2)/2!
20008(8t3+12t4-23t5+11t6-2t7)/(1-t)5(48+84t-138t2+24t3+6t4)/4!
30000(3t5+35t6-41t7+18t8-3t9)/(1-t)7(720-2652t-1662t2+1650t3-150t4-78t5+12t6)/6!
40000(18t8-18t9+7t10-t11)/(1-t)9(-171360t+91512t2+9632t3-11466t4+560t5+588t6-112t7+6t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Fo?_Q_sVpicture of the graph :Fo?_Q_sV
0000211
0000010
0000010
0000001
2000001
1110001
1001110
[4, 4, 4, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031017(3t+t2-4t3+2t4)/(1-t)3(4+4t+2t2)/2!
200010(10t3+5t4-22t5+13t6-2t7)/(1-t)5(312-228t-40t2+24t3+4t4)/4!
30000(9t5+30t6-50t7+22t8-3t9)/(1-t)7(14400-18144t+2612t2+2640t3-820t4+24t5+8t6)/6!
40000(27t8-27t9+9t10-t11)/(1-t)9(362880-557856t+164016t2+67648t3-43288t4+6496t5+224t6-128t7+8t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:FoGDG?bRpicture of the graph :FoGDG?bR
0000112
0000010
0000001
0000001
1000011
1100100
2011100
[5, 4, 3, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031120(3t+2t2-4t3+2t4)/(1-t)3(4+3t+3t2)/2!
20009(9t3+10t4-24t5+13t6-2t7)/(1-t)5(264-160t-54t2+16t3+6t4)/4!
30000(t5+41t6-47t7+20t8-3t9)/(1-t)7(6480-8892t+498t2+1410t3-150t4-78t5+12t6)/6!
40000(18t8-18t9+7t10-t11)/(1-t)9(-171360t+91512t2+9632t3-11466t4+560t5+588t6-112t7+6t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:FoG?S_bRpicture of the graph :FoG?S_bR
0000121
0000010
0000001
0000001
1000011
2100100
1011100
[4, 4, 4, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031017(3t+t2-4t3+2t4)/(1-t)3(4+4t+2t2)/2!
200010(10t3+15t4-13t5+2t6)/(1-t)4(102-59t-27t2+14t3)/3!
30000(3t5+44t6-60t7+24t8-3t9)/(1-t)7(17280-18384t+572t2+3600t3-940t4+24t5+8t6)/6!
40000(27t8-27t9+9t10-t11)/(1-t)9(362880-557856t+164016t2+67648t3-43288t4+6496t5+224t6-128t7+8t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Fo?_S_bRpicture of the graph :Fo?_S_bR
0000211
0000010
0000001
0000001
2000011
1100100
1011100
[4, 4, 4, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031016(3t+t2-5t3+3t4)/(1-t)3(8+2t+2t2)/2!
20009(9t3+17t4-14t5+2t6)/(1-t)4(114-65t-27t2+14t3)/3!
30000(3t5+44t6-60t7+24t8-3t9)/(1-t)7(17280-18384t+572t2+3600t3-940t4+24t5+8t6)/6!
40000(27t8-27t9+9t10-t11)/(1-t)9(362880-557856t+164016t2+67648t3-43288t4+6496t5+224t6-128t7+8t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:FoGDGGsVpicture of the graph :FoGDGGsV
0000111
0000010
0000001
0000001
1000011
1100101
1011110
[5, 4, 3, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031121(3t+2t2-3t3+t4)/(1-t)3(5t+3t2)/2!
200010(10t3+7t4-22t5+14t6-3t7)/(1-t)5(72-52t-66t2+16t3+6t4)/4!
30000(45t6-53t7+24t8-4t9)/(1-t)7(2160-6372t+138t2+1410t3-150t4-78t5+12t6)/6!
40000(18t8-18t9+7t10-t11)/(1-t)9(-171360t+91512t2+9632t3-11466t4+560t5+588t6-112t7+6t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Fo?EAlDVpicture of the graph :Fo?EAlDV
0000210
0000100
0000010
0000001
2100001
1010002
0001120
[4, 4, 4, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031117(3t+5t2-2t3)/(1-t)2-1+6t
200110(t2+5t3+12t4-22t5+9t6-t7)/(1-t)5(192-8t-124t2+32t3+4t4)/4!
30000(12t5+20t6-38t7+16t8-2t9)/(1-t)7(12960-14424t+812t2+2880t3-820t4+24t5+8t6)/6!
40000(27t8-27t9+9t10-t11)/(1-t)9(362880-557856t+164016t2+67648t3-43288t4+6496t5+224t6-128t7+8t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Fo?EAlCVpicture of the graph :Fo?EAlCV
0000210
0000100
0000010
0000001
2100002
1010001
0001210
[5, 4, 3, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031117(3t+5t2-2t3)/(1-t)2-1+6t
20006(6t3+16t4-24t5+9t6-t7)/(1-t)5(144+72t-150t2+24t3+6t4)/4!
30000(4t5+31t6-35t7+14t8-2t9)/(1-t)7(5040-5172t-1302t2+1650t3-150t4-78t5+12t6)/6!
40000(18t8-18t9+7t10-t11)/(1-t)9(-171360t+91512t2+9632t3-11466t4+560t5+588t6-112t7+6t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Fo?E?IsVpicture of the graph :Fo?E?IsV
0000220
0000100
0000010
0000001
2100001
2010001
0001110
[4, 4, 4, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031015(3t+4t2-2t3)/(1-t)25t
20008(8t3+17t4-10t5+t6)/(1-t)4(78-10t-48t2+16t3)/3!
30000(6t5+34t6-48t7+18t8-2t9)/(1-t)7(15840-14664t-1228t2+3840t3-940t4+24t5+8t6)/6!
40000(27t8-27t9+9t10-t11)/(1-t)9(362880-557856t+164016t2+67648t3-43288t4+6496t5+224t6-128t7+8t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Fo??WIsVpicture of the graph :Fo??WIsV
0000310
0000100
0000010
0000001
3100001
1010001
0001110
[5, 4, 3, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031116(3t+5t2-3t3)/(1-t)21+5t
20005(5t3+19t4-29t5+13t6-2t7)/(1-t)5(144+28t-126t2+20t3+6t4)/4!
30000(2t5+38t6-44t7+19t8-3t9)/(1-t)7(3600-5772t-582t2+1530t3-150t4-78t5+12t6)/6!
40000(18t8-18t9+7t10-t11)/(1-t)9(-171360t+91512t2+9632t3-11466t4+560t5+588t6-112t7+6t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Fo@_gLCVpicture of the graph :Fo@_gLCV
0000111
0000100
0000010
0000001
1100002
1010001
1001210
[5, 4, 3, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031117(3t+5t2-2t3)/(1-t)2-1+6t
20006(6t3+16t4-27t5+13t6-2t7)/(1-t)5(192-52t-90t2+16t3+6t4)/4!
30000(t5+41t6-47t7+20t8-3t9)/(1-t)7(6480-8892t+498t2+1410t3-150t4-78t5+12t6)/6!
40000(18t8-18t9+7t10-t11)/(1-t)9(-171360t+91512t2+9632t3-11466t4+560t5+588t6-112t7+6t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Fo@_g?sVpicture of the graph :Fo@_g?sV
0000112
0000100
0000010
0000001
1100001
1010001
2001110
[5, 4, 3, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031116(3t+5t2-3t3)/(1-t)21+5t
20005(5t3+19t4-30t5+14t6-2t7)/(1-t)5(240-76t-90t2+16t3+6t4)/4!
30000(t5+41t6-47t7+20t8-3t9)/(1-t)7(6480-8892t+498t2+1410t3-150t4-78t5+12t6)/6!
40000(18t8-18t9+7t10-t11)/(1-t)9(-171360t+91512t2+9632t3-11466t4+560t5+588t6-112t7+6t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Fo?EA_sVpicture of the graph :Fo?EA_sV
0000211
0000100
0000010
0000001
2100001
1010001
1001110
[4, 4, 4, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031015(3t+4t2-2t3)/(1-t)25t
20008(8t3+17t4-13t5+2t6)/(1-t)4(90-41t-33t2+14t3)/3!
30000(3t5+44t6-60t7+24t8-3t9)/(1-t)7(17280-18384t+572t2+3600t3-940t4+24t5+8t6)/6!
40000(27t8-27t9+9t10-t11)/(1-t)9(362880-557856t+164016t2+67648t3-43288t4+6496t5+224t6-128t7+8t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Fo@gw@DVpicture of the graph :Fo@gw@DV
0000102
0000100
0000010
0000010
1100001
0011002
2000120
[5, 4, 3, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031120(3t+2t2-4t3+t4)/(1-t)3(-2+8t+2t2)/2!
20009(9t3+9t4-19t5+8t6-t7)/(1-t)5(144+24t-126t2+24t3+6t4)/4!
30000(4t5+31t6-35t7+14t8-2t9)/(1-t)7(5040-5172t-1302t2+1650t3-150t4-78t5+12t6)/6!
40000(18t8-18t9+7t10-t11)/(1-t)9(-171360t+91512t2+9632t3-11466t4+560t5+588t6-112t7+6t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Fo?Eb`DVpicture of the graph :Fo?Eb`DV
0000201
0000100
0000010
0000010
2100001
0011002
1000120
[4, 4, 4, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031120(3t+2t2-4t3+t4)/(1-t)3(-2+8t+2t2)/2!
200113(t2+8t3+5t4-17t5+8t6-t7)/(1-t)5(192-56t-100t2+32t3+4t4)/4!
30000(12t5+20t6-38t7+16t8-2t9)/(1-t)7(12960-14424t+812t2+2880t3-820t4+24t5+8t6)/6!
40000(27t8-27t9+9t10-t11)/(1-t)9(362880-557856t+164016t2+67648t3-43288t4+6496t5+224t6-128t7+8t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Fo@_c_sVpicture of the graph :Fo@_c_sV
0000111
0000100
0000010
0000001
1100011
1010101
1001110
[4, 4, 4, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031016(3t+4t2-t3)/(1-t)2-2+6t
20009(9t3+15t4-15t5+3t6)/(1-t)4(90-66t-18t2+12t3)/3!
30000(54t6-72t7+30t8-4t9)/(1-t)7(18720-22104t+2372t2+3360t3-940t4+24t5+8t6)/6!
40000(27t8-27t9+9t10-t11)/(1-t)9(362880-557856t+164016t2+67648t3-43288t4+6496t5+224t6-128t7+8t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:FkHi?CQJpicture of the graph :FkHi?CQJ
0001002
0000102
0000012
1000000
0100000
0010000
2220000
[6, 3, 3, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031327(3t+4t2-3t3)/(1-t)3(-6+8t+4t2)/2!
20006(6t3+12t4-9t5+3t6)/(1-t)5(144-72t+24t2-36t3+12t4)/4!
30000(3t5+19t6-15t7+6t8-t9)/(1-t)7(-720+636t-762t2-150t3+390t4-126t5+12t6)/6!
40000(10t8-10t9+5t10-t11)/(1-t)9(-403200+319680t-86048t2+5768t3+4676t4-2800t5+728t6-88t7+4t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:FkH_gCPVpicture of the graph :FkH_gCPV
0001011
0000103
0000010
1000000
0100000
1010001
1300010
[5, 4, 3, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031118(3t+5t2-t3)/(1-t)2-3+7t
20007(7t3+13t4-23t5+11t6-2t7)/(1-t)5(48+76t-126t2+20t3+6t4)/4!
30000(2t5+38t6-44t7+19t8-3t9)/(1-t)7(3600-5772t-582t2+1530t3-150t4-78t5+12t6)/6!
40000(18t8-18t9+7t10-t11)/(1-t)9(-171360t+91512t2+9632t3-11466t4+560t5+588t6-112t7+6t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:FkH_g?PVpicture of the graph :FkH_g?PV
0001012
0000102
0000010
1000000
0100000
1010001
2200010
[5, 4, 3, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031118(3t+5t2-t3)/(1-t)2-3+7t
20007(7t3+13t4-21t5+8t6-t7)/(1-t)5(96+96t-150t2+24t3+6t4)/4!
30000(4t5+31t6-35t7+14t8-2t9)/(1-t)7(5040-5172t-1302t2+1650t3-150t4-78t5+12t6)/6!
40000(18t8-18t9+7t10-t11)/(1-t)9(-171360t+91512t2+9632t3-11466t4+560t5+588t6-112t7+6t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:FkH_A_PVpicture of the graph :FkH_A_PV
0001021
0000102
0000010
1000000
0100000
2010001
1200010
[4, 4, 4, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
1031118(3t+5t2-t3)/(1-t)2-3+7t
200111(t2+6t3+9t4-19t5+8t6-t7)/(1-t)5(144+16t-124t2+32t3+4t4)/4!
30000(12t5+20t6-38t7+16t8-2t9)/(1-t)7(12960-14424t+812t2+2880t3-820t4+24t5+8t6)/6!
40000(27t8-27t9+9t10-t11)/(1-t)9(362880-557856t+164016t2+67648t3-43288t4+6496t5+224t6-128t7+8t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:GsGCWCbRpicture of the graph :GsGCWCbR
00000111
00000021
00000001
00000001
00000001
10000000
12000000
11111000
[5, 3, 3, 3, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10210(2t+2t2-3t3+3t4-t5)/(1-t)4(6+3t+6t2+3t3)/3!
2000(7t3+t4-12t5+10t6-3t7)/(1-t)6(960-658t+95t2-65t3+25t4+3t5)/5!
3000(6t5+9t6-9t7+3t8)/(1-t)7(8640-9144t+3006t2-495t3+225t4-81t5+9t6)/6!
4000(6t8-4t9+t10)/(1-t)9(201600-255600t+114916t2-24332t3+5467t4-2240t5+574t6-68t7+3t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:GsGCgCRRpicture of the graph :GsGCgCRR
00000111
00000012
00000010
00000001
00000001
10000000
11100000
12011000
[5, 3, 3, 3, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10210(2t+4t2-4t3+t4)/(1-t)3(-2+5t+3t2)/2!
2000(2t3+15t4-11t5+3t6)/(1-t)5(96+2t-9t2-26t3+9t4)/4!
3000(t5+16t6-11t7+3t8)/(1-t)7(7200-6576t+1806t2-525t3+345t4-99t5+9t6)/6!
4000(6t8-4t9+t10)/(1-t)9(201600-255600t+114916t2-24332t3+5467t4-2240t5+574t6-68t7+3t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:GsGCQ_RRpicture of the graph :GsGCQ_RR
00000111
00000021
00000010
00000001
00000001
10000000
12100000
11011000
[4, 4, 3, 3, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
1029(2t+3t2-4t3+t4)/(1-t)3(-2+6t+2t2)/2!
2000(4t3+12t4-13t5+3t6)/(1-t)5(48+124t-114t2+8t3+6t4)/4!
3000(3t5+17t6-15t7+3t8)/(1-t)7(4320+408t-4468t2+2160t3-220t4-48t5+8t6)/6!
4000(9t8-6t9+t10)/(1-t)9(120960-51552t-82128t2+70840t3-19124t4+952t5+448t6-80t7+4t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Gs?_QlDZpicture of the graph :Gs?_QlDZ
00000210
00000010
00000010
00000001
00000001
20000001
11100001
00011110
[4, 4, 3, 3, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
1029(2t+3t2-2t3+t4)/(1-t)3(2+4t2)/2!
2000(6t3+2t4-13t5+12t6-3t7)/(1-t)6(720-144t-300t2+80t3+4t5)/5!
3000(9t5+9t6-13t7+3t8)/(1-t)7(5760-2016t-3568t2+2400t3-400t4-24t5+8t6)/6!
4000(9t8-6t9+t10)/(1-t)9(120960-51552t-82128t2+70840t3-19124t4+952t5+448t6-80t7+4t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:GsGDWGsVpicture of the graph :GsGDWGsV
00000111
00000010
00000001
00000001
00000001
10000011
11000100
10111100
[5, 3, 3, 3, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10210(2t+2t2-3t3+3t4-t5)/(1-t)4(6+3t+6t2+3t3)/3!
2000(7t3+8t4-10t5+4t6)/(1-t)5(240-150t+15t2-18t3+9t4)/4!
3000(19t6-14t7+4t8)/(1-t)7(10080-9696t+2886t2-645t3+345t4-99t5+9t6)/6!
4000(6t8-4t9+t10)/(1-t)9(201600-255600t+114916t2-24332t3+5467t4-2240t5+574t6-68t7+3t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:GsGCd_sVpicture of the graph :GsGCd_sV
00000111
00000010
00000010
00000001
00000001
10000011
11100100
10011100
[4, 4, 3, 3, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
1029(2t+3t2-2t3+t4)/(1-t)3(2+4t2)/2!
2000(6t3+8t4-14t5+4t6)/(1-t)5(144+48t-124t2+24t3+4t4)/4!
3000(24t6-20t7+4t8)/(1-t)7(5760+288t-5488t2+2640t3-280t4-48t5+8t6)/6!
4000(9t8-6t9+t10)/(1-t)9(120960-51552t-82128t2+70840t3-19124t4+952t5+448t6-80t7+4t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Gs@_A_sVpicture of the graph :Gs@_A_sV
00000121
00000100
00000010
00000001
00000001
11000001
20100000
10011100
[4, 4, 3, 3, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
1029(2t+3t2-3t3)/(1-t)3(-6+8t+2t2)/2!
2000(5t3+9t4-10t5+2t6)/(1-t)5(148t-114t2+8t3+6t4)/4!
3000(3t5+17t6-15t7+3t8)/(1-t)7(4320+408t-4468t2+2160t3-220t4-48t5+8t6)/6!
4000(9t8-6t9+t10)/(1-t)9(120960-51552t-82128t2+70840t3-19124t4+952t5+448t6-80t7+4t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Gs?EAlDZpicture of the graph :Gs?EAlDZ
00000210
00000100
00000010
00000001
00000001
21000001
10100001
00011110
[4, 4, 3, 3, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
1029(2t+3t2-4t3+t4)/(1-t)3(-2+6t+2t2)/2!
2000(4t3+12t4-13t5+3t6)/(1-t)5(48+124t-114t2+8t3+6t4)/4!
3000(3t5+17t6-15t7+3t8)/(1-t)7(4320+408t-4468t2+2160t3-220t4-48t5+8t6)/6!
4000(9t8-6t9+t10)/(1-t)9(120960-51552t-82128t2+70840t3-19124t4+952t5+448t6-80t7+4t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Gs@_gLDZpicture of the graph :Gs@_gLDZ
00000111
00000100
00000010
00000001
00000001
11000001
10100001
10011110
[5, 3, 3, 3, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10210(2t+4t2-4t3+t4)/(1-t)3(-2+5t+3t2)/2!
2000(2t3+15t4-12t5+4t6)/(1-t)5(192-102t+27t2-30t3+9t4)/4!
3000(19t6-14t7+4t8)/(1-t)7(10080-9696t+2886t2-645t3+345t4-99t5+9t6)/6!
4000(6t8-4t9+t10)/(1-t)9(201600-255600t+114916t2-24332t3+5467t4-2240t5+574t6-68t7+3t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Gs@_d_sVpicture of the graph :Gs@_d_sV
00000111
00000100
00000010
00000001
00000001
11000011
10100100
10011100
[4, 4, 3, 3, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
1029(2t+3t2-4t3+t4)/(1-t)3(-2+6t+2t2)/2!
2000(4t3+12t4-16t5+4t6)/(1-t)5(96+120t-148t2+24t3+4t4)/4!
3000(24t6-20t7+4t8)/(1-t)7(5760+288t-5488t2+2640t3-280t4-48t5+8t6)/6!
4000(9t8-6t9+t10)/(1-t)9(120960-51552t-82128t2+70840t3-19124t4+952t5+448t6-80t7+4t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:GoH_gCRZpicture of the graph :GoH_gCRZ
00001011
00000102
00000010
00000001
10000000
01000000
10100001
12010010
[5, 3, 3, 3, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
10210(2t+4t2-3t3)/(1-t)3(-6+7t+3t2)/2!
2000(3t3+12t4-8t5+2t6)/(1-t)5(48+26t-9t2-26t3+9t4)/4!
3000(t5+16t6-11t7+3t8)/(1-t)7(7200-6576t+1806t2-525t3+345t4-99t5+9t6)/6!
4000(6t8-4t9+t10)/(1-t)9(201600-255600t+114916t2-24332t3+5467t4-2240t5+574t6-68t7+3t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:GoH_@I@Npicture of the graph :GoH_@I@N
00001021
00000111
00000010
00000001
10000000
01000000
21100000
11010000
[4, 4, 3, 3, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
1029(2t+5t2-t3)/(1-t)2-3+6t
2000(2t3+16t4-17t5+3t6)/(1-t)5(-48+296t-208t2+28t3+4t4)/4!
3000(t5+21t6-17t7+3t8)/(1-t)7(2880+3408t-6568t2+2760t3-280t4-48t5+8t6)/6!
4000(9t8-6t9+t10)/(1-t)9(120960-51552t-82128t2+70840t3-19124t4+952t5+448t6-80t7+4t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:GoH_Q_RZpicture of the graph :GoH_Q_RZ
00001011
00000111
00000010
00000001
10000000
01000000
11100001
11010010
[4, 4, 3, 3, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
1029(2t+5t2-t3)/(1-t)2-3+6t
2000(2t3+16t4-18t5+4t6)/(1-t)5(48+192t-172t2+24t3+4t4)/4!
3000(24t6-20t7+4t8)/(1-t)7(5760+288t-5488t2+2640t3-280t4-48t5+8t6)/6!
4000(9t8-6t9+t10)/(1-t)9(120960-51552t-82128t2+70840t3-19124t4+952t5+448t6-80t7+4t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:GoGEb`UZpicture of the graph :GoGEb`UZ
00001101
00000100
00000010
00000010
10000000
11000001
00110002
10000120
[4, 4, 3, 3, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
1029(2t+3t2-3t3)/(1-t)3(-6+8t+2t2)/2!
2000(5t3+9t4-12t5+2t6)/(1-t)5(-48+248t-184t2+28t3+4t4)/4!
3000(t5+21t6-17t7+3t8)/(1-t)7(2880+3408t-6568t2+2760t3-280t4-48t5+8t6)/6!
4000(9t8-6t9+t10)/(1-t)9(120960-51552t-82128t2+70840t3-19124t4+952t5+448t6-80t7+4t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:HiAK?a_CXNpicture of the graph :HiAK?a_CXN
000001011
000000111
000000010
000000001
000000001
100000000
010000000
111000000
110110000
[4, 3, 3, 3, 1, 1, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k01Poincaré seriesstable polynomial value
0111/(1-t)1
101(t+4t2-3t3)/(1-t)3(-6+6t+2t2)/2!
200(12t4-6t5)/(1-t)5(-144+228t-78t2-12t3+6t4)/4!
300(10t6-4t7)/(1-t)7(-2880+5856t-3756t2+690t3+150t4-66t5+6t6)/6!
400(3t8-t9)/(1-t)9(-40320+94464t-78920t2+27888t3-2142t4-1344t5+420t6-48t7+2t8)/8!

Data for graphs with 5 essential vertices

sparse6 nameimageadjacency matrixdegree sequence
:Dg?cWCbpicture of the graph :Dg?cWCb
00201
00021
20001
02001
11110
[4, 3, 3, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
10481012(4t-2t3)/(1-t)24+2t
20031332(3t2+4t3+2t4+t6)/(1-t)3(40-34t+10t2)/2!
300003(3t4+6t5-4t6-4t7+3t8)/(1-t)5(744-248t+20t2-16t3+4t4)/4!
400000(6t7+5t8-3t9)/(1-t)6(3240+2202t-3145t2+1090t3-155t4+8t5)/5!
500000(3t10-t11)/(1-t)8(60480+60744t-95858t2+43883t3-9905t4+1211t5-77t6+2t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Dg?_@cQpicture of the graph :Dg?_@cQ
00220
00012
20001
21000
02100
[4, 3, 3, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104777(4t+3t2)/(1-t)7
20021026(2t2+4t3+2t4-3t5)/(1-t)3(-16-3t+5t2)/2!
300002(2t4+5t5-6t7+t8)/(1-t)5(-1200+1152t-338t2+24t3+2t4)/4!
400000(5t7+5t8-2t9)/(1-t)6(-2760+7102t-4635t2+1290t3-165t4+8t5)/5!
500000(3t10-t11)/(1-t)8(60480+60744t-95858t2+43883t3-9905t4+1211t5-77t6+2t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Dg?_P_Qpicture of the graph :Dg?_P_Q
00211
00021
20001
12000
11100
[4, 3, 3, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104777(4t+3t2)/(1-t)7
20021025(2t2+4t3+t4-3t5+t6)/(1-t)3(-2-7t+5t2)/2!
300001(t4+7t5-9t7+3t8)/(1-t)5(-552+808t-278t2+20t3+2t4)/4!
400000(4t7+7t8-3t9)/(1-t)6(-360+5622t-4335t2+1270t3-165t4+8t5)/5!
500000(3t10-t11)/(1-t)8(60480+60744t-95858t2+43883t3-9905t4+1211t5-77t6+2t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Dg@_@_Qpicture of the graph :Dg@_@_Q
00121
00111
11001
21000
11100
[4, 3, 3, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104666(4t+2t2)/(1-t)6
2001923(t2+6t3-t4-5t5+t6)/(1-t)3(-34+12t+2t2)/2!
300000(7t5+10t6-4t7)/(1-t)4(-288+356t-123t2+13t3)/3!
400000(t7+11t8-4t9)/(1-t)6(-1560+7562t-5225t2+1430t3-175t4+8t5)/5!
500000(3t10-t11)/(1-t)8(60480+60744t-95858t2+43883t3-9905t4+1211t5-77t6+2t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Dg@_WCbpicture of the graph :Dg@_WCb
00111
00111
11001
11001
11110
[4, 3, 3, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104555(4t+t2)/(1-t)5
2000822(8t3+6t4-2t5)/(1-t)2-26+12t
300000(4t5+14t6-6t7)/(1-t)4(-216+318t-114t2+12t3)/3!
400000(13t8-5t9)/(1-t)6(840+6082t-4925t2+1410t3-175t4+8t5)/5!
500000(3t10-t11)/(1-t)8(60480+60744t-95858t2+43883t3-9905t4+1211t5-77t6+2t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Ek?_Pcbpicture of the graph :Ek?_Pcb
000210
000021
000001
200001
120000
011100
[3, 3, 3, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
10367(3t-2t3)/(1-t)24+t
20016(t2+3t3+3t4-t5)/(1-t)3(12-18t+6t2)/2!
30000(t4+3t5+t6-3t7)/(1-t)5(-888+716t-170t2+4t3+2t4)/4!
40000(2t7+3t8)/(1-t)6(-9000+10350t-4685t2+1045t3-115t4+5t5)/5!
50000t10/(1-t)8(-181440+241128t-133938t2+40369t3-7140t4+742t5-42t6+t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Ek@_a_bpicture of the graph :Ek@_a_b
000111
000100
000021
110001
102000
101100
[3, 3, 3, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
10367(3t-2t3)/(1-t)24+t
20016(t2+3t3+2t4-2t5)/(1-t)3(-6-6t+4t2)/2!
30000(4t5+2t6-5t7)/(1-t)5(-1464+1202t-313t2+22t3+t4)/4!
40000(t7+4t8)/(1-t)6(-10800+12060t-5280t2+1135t3-120t4+5t5)/5!
50000t10/(1-t)8(-181440+241128t-133938t2+40369t3-7140t4+742t5-42t6+t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Ek@_Q_Rpicture of the graph :Ek@_Q_R
000111
000111
000010
110001
111000
110100
[3, 3, 3, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
10356(3t-t2-t3)/(1-t)23+t
20005(5t3+t4-4t5)/(1-t)3(-32+8t+2t2)/2!
30000(2t5+8t6)/(1-t)4(-528+428t-114t2+10t3)/3!
400005t8/(1-t)6(-12600+13770t-5875t2+1225t3-125t4+5t5)/5!
50000t10/(1-t)8(-181440+241128t-133938t2+40369t3-7140t4+742t5-42t6+t7)/7!

sparse6 nameimageadjacency matrixdegree sequence
:Dk?E@CaJpicture of the graph :Dk?E@CaJ
00021
00012
00003
21000
12300
[6, 3, 3, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10512162024(5t+2t2-3t3)/(1-t)24+4t
20031960130(3t2+7t3+2t4-8t5+6t6-2t7)/(1-t)4(60-41t-3t2+8t3)/3!
30000331(3t4+13t5-t6-22t7+16t8-6t9+t10)/(1-t)6(840-3274t+2645t2-750t3+55t4+4t5)/5!
4000000(13t7+10t8-13t9+8t10-2t11)/(1-t)7(-20880-10044t+21694t2-11220t3+2770t4-336t5+16t6)/6!
5000000(10t10-10t11+5t12-t13)/(1-t)9(-1209600+176160t+456592t2-316568t3+105476t4-20720t5+2408t6-152t7+4t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dk?CWCaJpicture of the graph :Dk?CWCaJ
00021
00021
00003
22000
11300
[5, 4, 3, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10511141720(5t+t2-3t3)/(1-t)25+3t
20042364127(4t2+7t3-4t4-7t5+5t6-2t7)/(1-t)4(132-129t+36t2+3t3)/3!
30000442(4t4+22t5+7t6-13t7+7t8-t9)/(1-t)5(888-1156t+766t2-236t3+26t4)/4!
4000000(18t7+14t8-24t9+12t10-2t11)/(1-t)7(23040-21768t+14832t2-8130t3+2430t4-342t5+18t6)/6!
5000000(18t10-18t11+7t12-t13)/(1-t)9(483840-179328t-59128t2-43792t3+56294t4-18592t5+2828t6-208t7+6t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dk?CQ_QJpicture of the graph :Dk?CQ_QJ
00021
00021
00012
22100
11200
[5, 4, 3, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
1059999(5t+4t2)/(1-t)9
20021854101(2t2+12t3+6t4-9t5+3t6)/(1-t)3(12-32t+14t2)/2!
30000227(2t4+17t5+21t6-27t7+9t8-t9)/(1-t)5(-912+462t+255t2-162t3+21t4)/4!
4000000(12t7+27t8-32t9+13t10-2t11)/(1-t)7(-16560+20652t-1218t2-5550t3+2280t4-342t5+18t6)/6!
5000000(18t10-18t11+7t12-t13)/(1-t)9(483840-179328t-59128t2-43792t3+56294t4-18592t5+2828t6-208t7+6t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dk?CQI@Jpicture of the graph :Dk?CQI@J
00021
00021
00021
22200
11100
[6, 3, 3, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
1059999(5t+4t2)/(1-t)9
2000124693(12t3+10t4-9t5+3t6)/(1-t)3(36-50t+16t2)/2!
3000009(9t5+31t6-24t7+9t8-t9)/(1-t)5(1176-1692t+1020t2-264t3+24t4)/4!
4000000(3t7+29t8-25t9+11t10-2t11)/(1-t)7(7200-30960t+30304t2-13680t3+3160t4-360t5+16t6)/6!
5000000(10t10-10t11+5t12-t13)/(1-t)9(-1209600+176160t+456592t2-316568t3+105476t4-20720t5+2408t6-152t7+4t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dg?cP_PJpicture of the graph :Dg?cP_PJ
00201
00032
20001
03000
12100
[5, 4, 3, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10512172227(5t+2t2-2t3)/(1-t)22+5t
20052672149(5t2+6t3-2t4-3t5+4t6-t7)/(1-t)4(-36+21t-12t2+9t3)/3!
30000757(7t4+15t5-19t6-7t7+16t8-7t9+t10)/(1-t)6(-1080+1534t-15t2-220t3+15t4+6t5)/5!
4000000(25t7+6t8-23t9+12t10-2t11)/(1-t)7(7920+5556t-2478t2-3090t3+1740t4-306t5+18t6)/6!
5000000(18t10-18t11+7t12-t13)/(1-t)9(483840-179328t-59128t2-43792t3+56294t4-18592t5+2828t6-208t7+6t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dg?e@CbNpicture of the graph :Dg?e@CbN
00201
00012
20001
01002
12120
[6, 3, 3, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10512162024(5t+2t2-3t3)/(1-t)24+4t
20031959128(3t2+7t3+t4-6t5+5t6-2t7)/(1-t)4(78-47t-3t2+8t3)/3!
30000229(2t4+17t5-7t6-19t7+17t8-7t9+t10)/(1-t)6(3600-4874t+2945t2-770t3+55t4+4t5)/5!
4000000(12t7+13t8-16t9+9t10-2t11)/(1-t)7(-6480-18924t+23494t2-11340t3+2770t4-336t5+16t6)/6!
5000000(10t10-10t11+5t12-t13)/(1-t)9(-1209600+176160t+456592t2-316568t3+105476t4-20720t5+2408t6-152t7+4t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dg?cW?QNpicture of the graph :Dg?cW?QN
00202
00021
20001
02001
21110
[5, 4, 3, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10511141720(5t+t2-3t3)/(1-t)25+3t
20042367140(4t2+7t3-t4-6t5+4t6-2t7)/(1-t)4(150-117t+21t2+6t3)/3!
30000755(7t4+13t5-15t6-10t7+19t8-9t9+t10)/(1-t)6(6480-4176t+1540t2-390t3+20t4+6t5)/5!
4000000(25t7+7t8-25t9+13t10-2t11)/(1-t)7(33120-13584t+2892t2-3750t3+1770t4-306t5+18t6)/6!
5000000(18t10-18t11+7t12-t13)/(1-t)9(483840-179328t-59128t2-43792t3+56294t4-18592t5+2828t6-208t7+6t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dg?AP_QNpicture of the graph :Dg?AP_QN
00301
00021
30001
02001
11110
[4, 4, 4, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10511131517(5t+t2-4t3)/(1-t)27+2t
20052463124(5t2+4t3-3t4-4t5+5t6-3t7)/(1-t)4(174-121t+27t2+4t3)/3!
30000760(7t4+18t5-29t6-5t7+29t8-13t9+t10)/(1-t)6(6240+1092t-1930t2+400t3-50t4+8t5)/5!
4000000(34t7+6t8-40t9+18t10-2t11)/(1-t)7(34560+45768t-47036t2+12000t3-500t4-168t5+16t6)/6!
5000000(27t10-27t11+9t12-t13)/(1-t)9(725760+1394208t-1646352t2+551936t3-50008t4-10528t5+2912t6-256t7+8t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dg?_@EPJpicture of the graph :Dg?_@EPJ
00220
00022
20001
22000
02100
[4, 4, 4, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
1059999(5t+4t2)/(1-t)9
20032055102(3t2+11t3+4t4-6t5)/(1-t)3(-26-14t+12t2)/2!
30000546(5t4+21t5+3t6-17t7+4t8)/(1-t)5(-1896+1720t-304t2-64t3+16t4)/4!
4000000(24t7+13t8-31t9+11t10-t11)/(1-t)7(-28080+79896t-45656t2+8160t3+280t4-216t5+16t6)/6!
5000000(27t10-27t11+9t12-t13)/(1-t)9(725760+1394208t-1646352t2+551936t3-50008t4-10528t5+2912t6-256t7+8t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dg?A@EPJpicture of the graph :Dg?A@EPJ
00310
00022
30001
12000
02100
[4, 4, 4, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10510101010(5t+5t2)/(1-t)10
20042155103(4t2+5t3-5t4-7t5+9t6-2t7)/(1-t)4(-102+44t+4t3)/3!
30000446(4t4+26t5+2t6-22t7+9t8-t9)/(1-t)5(-1176+1216t-162t2-88t3+18t4)/4!
4000000(24t7+16t8-38t9+16t10-2t11)/(1-t)7(-2880+54456t-37076t2+6960t3+340t4-216t5+16t6)/6!
5000000(27t10-27t11+9t12-t13)/(1-t)9(725760+1394208t-1646352t2+551936t3-50008t4-10528t5+2912t6-256t7+8t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dg?A?EPJpicture of the graph :Dg?A?EPJ
00320
00012
30001
21000
02100
[5, 4, 3, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10510101010(5t+5t2)/(1-t)10
20031958118(3t2+7t3-12t5+10t6-2t7)/(1-t)4(-72+21t-3t2+6t3)/3!
30000543(5t4+13t5-3t6-28t7+26t8-8t9+t10)/(1-t)6(-6360+5554t-1025t2-100t3+5t4+6t5)/5!
4000000(23t7+10t8-25t9+12t10-2t11)/(1-t)7(-13680+26076t-9618t2-2010t3+1680t4-306t5+18t6)/6!
5000000(18t10-18t11+7t12-t13)/(1-t)9(483840-179328t-59128t2-43792t3+56294t4-18592t5+2828t6-208t7+6t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dg?_P_QJpicture of the graph :Dg?_P_QJ
00211
00021
20002
12000
11200
[4, 4, 4, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
1059999(5t+4t2)/(1-t)9
20032056102(3t2+11t3+5t4-9t5+3t6)/(1-t)3(4-25t+13t2)/2!
30000646(6t4+10t5-3t6-30t7+36t8-12t9+t10)/(1-t)6(-3240+7152t-3180t2+520t3-60t4+8t5)/5!
4000000(33t7+7t8-39t9+17t10-2t11)/(1-t)7(-1440+75168t-55976t2+13200t3-560t4-168t5+16t6)/6!
5000000(27t10-27t11+9t12-t13)/(1-t)9(725760+1394208t-1646352t2+551936t3-50008t4-10528t5+2912t6-256t7+8t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dg?_P_PJpicture of the graph :Dg?_P_PJ
00211
00022
20001
12000
12100
[4, 4, 4, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
1059999(5t+4t2)/(1-t)9
2003205498(3t2+11t3+3t4-7t5+2t6)/(1-t)3(-4-20t+12t2)/2!
30000442(4t4+22t5+6t6-25t7+10t8-t9)/(1-t)5(-1032+1188t-196t2-72t3+16t4)/4!
4000000(21t7+23t8-43t9+17t10-2t11)/(1-t)7(-10080+66096t-42416t2+7920t3+280t4-216t5+16t6)/6!
5000000(27t10-27t11+9t12-t13)/(1-t)9(725760+1394208t-1646352t2+551936t3-50008t4-10528t5+2912t6-256t7+8t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dg?_PE@Jpicture of the graph :Dg?_PE@J
00211
00031
20001
13000
11100
[4, 4, 4, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10510101010(5t+5t2)/(1-t)10
2004215397(4t2+5t3-7t4-5t5+11t6-4t7)/(1-t)4(-18+20t+4t3)/3!
30000240(2t4+30t5+2t6-35t7+17t8-2t9)/(1-t)5(-720+1436t-410t2-32t3+14t4)/4!
4000000(15t7+40t8-60t9+24t10-3t11)/(1-t)7(720+63936t-44516t2+8640t3+220t4-216t5+16t6)/6!
5000000(27t10-27t11+9t12-t13)/(1-t)9(725760+1394208t-1646352t2+551936t3-50008t4-10528t5+2912t6-256t7+8t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dg?_P_@Jpicture of the graph :Dg?_P_@J
00212
00021
20001
12000
21100
[5, 4, 3, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10510101010(5t+5t2)/(1-t)10
20031957115(3t2+7t3-t4-11t5+11t6-3t7)/(1-t)4(-30+9t-3t2+6t3)/3!
30000440(4t4+16t5-5t6-31t7+31t8-10t9+t10)/(1-t)6(-3120+3834t-725t2-120t3+5t4+6t5)/5!
4000000(22t7+13t8-28t9+13t10-2t11)/(1-t)7(720+17196t-7818t2-2130t3+1680t4-306t5+18t6)/6!
5000000(18t10-18t11+7t12-t13)/(1-t)9(483840-179328t-59128t2-43792t3+56294t4-18592t5+2828t6-208t7+6t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dg?_@_PJpicture of the graph :Dg?_@_PJ
00221
00012
20001
21000
12100
[5, 4, 3, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
1059999(5t+4t2)/(1-t)9
20021854102(2t2+12t3+6t4-8t5+2t6)/(1-t)3(4-30t+14t2)/2!
30000228(2t4+18t5+18t6-24t7+8t8-t9)/(1-t)5(-1008+486t+255t2-162t3+21t4)/4!
4000000(12t7+27t8-32t9+13t10-2t11)/(1-t)7(-16560+20652t-1218t2-5550t3+2280t4-342t5+18t6)/6!
5000000(18t10-18t11+7t12-t13)/(1-t)9(483840-179328t-59128t2-43792t3+56294t4-18592t5+2828t6-208t7+6t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dg?_@E@Jpicture of the graph :Dg?_@E@J
00221
00021
20001
22000
11100
[5, 4, 3, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
1059999(5t+4t2)/(1-t)9
20021853100(2t2+12t3+5t4-7t5+2t6)/(1-t)3(10-32t+14t2)/2!
30000126(t4+21t5+15t6-25t7+10t8-t9)/(1-t)5(24-130t+375t2-170t3+21t4)/4!
4000000(10t7+33t8-38t9+15t10-2t11)/(1-t)7(12240+2892t+2382t2-5790t3+2280t4-342t5+18t6)/6!
5000000(18t10-18t11+7t12-t13)/(1-t)9(483840-179328t-59128t2-43792t3+56294t4-18592t5+2828t6-208t7+6t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dg?A@E@Jpicture of the graph :Dg?A@E@J
00311
00021
30001
12000
11100
[5, 4, 3, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10510101010(5t+5t2)/(1-t)10
20031956112(3t2+7t3-2t4-10t5+12t6-4t7)/(1-t)4(12-3t-3t2+6t3)/3!
30000337(3t4+19t5-7t6-34t7+36t8-12t9+t10)/(1-t)6(120+2114t-425t2-140t3+5t4+6t5)/5!
4000000(21t7+16t8-31t9+14t10-2t11)/(1-t)7(15120+8316t-6018t2-2250t3+1680t4-306t5+18t6)/6!
5000000(18t10-18t11+7t12-t13)/(1-t)9(483840-179328t-59128t2-43792t3+56294t4-18592t5+2828t6-208t7+6t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:DgGE@CaNpicture of the graph :DgGE@CaN
00111
00012
10002
11001
12210
[6, 3, 3, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
1059999(5t+4t2)/(1-t)9
2000124693(12t3+10t4-9t5+3t6)/(1-t)3(36-50t+16t2)/2!
3000009(9t5+31t6-25t7+11t8-2t9)/(1-t)5(816-1560t+1008t2-264t3+24t4)/4!
4000000(2t7+33t8-31t9+15t10-3t11)/(1-t)7(-3600-27000t+29944t2-13680t3+3160t4-360t5+16t6)/6!
5000000(10t10-10t11+5t12-t13)/(1-t)9(-1209600+176160t+456592t2-316568t3+105476t4-20720t5+2408t6-152t7+4t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dg?_WCQNpicture of the graph :Dg?_WCQN
00211
00012
20001
11001
12110
[5, 4, 3, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
1059999(5t+4t2)/(1-t)9
2002185399(2t2+12t3+5t4-8t5+3t6)/(1-t)3(18-34t+14t2)/2!
30000125(t4+20t5+18t6-29t7+13t8-2t9)/(1-t)5(-240-22t+363t2-170t3+21t4)/4!
4000000(9t7+37t8-44t9+19t10-3t11)/(1-t)7(1440+6852t+2022t2-5790t3+2280t4-342t5+18t6)/6!
5000000(18t10-18t11+7t12-t13)/(1-t)9(483840-179328t-59128t2-43792t3+56294t4-18592t5+2828t6-208t7+6t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dg?_P_QNpicture of the graph :Dg?_P_QN
00211
00021
20001
12001
11110
[4, 4, 4, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
1059999(5t+4t2)/(1-t)9
2003205395(3t2+11t3+2t4-7t5+3t6)/(1-t)3(10-24t+12t2)/2!
30000339(3t4+24t5+6t6-30t7+15t8-2t9)/(1-t)5(-264+680t-88t2-80t3+16t4)/4!
4000000(18t7+33t8-55t9+23t10-3t11)/(1-t)7(7920+52296t-39176t2+7680t3+280t4-216t5+16t6)/6!
5000000(27t10-27t11+9t12-t13)/(1-t)9(725760+1394208t-1646352t2+551936t3-50008t4-10528t5+2912t6-256t7+8t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:DgG?gCPJpicture of the graph :DgG?gCPJ
00121
00003
10011
20100
13100
[5, 4, 3, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10511141720(5t+t2-3t3)/(1-t)25+3t
20042362120(4t2+7t3-6t4-6t5+6t6-2t7)/(1-t)4(60-78t+27t2+3t3)/3!
30000235(2t4+25t5+7t6-20t7+11t8-2t9)/(1-t)5(120-386t+481t2-190t3+23t4)/4!
4000000(12t7+30t8-39t9+18t10-3t11)/(1-t)7(8640-4788t+7362t2-6750t3+2340t4-342t5+18t6)/6!
5000000(18t10-18t11+7t12-t13)/(1-t)9(483840-179328t-59128t2-43792t3+56294t4-18592t5+2828t6-208t7+6t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:DgGI@CQNpicture of the graph :DgGI@CQN
00111
00003
10011
10101
13110
[6, 3, 3, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
10511151923(5t+t2-2t3)/(1-t)23+4t
20021856116(2t2+10t3-4t4-8t5+5t6-t7)/(1-t)4(36-73t+21t2+4t3)/3!
30000018(18t5+15t6-16t7+10t8-3t9)/(1-t)5(-168-920t+828t2-244t3+24t4)/4!
4000000(2t7+34t8-34t9+18t10-4t11)/(1-t)7(-28800-14160t+27784t2-13560t3+3160t4-360t5+16t6)/6!
5000000(10t10-10t11+5t12-t13)/(1-t)9(-1209600+176160t+456592t2-316568t3+105476t4-20720t5+2408t6-152t7+4t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:DgGCQ_QNpicture of the graph :DgGCQ_QN
00111
00021
10011
12101
11110
[5, 4, 3, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
1058888(5t+3t2)/(1-t)8
2001175191(t2+14t3+3t4-12t5+3t6)/(1-t)3(-38-t+9t2)/2!
30000018(18t5+25t6-39t7+17t8-3t9)/(1-t)5(-1368+940t+54t2-124t3+18t4)/4!
4000000(3t7+53t8-59t9+25t10-4t11)/(1-t)7(-12960+23832t-5448t2-4410t3+2190t4-342t5+18t6)/6!
5000000(18t10-18t11+7t12-t13)/(1-t)9(483840-179328t-59128t2-43792t3+56294t4-18592t5+2828t6-208t7+6t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dg@_@_QJpicture of the graph :Dg@_@_QJ
00121
00111
11002
21000
11200
[4, 4, 4, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
1058888(5t+3t2)/(1-t)8
2002195082(2t2+13t3-t4-13t5+5t6)/(1-t)3(-36+10t+6t2)/2!
30000127(t4+22t5+18t6-46t7+19t8-2t9)/(1-t)5(-1272+1864t-516t2-16t3+12t4)/4!
4000000(12t7+47t8-65t9+25t10-3t11)/(1-t)7(-6480+75576t-49856t2+9600t3+160t4-216t5+16t6)/6!
5000000(27t10-27t11+9t12-t13)/(1-t)9(725760+1394208t-1646352t2+551936t3-50008t4-10528t5+2912t6-256t7+8t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dg@_@E@Jpicture of the graph :Dg@_@E@J
00121
00121
11001
22000
11100
[4, 4, 4, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
1058888(5t+3t2)/(1-t)8
2002195087(2t2+13t3-t4-8t5+2t6)/(1-t)3(-36+2t+8t2)/2!
30000132(t4+27t5+5t6-41t7+18t8-2t9)/(1-t)5(-1752+2544t-848t2+48t3+8t4)/4!
4000000(6t7+61t8-75t9+27t10-3t11)/(1-t)7(-20880+98856t-60536t2+11520t3+40t4-216t5+16t6)/6!
5000000(27t10-27t11+9t12-t13)/(1-t)9(725760+1394208t-1646352t2+551936t3-50008t4-10528t5+2912t6-256t7+8t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dg@_?E@Jpicture of the graph :Dg@_?E@J
00131
00111
11001
31000
11100
[5, 4, 3, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
1059999(5t+4t2)/(1-t)9
20021852102(2t2+10t3-8t4-6t5+11t6-3t7)/(1-t)4(-108+69t-15t2+6t3)/3!
30000028(28t5+11t6-36t7+18t8-3t9)/(1-t)5(-888+932t-54t2-104t3+18t4)/4!
4000000(2t7+56t8-62t9+26t10-4t11)/(1-t)7(1440+14952t-3648t2-4530t3+2190t4-342t5+18t6)/6!
5000000(18t10-18t11+7t12-t13)/(1-t)9(483840-179328t-59128t2-43792t3+56294t4-18592t5+2828t6-208t7+6t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dg?E@E@Jpicture of the graph :Dg?E@E@J
00211
00121
21001
12000
11100
[4, 4, 4, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
1058888(5t+3t2)/(1-t)8
2002195083(2t2+13t3-t4-12t5+4t6)/(1-t)3(-44+12t+6t2)/2!
30000128(t4+23t5+15t6-43t7+18t8-2t9)/(1-t)5(-1368+1888t-516t2-16t3+12t4)/4!
4000000(12t7+47t8-65t9+25t10-3t11)/(1-t)7(-6480+75576t-49856t2+9600t3+160t4-216t5+16t6)/6!
5000000(27t10-27t11+9t12-t13)/(1-t)9(725760+1394208t-1646352t2+551936t3-50008t4-10528t5+2912t6-256t7+8t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dg?E?E@Jpicture of the graph :Dg?E?E@J
00221
00111
21001
21000
11100
[5, 4, 3, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
1058888(5t+3t2)/(1-t)8
2001175190(t2+14t3+3t4-13t5+4t6)/(1-t)3(-30-3t+9t2)/2!
30000017(17t5+28t6-41t7+16t8-2t9)/(1-t)5(-912+784t+66t2-124t3+18t4)/4!
4000000(4t7+49t8-53t9+21t10-3t11)/(1-t)7(-2160+19872t-5088t2-4410t3+2190t4-342t5+18t6)/6!
5000000(18t10-18t11+7t12-t13)/(1-t)9(483840-179328t-59128t2-43792t3+56294t4-18592t5+2828t6-208t7+6t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dg@_W?QNpicture of the graph :Dg@_W?QN
00112
00111
11001
11001
21110
[5, 4, 3, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
1057777(5t+2t2)/(1-t)7
2000165084(16t3+2t4-18t5+6t6)/(1-t)3(-52+14t+6t2)/2!
30000012(12t5+40t6-53t7+22t8-3t9)/(1-t)5(-552+528t+138t2-132t3+18t4)/4!
4000000(t7+59t8-65t9+27t10-4t11)/(1-t)7(15840+6072t-1848t2-4650t3+2190t4-342t5+18t6)/6!
5000000(18t10-18t11+7t12-t13)/(1-t)9(483840-179328t-59128t2-43792t3+56294t4-18592t5+2828t6-208t7+6t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dg?E@_QNpicture of the graph :Dg?E@_QN
00211
00111
21001
11001
11110
[4, 4, 4, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
1057777(5t+2t2)/(1-t)7
2001184877(t2+15t3-3t4-14t5+5t6)/(1-t)3(-56+22t+4t2)/2!
30000023(23t5+19t6-56t7+25t8-3t9)/(1-t)5(-1368+2324t-788t2+40t3+8t4)/4!
4000000(3t7+71t8-87t9+33t10-4t11)/(1-t)7(-2880+85056t-57296t2+11280t3+40t4-216t5+16t6)/6!
5000000(27t10-27t11+9t12-t13)/(1-t)9(725760+1394208t-1646352t2+551936t3-50008t4-10528t5+2912t6-256t7+8t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Dg@_Q_QNpicture of the graph :Dg@_Q_QN
00111
00111
11011
11101
11110
[4, 4, 4, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k012345Poincaré seriesstable polynomial value
01111111/(1-t)1
1056666(5t+t2)/(1-t)6
2000174771(17t3+13t4-6t5)/(1-t)2-49+24t
30000018(18t5+30t6-66t7+30t8-4t9)/(1-t)5(-1248+2176t-728t2+32t3+8t4)/4!
4000000(81t8-99t9+39t10-5t11)/(1-t)7(15120+71256t-54056t2+11040t3+40t4-216t5+16t6)/6!
5000000(27t10-27t11+9t12-t13)/(1-t)9(725760+1394208t-1646352t2+551936t3-50008t4-10528t5+2912t6-256t7+8t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Ek?cWCbRpicture of the graph :Ek?cWCbR
000201
000021
000001
200001
020001
111110
[5, 3, 3, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104111930(4t-t2-2t3+2t4)/(1-t)3(8+t+3t2)/2!
20031962(3t2+7t3+4t4-2t5+t6-t7)/(1-t)4(84-24t-24t2+12t3)/3!
300006(6t4+6t5-7t6-3t7+7t8-3t9)/(1-t)6(5520-3496t+1030t2-170t3-10t4+6t5)/5!
400000(12t7+5t8-8t9+3t10)/(1-t)7(54000-45540t+21498t2-7860t3+1890t4-240t5+12t6)/6!
500000(6t10-4t11+t12)/(1-t)9(1572480-1505136t+760148t2-292964t3+84707t4-16184t5+1862t6-116t7+3t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Ek?A@E@Jpicture of the graph :Ek?A@E@J
000311
000021
000001
300000
120000
111000
[5, 3, 3, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104101418(4t+2t2-2t3)/(1-t)22+4t
20021446(2t2+6t3+2t4-6t5+3t6-t7)/(1-t)4(72-57t+3t2+6t3)/3!
300002(2t4+10t5-t6-15t7+10t8-3t9)/(1-t)6(5880-5998t+2895t2-665t3+45t4+3t5)/5!
400000(8t7+10t8-9t9+3t10)/(1-t)7(56160-54072t+28368t2-10110t3+2220t4-258t5+12t6)/6!
500000(6t10-4t11+t12)/(1-t)9(1572480-1505136t+760148t2-292964t3+84707t4-16184t5+1862t6-116t7+3t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:EkG?XCbNpicture of the graph :EkG?XCbN
000120
000012
000001
100002
210000
021200
[5, 3, 3, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104101316(4t+2t2-3t3)/(1-t)24+3t
20021344(2t2+5t3+4t4-8t5+3t6)/(1-t)4(-12-15t-3t2+6t3)/3!
300002(2t4+9t5+t6-15t7+7t8-t9)/(1-t)6(-240-1848t+1880t2-555t3+40t4+3t5)/5!
400000(8t7+9t8-7t9+2t10)/(1-t)7(30960-34932t+22998t2-9450t3+2190t4-258t5+12t6)/6!
500000(6t10-4t11+t12)/(1-t)9(1572480-1505136t+760148t2-292964t3+84707t4-16184t5+1862t6-116t7+3t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Ek?_PcQNpicture of the graph :Ek?_PcQN
000210
000022
000001
200001
120000
021100
[4, 4, 3, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
10491113(4t+t2-3t3)/(1-t)25+2t
20021446(2t2+6t3+2t4-9t5+3t6)/(1-t)4(24-61t+15t2+4t3)/3!
300004(4t4+7t5-t6-14t7+9t8-t9)/(1-t)6(-5760+4096t-490t2-140t3+10t4+4t5)/5!
400000(13t7+8t8-11t9+2t10)/(1-t)7(-51120+62484t-22602t2+1080t3+990t4-204t5+12t6)/6!
500000(9t10-6t11+t12)/(1-t)9(-967680+1689216t-873856t2+138264t3+25116t4-12936t5+2016t6-144t7+4t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Ek?_@cQNpicture of the graph :Ek?_@cQN
000220
000012
000001
200001
210000
021100
[4, 4, 3, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
10491113(4t+t2-3t3)/(1-t)25+2t
20021444(2t2+6t3-9t5+3t6)/(1-t)4(36-83t+27t2+2t3)/3!
300002(2t4+13t5+10t6-8t7+t8)/(1-t)5(-528-104t+414t2-160t3+18t4)/4!
400000(9t7+12t8-11t9+2t10)/(1-t)7(-33840+37428t-8682t2-2640t3+1470t4-228t5+12t6)/6!
500000(9t10-6t11+t12)/(1-t)9(-967680+1689216t-873856t2+138264t3+25116t4-12936t5+2016t6-144t7+4t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Ek?_@EQNpicture of the graph :Ek?_@EQN
000220
000021
000001
200001
220000
011100
[4, 4, 3, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
1048910(4t-3t3)/(1-t)26+t
20011240(t2+9t3+7t4-3t5)/(1-t)3(24-42t+14t2)/2!
300001(t4+13t5+11t6-10t7+t8)/(1-t)5(-1128+432t+236t2-132t3+16t4)/4!
400000(7t7+16t8-13t9+2t10)/(1-t)7(-55440+57948t-15822t2-1560t3+1410t4-228t5+12t6)/6!
500000(9t10-6t11+t12)/(1-t)9(-967680+1689216t-873856t2+138264t3+25116t4-12936t5+2016t6-144t7+4t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Ek?A@EQNpicture of the graph :Ek?A@EQN
000310
000021
000001
300001
120000
011100
[4, 4, 3, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
10491011(4t+t2-4t3)/(1-t)27+t
20021342(2t2+5t3+2t4-9t5+5t6-t7)/(1-t)4(24-43t+9t2+4t3)/3!
300002(2t4+12t5-3t6-20t7+16t8-3t9)/(1-t)6(-5400+4806t-905t2-70t3+5t4+4t5)/5!
400000(11t7+13t8-15t9+3t10)/(1-t)7(-47520+63864t-24372t2+1500t3+960t4-204t5+12t6)/6!
500000(9t10-6t11+t12)/(1-t)9(-967680+1689216t-873856t2+138264t3+25116t4-12936t5+2016t6-144t7+4t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:EkGCWCbNpicture of the graph :EkGCWCbN
000111
000021
000001
100002
120000
111200
[5, 3, 3, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104101316(4t+2t2-3t3)/(1-t)24+3t
20021343(2t2+5t3+3t4-7t5+4t6-t7)/(1-t)4(30-27t-3t2+6t3)/3!
300001(t4+12t5-t6-18t7+12t8-3t9)/(1-t)6(3000-3568t+2180t2-575t3+40t4+3t5)/5!
400000(7t7+12t8-10t9+3t10)/(1-t)7(45360-43812t+24798t2-9570t3+2190t4-258t5+12t6)/6!
500000(6t10-4t11+t12)/(1-t)9(1572480-1505136t+760148t2-292964t3+84707t4-16184t5+1862t6-116t7+3t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Ek?_P_QNpicture of the graph :Ek?_P_QN
000211
000021
000001
200001
120000
111100
[4, 4, 3, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
10491113(4t+t2-3t3)/(1-t)25+2t
20021445(2t2+6t3+t4-8t5+4t6-t7)/(1-t)4(66-73t+15t2+4t3)/3!
300003(3t4+10t5-3t6-17t7+14t8-3t9)/(1-t)6(-2520+2376t-190t2-160t3+10t4+4t5)/5!
400000(12t7+11t8-14t9+3t10)/(1-t)7(-36720+53604t-20802t2+960t3+990t4-204t5+12t6)/6!
500000(9t10-6t11+t12)/(1-t)9(-967680+1689216t-873856t2+138264t3+25116t4-12936t5+2016t6-144t7+4t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:EkHCg?QJpicture of the graph :EkHCg?QJ
000102
000021
000012
100000
021000
212000
[5, 3, 3, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104101418(4t+2t2-2t3)/(1-t)22+4t
20021446(2t2+6t3+2t4-7t5+3t6)/(1-t)4(-24-9t-3t2+6t3)/3!
300002(2t4+9t5+t6-15t7+7t8-t9)/(1-t)6(-240-1848t+1880t2-555t3+40t4+3t5)/5!
400000(8t7+9t8-7t9+2t10)/(1-t)7(30960-34932t+22998t2-9450t3+2190t4-258t5+12t6)/6!
500000(6t10-4t11+t12)/(1-t)9(1572480-1505136t+760148t2-292964t3+84707t4-16184t5+1862t6-116t7+3t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:EkHCa_@Jpicture of the graph :EkHCa_@J
000102
000021
000021
100000
022000
211000
[4, 4, 3, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
10491215(4t+t2-2t3)/(1-t)23+3t
20021546(2t2+7t3-2t4-8t5+3t6)/(1-t)4(24-77t+27t2+2t3)/3!
300002(2t4+13t5+10t6-8t7+t8)/(1-t)5(-528-104t+414t2-160t3+18t4)/4!
400000(9t7+12t8-11t9+2t10)/(1-t)7(-33840+37428t-8682t2-2640t3+1470t4-228t5+12t6)/6!
500000(9t10-6t11+t12)/(1-t)9(-967680+1689216t-873856t2+138264t3+25116t4-12936t5+2016t6-144t7+4t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Ek?cQ_PNpicture of the graph :Ek?cQ_PN
000201
000022
000010
200001
021000
120100
[4, 4, 3, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104101520(4t+2t2-t3)/(1-t)25t
20031853(3t2+6t3-t4-4t5+2t6)/(1-t)4(-18-12t+6t3)/3!
300004(4t4+10t5-8t6-9t7+8t8-t9)/(1-t)6(-6000+4716t-790t2-100t3+10t4+4t5)/5!
400000(13t7+8t8-11t9+2t10)/(1-t)7(-51120+62484t-22602t2+1080t3+990t4-204t5+12t6)/6!
500000(9t10-6t11+t12)/(1-t)9(-967680+1689216t-873856t2+138264t3+25116t4-12936t5+2016t6-144t7+4t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Ek?cgCRRpicture of the graph :Ek?cgCRR
000201
000012
000010
200001
011001
120110
[5, 3, 3, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104101418(4t+2t2-2t3)/(1-t)22+4t
20021445(2t2+6t3+t4-5t5+3t6-t7)/(1-t)4(54-42t+6t3)/3!
300001(t4+13t5-4t6-15t7+11t8-3t9)/(1-t)6(3720-3988t+2240t2-575t3+40t4+3t5)/5!
400000(7t7+12t8-10t9+3t10)/(1-t)7(45360-43812t+24798t2-9570t3+2190t4-258t5+12t6)/6!
500000(6t10-4t11+t12)/(1-t)9(1572480-1505136t+760148t2-292964t3+84707t4-16184t5+1862t6-116t7+3t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Ek?cQ_RRpicture of the graph :Ek?cQ_RR
000201
000021
000010
200001
021001
110110
[4, 4, 3, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104101418(4t+2t2-2t3)/(1-t)22+4t
20031750(3t2+5t3-4t5+3t6-t7)/(1-t)4(36-30t+6t3)/3!
300003(3t4+13t5-10t6-12t7+13t8-3t9)/(1-t)6(-2760+2996t-490t2-120t3+10t4+4t5)/5!
400000(12t7+11t8-14t9+3t10)/(1-t)7(-36720+53604t-20802t2+960t3+990t4-204t5+12t6)/6!
500000(9t10-6t11+t12)/(1-t)9(-967680+1689216t-873856t2+138264t3+25116t4-12936t5+2016t6-144t7+4t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:EkGCwCQNpicture of the graph :EkGCwCQN
000111
000012
000001
100011
110100
121100
[5, 3, 3, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
10491215(4t+t2-2t3)/(1-t)23+3t
20011241(t2+8t3-t4-10t5+6t6-t7)/(1-t)4(6-48t+15t2+3t3)/3!
300000(10t5+18t6-14t7+4t8)/(1-t)5(720-1036t+678t2-188t3+18t4)/4!
400000(t7+22t8-15t9+4t10)/(1-t)7(51120-50964t+29898t2-11400t3+2490t4-276t5+12t6)/6!
500000(6t10-4t11+t12)/(1-t)9(1572480-1505136t+760148t2-292964t3+84707t4-16184t5+1862t6-116t7+3t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:EkGCR_QNpicture of the graph :EkGCR_QN
000111
000021
000001
100011
120100
111100
[4, 4, 3, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
10481012(4t-2t3)/(1-t)24+2t
20011341(t2+10t3+5t4-5t5+t6)/(1-t)3(10-30t+12t2)/2!
300000(13t5+15t6-18t7+4t8)/(1-t)5(-1008+644t+94t2-104t3+14t4)/4!
400000(3t7+26t8-21t9+4t10)/(1-t)7(-48240+60708t-19362t2-720t3+1350t4-228t5+12t6)/6!
500000(9t10-6t11+t12)/(1-t)9(-967680+1689216t-873856t2+138264t3+25116t4-12936t5+2016t6-144t7+4t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Ek?E@E@Jpicture of the graph :Ek?E@E@J
000211
000121
000001
210000
120000
111000
[4, 4, 3, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
1048910(4t-3t3)/(1-t)26+t
20011240(t2+9t3+7t4-6t5+t6)/(1-t)3(8-30t+12t2)/2!
300001(t4+10t5+18t6-16t7+3t8)/(1-t)5(-840+280t+272t2-136t3+16t4)/4!
400000(6t7+19t8-16t9+3t10)/(1-t)7(-41040+49068t-14022t2-1680t3+1410t4-228t5+12t6)/6!
500000(9t10-6t11+t12)/(1-t)9(-967680+1689216t-873856t2+138264t3+25116t4-12936t5+2016t6-144t7+4t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Ek?E?E@Jpicture of the graph :Ek?E?E@J
000221
000111
000001
210000
210000
111000
[5, 3, 3, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
1048910(4t-3t3)/(1-t)26+t
2000936(9t3+9t4-6t5+t6)/(1-t)3(20-39t+13t2)/2!
300000(6t5+23t6-14t7+3t8)/(1-t)5(384-968t+714t2-196t3+18t4)/4!
400000(2t7+19t8-12t9+3t10)/(1-t)7(36720-42084t+28098t2-11280t3+2490t4-276t5+12t6)/6!
500000(6t10-4t11+t12)/(1-t)9(1572480-1505136t+760148t2-292964t3+84707t4-16184t5+1862t6-116t7+3t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Ek@_@_QNpicture of the graph :Ek@_@_QN
000121
000111
000001
110001
210000
111100
[4, 4, 3, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
10481012(4t-2t3)/(1-t)24+2t
20011341(t2+10t3+5t4-7t5+t6)/(1-t)3(-14-16t+10t2)/2!
300000(11t5+19t6-20t7+4t8)/(1-t)5(-1296+812t+70t2-104t3+14t4)/4!
400000(3t7+26t8-21t9+4t10)/(1-t)7(-48240+60708t-19362t2-720t3+1350t4-228t5+12t6)/6!
500000(9t10-6t11+t12)/(1-t)9(-967680+1689216t-873856t2+138264t3+25116t4-12936t5+2016t6-144t7+4t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Ek@_WCbRpicture of the graph :Ek@_WCbR
000111
000111
000001
110001
110001
111110
[5, 3, 3, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
10481114(4t-t3)/(1-t)22+3t
20001140(11t3+7t4-8t5+2t6)/(1-t)3(8-30t+12t2)/2!
300000(4t5+28t6-20t7+6t8)/(1-t)5(1296-1500t+822t2-204t3+18t4)/4!
400000(25t8-18t9+5t10)/(1-t)7(65520-59844t+31698t2-11520t3+2490t4-276t5+12t6)/6!
500000(6t10-4t11+t12)/(1-t)9(1572480-1505136t+760148t2-292964t3+84707t4-16184t5+1862t6-116t7+3t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Ek@_aIANpicture of the graph :Ek@_aIAN
000111
000100
000031
110001
103000
101100
[4, 4, 3, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
10491011(4t+t2-4t3)/(1-t)27+t
20021340(2t2+5t3-9t5+7t6-t7)/(1-t)4(-84+29t-3t2+4t3)/3!
300000(16t5+13t6-20t7+4t8)/(1-t)5(-1896+1486t-181t2-70t3+13t4)/4!
400000(2t7+28t8-22t9+4t10)/(1-t)7(-59040+70968t-22932t2-180t3+1320t4-228t5+12t6)/6!
500000(9t10-6t11+t12)/(1-t)9(-967680+1689216t-873856t2+138264t3+25116t4-12936t5+2016t6-144t7+4t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Ek@_a_ANpicture of the graph :Ek@_a_AN
000112
000100
000021
110001
102000
201100
[4, 4, 3, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
10491011(4t+t2-4t3)/(1-t)27+t
20021341(2t2+5t3+t4-9t5+6t6-t7)/(1-t)4(-30-7t+3t2+4t3)/3!
300001(t4+14t5-3t6-23t7+18t8-3t9)/(1-t)6(-8280+7236t-1620t2+20t3+4t5)/5!
400000(10t7+15t8-16t9+3t10)/(1-t)7(-58320+74124t-27942t2+2040t3+930t4-204t5+12t6)/6!
500000(9t10-6t11+t12)/(1-t)9(-967680+1689216t-873856t2+138264t3+25116t4-12936t5+2016t6-144t7+4t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Ek@_A_aNpicture of the graph :Ek@_A_aN
000121
000100
000012
110001
201000
102100
[4, 4, 3, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
1048910(4t-3t3)/(1-t)26+t
20011240(t2+9t3+7t4-5t5)/(1-t)3(-28t+12t2)/2!
300001(t4+11t5+15t6-13t7+2t8)/(1-t)5(-936+304t+272t2-136t3+16t4)/4!
400000(6t7+19t8-16t9+3t10)/(1-t)7(-41040+49068t-14022t2-1680t3+1410t4-228t5+12t6)/6!
500000(9t10-6t11+t12)/(1-t)9(-967680+1689216t-873856t2+138264t3+25116t4-12936t5+2016t6-144t7+4t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Ek@_AIANpicture of the graph :Ek@_AIAN
000121
000100
000021
110001
202000
101100
[4, 4, 3, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
1048910(4t-3t3)/(1-t)26+t
20011239(t2+9t3+6t4-5t5)/(1-t)3(-6-23t+11t2)/2!
300000(13t5+14t6-15t7+2t8)/(1-t)5(-1728+1048t+22t2-100t3+14t4)/4!
400000(4t7+23t8-18t9+3t10)/(1-t)7(-62640+69588t-21162t2-600t3+1350t4-228t5+12t6)/6!
500000(9t10-6t11+t12)/(1-t)9(-967680+1689216t-873856t2+138264t3+25116t4-12936t5+2016t6-144t7+4t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Ek?EAIANpicture of the graph :Ek?EAIAN
000211
000100
000021
210001
102000
101100
[4, 4, 3, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
10491113(4t+t2-3t3)/(1-t)25+2t
20021443(2t2+6t3-t4-8t5+6t6-t7)/(1-t)4(-42-t+3t2+4t3)/3!
300001(t4+14t5-3t6-23t7+18t8-3t9)/(1-t)6(-8280+7236t-1620t2+20t3+4t5)/5!
400000(10t7+15t8-16t9+3t10)/(1-t)7(-58320+74124t-27942t2+2040t3+930t4-204t5+12t6)/6!
500000(9t10-6t11+t12)/(1-t)9(-967680+1689216t-873856t2+138264t3+25116t4-12936t5+2016t6-144t7+4t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Ek@CWIBRpicture of the graph :Ek@CWIBR
000111
000300
000010
130001
101001
100110
[5, 3, 3, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104101418(4t+2t2-2t3)/(1-t)22+4t
20021444(2t2+6t3-7t5+3t6-t7)/(1-t)4(108-105t+24t2+3t3)/3!
300000(13t5+12t6-10t7+4t8)/(1-t)5(1512-1630t+833t2-206t3+19t4)/4!
400000(2t7+20t8-14t9+4t10)/(1-t)7(61920-61224t+33468t2-11940t3+2520t4-276t5+12t6)/6!
500000(6t10-4t11+t12)/(1-t)9(1572480-1505136t+760148t2-292964t3+84707t4-16184t5+1862t6-116t7+3t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Ek@_AcRRpicture of the graph :Ek@_AcRR
000120
000102
000010
110001
201001
020110
[4, 4, 3, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
10491113(4t+t2-3t3)/(1-t)25+2t
20021443(2t2+6t3-t4-10t5+6t6-t7)/(1-t)4(6-53t+21t2+2t3)/3!
300001(t4+13t5+14t6-15t7+3t8)/(1-t)5(-888+404t+212t2-128t3+16t4)/4!
400000(6t7+19t8-16t9+3t10)/(1-t)7(-41040+49068t-14022t2-1680t3+1410t4-228t5+12t6)/6!
500000(9t10-6t11+t12)/(1-t)9(-967680+1689216t-873856t2+138264t3+25116t4-12936t5+2016t6-144t7+4t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Ek@E?IRRpicture of the graph :Ek@E?IRR
000120
000201
000010
120001
201001
010110
[4, 4, 3, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
10491113(4t+t2-3t3)/(1-t)25+2t
20021443(2t2+6t3-t4-10t5+6t6-t7)/(1-t)4(6-53t+21t2+2t3)/3!
300001(t4+13t5+14t6-15t7+3t8)/(1-t)5(-888+404t+212t2-128t3+16t4)/4!
400000(6t7+19t8-16t9+3t10)/(1-t)7(-41040+49068t-14022t2-1680t3+1410t4-228t5+12t6)/6!
500000(9t10-6t11+t12)/(1-t)9(-967680+1689216t-873856t2+138264t3+25116t4-12936t5+2016t6-144t7+4t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Ek?EAcRRpicture of the graph :Ek?EAcRR
000210
000102
000010
210001
101001
020110
[4, 4, 3, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
1048910(4t-3t3)/(1-t)26+t
20011240(t2+9t3+7t4-5t5+t6)/(1-t)3(20-37t+13t2)/2!
300001(t4+11t5+16t6-15t7+3t8)/(1-t)5(-696+196t+284t2-136t3+16t4)/4!
400000(6t7+19t8-16t9+3t10)/(1-t)7(-41040+49068t-14022t2-1680t3+1410t4-228t5+12t6)/6!
500000(9t10-6t11+t12)/(1-t)9(-967680+1689216t-873856t2+138264t3+25116t4-12936t5+2016t6-144t7+4t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Ek?CWIRRpicture of the graph :Ek?CWIRR
000210
000201
000010
220001
101001
010110
[5, 3, 3, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
1048910(4t-3t3)/(1-t)26+t
2000936(9t3+9t4-5t5+t6)/(1-t)3(32-46t+14t2)/2!
300000(7t5+21t6-13t7+3t8)/(1-t)5(528-1052t+726t2-196t3+18t4)/4!
400000(2t7+19t8-12t9+3t10)/(1-t)7(36720-42084t+28098t2-11280t3+2490t4-276t5+12t6)/6!
500000(6t10-4t11+t12)/(1-t)9(1572480-1505136t+760148t2-292964t3+84707t4-16184t5+1862t6-116t7+3t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Ek@_gCRRpicture of the graph :Ek@_gCRR
000111
000102
000010
110001
101001
120110
[5, 3, 3, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
1048910(4t-3t3)/(1-t)26+t
2000936(9t3+9t4-6t5+t6)/(1-t)3(20-39t+13t2)/2!
300000(6t5+23t6-15t7+4t8)/(1-t)5(864-1264t+774t2-200t3+18t4)/4!
400000(t7+22t8-15t9+4t10)/(1-t)7(51120-50964t+29898t2-11400t3+2490t4-276t5+12t6)/6!
500000(6t10-4t11+t12)/(1-t)9(1572480-1505136t+760148t2-292964t3+84707t4-16184t5+1862t6-116t7+3t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Ek@EA_RRpicture of the graph :Ek@EA_RR
000111
000201
000010
120001
101001
110110
[4, 4, 3, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
1048910(4t-3t3)/(1-t)26+t
20011239(t2+9t3+6t4-6t5+t6)/(1-t)3(2-25t+11t2)/2!
300000(12t5+17t6-19t7+4t8)/(1-t)5(-1152+728t+82t2-104t3+14t4)/4!
400000(3t7+26t8-21t9+4t10)/(1-t)7(-48240+60708t-19362t2-720t3+1350t4-228t5+12t6)/6!
500000(9t10-6t11+t12)/(1-t)9(-967680+1689216t-873856t2+138264t3+25116t4-12936t5+2016t6-144t7+4t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Ek@_Q_RNpicture of the graph :Ek@_Q_RN
000111
000111
000010
110002
111000
110200
[4, 4, 3, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104789(4t-t2-2t3)/(1-t)25+t
20001138(11t3+5t4-12t5+2t6)/(1-t)3(-52+8t+6t2)/2!
300000(6t5+30t6-29t7+5t8)/(1-t)5(-2496+1808t-216t2-68t3+12t4)/4!
400000(t7+30t8-23t9+4t10)/(1-t)7(-69840+81228t-26502t2+360t3+1290t4-228t5+12t6)/6!
500000(9t10-6t11+t12)/(1-t)9(-967680+1689216t-873856t2+138264t3+25116t4-12936t5+2016t6-144t7+4t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Ek@_@I@Npicture of the graph :Ek@_@I@N
000121
000111
000010
110001
211000
110100
[4, 4, 3, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
10481012(4t-2t3)/(1-t)24+2t
20011341(t2+9t3-5t4-8t5+8t6-t7)/(1-t)4(-138+56t-6t2+4t3)/3!
300000(15t5+15t6-22t7+4t8)/(1-t)5(-2400+1912t-312t2-52t3+12t4)/4!
400000(t7+30t8-23t9+4t10)/(1-t)7(-69840+81228t-26502t2+360t3+1290t4-228t5+12t6)/6!
500000(9t10-6t11+t12)/(1-t)9(-967680+1689216t-873856t2+138264t3+25116t4-12936t5+2016t6-144t7+4t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Ek?E@I@Npicture of the graph :Ek?E@I@N
000211
000111
000010
210001
111000
110100
[4, 4, 3, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104789(4t-t2-2t3)/(1-t)25+t
20001138(11t3+5t4-11t5+2t6)/(1-t)3(-40+t+7t2)/2!
300000(7t5+28t6-28t7+5t8)/(1-t)5(-2352+1724t-204t2-68t3+12t4)/4!
400000(t7+30t8-23t9+4t10)/(1-t)7(-69840+81228t-26502t2+360t3+1290t4-228t5+12t6)/6!
500000(9t10-6t11+t12)/(1-t)9(-967680+1689216t-873856t2+138264t3+25116t4-12936t5+2016t6-144t7+4t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Ek@_R_QNpicture of the graph :Ek@_R_QN
000111
000111
000001
110011
110100
111100
[4, 4, 3, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
1047911(4t-t2-t3)/(1-t)23+2t
20001240(12t3+4t4-10t5+2t6)/(1-t)3(-32-4t+8t2)/2!
300000(8t5+26t6-28t7+6t8)/(1-t)5(-1728+1344t-132t2-72t3+12t4)/4!
400000(33t8-26t9+5t10)/(1-t)7(-55440+72348t-24702t2+240t3+1290t4-228t5+12t6)/6!
500000(9t10-6t11+t12)/(1-t)9(-967680+1689216t-873856t2+138264t3+25116t4-12936t5+2016t6-144t7+4t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:EgH_A_PJpicture of the graph :EgH_A_PJ
001021
000102
100011
010000
201000
121000
[4, 4, 3, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
10491215(4t+t2-2t3)/(1-t)23+3t
20021545(2t2+7t3-3t4-8t5+4t6)/(1-t)4(-30-41t+21t2+2t3)/3!
300001(t4+14t5+11t6-12t7+2t8)/(1-t)5(-984+428t+212t2-128t3+16t4)/4!
400000(6t7+19t8-16t9+3t10)/(1-t)7(-41040+49068t-14022t2-1680t3+1410t4-228t5+12t6)/6!
500000(9t10-6t11+t12)/(1-t)9(-967680+1689216t-873856t2+138264t3+25116t4-12936t5+2016t6-144t7+4t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:EgH_gCQRpicture of the graph :EgH_gCQR
001011
000102
100011
010000
101001
121010
[5, 3, 3, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
10491317(4t+t2-t3)/(1-t)21+4t
20011343(t2+9t3-3t4-8t5+4t6)/(1-t)4(-30-36t+15t2+3t3)/3!
300000(11t5+15t6-11t7+3t8)/(1-t)5(624-1012t+678t2-188t3+18t4)/4!
400000(t7+22t8-15t9+4t10)/(1-t)7(51120-50964t+29898t2-11400t3+2490t4-276t5+12t6)/6!
500000(6t10-4t11+t12)/(1-t)9(1572480-1505136t+760148t2-292964t3+84707t4-16184t5+1862t6-116t7+3t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:EgH_Q_QRpicture of the graph :EgH_Q_QR
001011
000111
100011
010000
111001
111010
[4, 4, 3, 3, 3, 1]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104789(4t-t2-2t3)/(1-t)25+t
20001138(11t3+5t4-10t5+2t6)/(1-t)3(-28-6t+8t2)/2!
300000(8t5+26t6-28t7+6t8)/(1-t)5(-1728+1344t-132t2-72t3+12t4)/4!
400000(33t8-26t9+5t10)/(1-t)7(-55440+72348t-24702t2+240t3+1290t4-228t5+12t6)/6!
500000(9t10-6t11+t12)/(1-t)9(-967680+1689216t-873856t2+138264t3+25116t4-12936t5+2016t6-144t7+4t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Fo?_PcbRpicture of the graph :Fo?_PcbR
0000210
0000021
0000001
0000001
2000001
1200000
0111100
[4, 3, 3, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
103813(3t-t2-2t3+2t4)/(1-t)3(8+2t2)/2!
200110(t2+6t3+4t4-4t5+t6)/(1-t)4(12-2t-18t2+8t3)/3!
30000(3t4+4t5-6t7+3t8)/(1-t)6(-3240+2076t-230t2-40t3-10t4+4t5)/5!
40000(6t7+5t8-3t9)/(1-t)7(-30960+22932t-1198t2-3330t3+1190t4-162t5+8t6)/6!
50000(3t10-t11)/(1-t)9(-725760+601632t-53496t2-106400t3+52178t4-11312t5+1316t6-80t7+2t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Fo?_PIRRpicture of the graph :Fo?_PIRR
0000210
0000021
0000010
0000001
2000001
1210000
0101100
[4, 3, 3, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
103811(3t+2t2-2t3)/(1-t)22+3t
20018(t2+4t3+4t4-6t5+t6)/(1-t)4(60-58t+6t2+4t3)/3!
30000(t4+6t5+2t6-10t7+3t8)/(1-t)6(-600-1492t+1530t2-430t3+30t4+2t5)/5!
40000(4t7+7t8-3t9)/(1-t)7(-22320+10404t+5762t2-5190t3+1430t4-174t5+8t6)/6!
50000(3t10-t11)/(1-t)9(-725760+601632t-53496t2-106400t3+52178t4-11312t5+1316t6-80t7+2t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Fo@_P_bRpicture of the graph :Fo@_P_bR
0000111
0000120
0000001
0000001
1100001
1200000
1011100
[4, 3, 3, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
103813(3t-t2-2t3+2t4)/(1-t)3(8+2t2)/2!
200110(t2+6t3+t4-6t5+2t6)/(1-t)4(18-40t+6t2+4t3)/3!
30000(8t5+2t6-13t7+5t8)/(1-t)6(-3480+938t+815t2-340t3+25t4+2t5)/5!
40000(3t7+9t8-4t9)/(1-t)7(-33120+20664t+2192t2-4650t3+1400t4-174t5+8t6)/6!
50000(3t10-t11)/(1-t)9(-725760+601632t-53496t2-106400t3+52178t4-11312t5+1316t6-80t7+2t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Fo@_AIbRpicture of the graph :Fo@_AIbR
0000120
0000100
0000021
0000001
1100001
2020000
0011100
[4, 3, 3, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
10379(3t+t2-2t3)/(1-t)23+2t
20006(6t3+2t4-8t5+t6)/(1-t)4(120-127t+30t2+t3)/3!
30000(6t5+11t6-3t7)/(1-t)5(384-968t+634t2-160t3+14t4)/4!
40000(2t7+9t8-3t9)/(1-t)7(-13680-2124t+12722t2-7050t3+1670t4-186t5+8t6)/6!
50000(3t10-t11)/(1-t)9(-725760+601632t-53496t2-106400t3+52178t4-11312t5+1316t6-80t7+2t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Fo?EAIbRpicture of the graph :Fo?EAIbR
0000210
0000100
0000021
0000001
2100001
1020000
0011100
[4, 3, 3, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
103811(3t+2t2-2t3)/(1-t)22+3t
20018(t2+4t3+4t4-6t5+t6)/(1-t)4(60-58t+6t2+4t3)/3!
30000(t4+6t5+2t6-10t7+3t8)/(1-t)6(-600-1492t+1530t2-430t3+30t4+2t5)/5!
40000(4t7+7t8-3t9)/(1-t)7(-22320+10404t+5762t2-5190t3+1430t4-174t5+8t6)/6!
50000(3t10-t11)/(1-t)9(-725760+601632t-53496t2-106400t3+52178t4-11312t5+1316t6-80t7+2t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Fo@_a_bRpicture of the graph :Fo@_a_bR
0000111
0000100
0000021
0000001
1100001
1020000
1011100
[4, 3, 3, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
103811(3t+2t2-2t3)/(1-t)22+3t
20018(t2+4t3+3t4-6t5+2t6)/(1-t)4(6-22t+4t3)/3!
30000(8t5+2t6-13t7+5t8)/(1-t)6(-3480+938t+815t2-340t3+25t4+2t5)/5!
40000(3t7+9t8-4t9)/(1-t)7(-33120+20664t+2192t2-4650t3+1400t4-174t5+8t6)/6!
50000(3t10-t11)/(1-t)9(-725760+601632t-53496t2-106400t3+52178t4-11312t5+1316t6-80t7+2t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Fo?E@I@Npicture of the graph :Fo?E@I@N
0000211
0000111
0000010
0000001
2100000
1110000
1101000
[4, 3, 3, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
10379(3t+t2-2t3)/(1-t)23+2t
20006(6t3+8t4-3t5)/(1-t)3(24-37t+11t2)/2!
30000(3t5+16t6-6t7)/(1-t)5(-168-562t+527t2-146t3+13t4)/4!
40000(t7+11t8-4t9)/(1-t)7(-24480+8136t+9152t2-6510t3+1640t4-186t5+8t6)/6!
50000(3t10-t11)/(1-t)9(-725760+601632t-53496t2-106400t3+52178t4-11312t5+1316t6-80t7+2t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Fo@_Q_RRpicture of the graph :Fo@_Q_RR
0000111
0000111
0000010
0000001
1100001
1110000
1101100
[4, 3, 3, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
103710(3t+t2-t3)/(1-t)21+3t
20007(7t3+7t4-4t5)/(1-t)3(8-28t+10t2)/2!
30000(2t5+18t6-8t7)/(1-t)5(-672-136t+396t2-128t3+12t4)/4!
40000(13t8-5t9)/(1-t)7(-35280+18396t+5582t2-5970t3+1610t4-186t5+8t6)/6!
50000(3t10-t11)/(1-t)9(-725760+601632t-53496t2-106400t3+52178t4-11312t5+1316t6-80t7+2t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Fo@_S_QNpicture of the graph :Fo@_S_QN
0000111
0000111
0000001
0000001
1100010
1100100
1111000
[4, 3, 3, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
103712(3t-2t2+t4)/(1-t)3(6+2t2)/2!
20009(9t3-2t4-7t5+4t6)/(1-t)4(-60+2t+4t3)/3!
30000(6t5+14t6-8t7)/(1-t)5(-1056+280t+252t2-112t3+12t4)/4!
40000(13t8-5t9)/(1-t)7(-35280+18396t+5582t2-5970t3+1610t4-186t5+8t6)/6!
50000(3t10-t11)/(1-t)9(-725760+601632t-53496t2-106400t3+52178t4-11312t5+1316t6-80t7+2t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:FkH_a_PJpicture of the graph :FkH_a_PJ
0001011
0000102
0000021
1000000
0100000
1020000
1210000
[4, 3, 3, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
103812(3t+2t2-t3)/(1-t)24t
20019(t2+5t3+2t4-5t5+t6)/(1-t)4(48-52t+6t2+4t3)/3!
30000(t4+6t5+2t6-10t7+3t8)/(1-t)6(-600-1492t+1530t2-430t3+30t4+2t5)/5!
40000(4t7+7t8-3t9)/(1-t)7(-22320+10404t+5762t2-5190t3+1430t4-174t5+8t6)/6!
50000(3t10-t11)/(1-t)9(-725760+601632t-53496t2-106400t3+52178t4-11312t5+1316t6-80t7+2t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:FkHEA_SVpicture of the graph :FkHEA_SV
0001011
0000201
0000010
1000000
0200001
1010001
1100110
[4, 3, 3, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
103812(3t+2t2-t3)/(1-t)24t
20019(t2+5t3+t4-4t5+2t6)/(1-t)4(-30+10t-9t2+5t3)/3!
30000(9t5-12t7+5t8)/(1-t)6(-3960+1458t+635t2-320t3+25t4+2t5)/5!
40000(3t7+9t8-4t9)/(1-t)7(-33120+20664t+2192t2-4650t3+1400t4-174t5+8t6)/6!
50000(3t10-t11)/(1-t)9(-725760+601632t-53496t2-106400t3+52178t4-11312t5+1316t6-80t7+2t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Fk?e@M@Jpicture of the graph :Fk?e@M@J
0002011
0000111
0000001
2000010
0100000
1101000
1110000
[4, 3, 3, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
10379(3t+t2-2t3)/(1-t)23+2t
20006(6t3+2t4-10t5+3t6)/(1-t)4(48-85t+24t2+t3)/3!
30000(4t5+15t6-6t7)/(1-t)5(-264-458t+491t2-142t3+13t4)/4!
40000(t7+11t8-4t9)/(1-t)7(-24480+8136t+9152t2-6510t3+1640t4-186t5+8t6)/6!
50000(3t10-t11)/(1-t)9(-725760+601632t-53496t2-106400t3+52178t4-11312t5+1316t6-80t7+2t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:FkH_R_QNpicture of the graph :FkH_R_QN
0001011
0000111
0000001
1000011
0100000
1101000
1111000
[4, 3, 3, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
103710(3t+t2-t3)/(1-t)21+3t
20007(7t3-9t5+4t6)/(1-t)4(-24-32t+12t2+2t3)/3!
30000(4t5+16t6-8t7)/(1-t)5(-864+72t+324t2-120t3+12t4)/4!
40000(13t8-5t9)/(1-t)7(-35280+18396t+5582t2-5970t3+1610t4-186t5+8t6)/6!
50000(3t10-t11)/(1-t)9(-725760+601632t-53496t2-106400t3+52178t4-11312t5+1316t6-80t7+2t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:FkGEPI@Rpicture of the graph :FkGEPI@R
0001101
0000121
0000010
1000000
1100001
0210000
1100100
[4, 3, 3, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
103812(3t+2t2-t3)/(1-t)24t
20019(t2+5t3+t4-6t5+t6)/(1-t)4(78-89t+21t2+2t3)/3!
30000(7t5+10t6-4t7)/(1-t)5(-72-522t+479t2-138t3+13t4)/4!
40000(t7+11t8-4t9)/(1-t)7(-24480+8136t+9152t2-6510t3+1640t4-186t5+8t6)/6!
50000(3t10-t11)/(1-t)9(-725760+601632t-53496t2-106400t3+52178t4-11312t5+1316t6-80t7+2t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:FkGCXI@Vpicture of the graph :FkGCXI@V
0001101
0000211
0000010
1000000
1200000
0110001
1100010
[4, 3, 3, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
10379(3t+t2-2t3)/(1-t)23+2t
20006(6t3+8t4-2t5)/(1-t)3(36-44t+12t2)/2!
30000(4t5+14t6-5t7)/(1-t)5(-24-646t+539t2-146t3+13t4)/4!
40000(t7+11t8-4t9)/(1-t)7(-24480+8136t+9152t2-6510t3+1640t4-186t5+8t6)/6!
50000(3t10-t11)/(1-t)9(-725760+601632t-53496t2-106400t3+52178t4-11312t5+1316t6-80t7+2t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:FkG?XI@Vpicture of the graph :FkG?XI@V
0001201
0000111
0000010
1000000
2100000
0110001
1100010
[4, 3, 3, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
103811(3t+2t2-2t3)/(1-t)22+3t
20018(t2+4t3+3t4-8t5+2t6)/(1-t)4(54-74t+18t2+2t3)/3!
30000(6t5+12t6-5t7)/(1-t)5(-216-438t+467t2-138t3+13t4)/4!
40000(t7+11t8-4t9)/(1-t)7(-24480+8136t+9152t2-6510t3+1640t4-186t5+8t6)/6!
50000(3t10-t11)/(1-t)9(-725760+601632t-53496t2-106400t3+52178t4-11312t5+1316t6-80t7+2t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:FkGEQ_SVpicture of the graph :FkGEQ_SV
0001101
0000111
0000010
1000000
1100001
0110001
1100110
[4, 3, 3, 3, 3, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k0123Poincaré seriesstable polynomial value
011111/(1-t)1
10379(3t+t2-2t3)/(1-t)23+2t
20006(6t3+8t4-3t5)/(1-t)3(24-37t+11t2)/2!
30000(3t5+16t6-7t7)/(1-t)5(-528-220t+408t2-128t3+12t4)/4!
40000(13t8-5t9)/(1-t)7(-35280+18396t+5582t2-5970t3+1610t4-186t5+8t6)/6!
50000(3t10-t11)/(1-t)9(-725760+601632t-53496t2-106400t3+52178t4-11312t5+1316t6-80t7+2t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:GoGCXIBZpicture of the graph :GoGCXIBZ
00001101
00000210
00000010
00000001
10000000
12000000
01100001
10010010
[3, 3, 3, 3, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
1026(2t+2t2-t3)/(1-t)23t
2000(3t3+4t4-4t5)/(1-t)4(72-54t+3t2+3t3)/3!
3000(3t5+4t6-6t7)/(1-t)6(3840-5096t+2430t2-485t3+30t4+t5)/5!
4000(t7+4t8)/(1-t)7(20880-33876t+22040t2-7395t3+1355t4-129t5+5t6)/6!
5000t10/(1-t)9(362880-663696t+509004t2-214676t3+54649t4-8624t5+826t6-44t7+t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:GoHI@M@Vpicture of the graph :GoHI@M@V
00001011
00000111
00000100
00000010
10000000
01100001
11010000
11000100
[3, 3, 3, 3, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
1026(2t+2t2-t3)/(1-t)23t
2000(3t3+4t4-6t5)/(1-t)4(120-106t+21t2+t3)/3!
3000(t5+9t6)/(1-t)5(1104-1436t+674t2-136t3+10t4)/4!
40005t8/(1-t)7(25200-40140t+25520t2-8325t3+1475t4-135t5+5t6)/6!
5000t10/(1-t)9(362880-663696t+509004t2-214676t3+54649t4-8624t5+826t6-44t7+t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:GkHi@I@Jpicture of the graph :GkHi@I@J
00010011
00001011
00000111
10000000
01000000
00100000
11100000
11100000
[3, 3, 3, 3, 3, 1, 1, 1]

Betti numbers βi(Bk(Γ)):

i\k012Poincaré seriesstable polynomial value
01111/(1-t)1
1026(2t+2t2-t3)/(1-t)23t
2000(3t3+7t4)/(1-t)3(48-44t+10t2)/2!
300010t6/(1-t)5(1200-1540t+710t2-140t3+10t4)/4!
40005t8/(1-t)7(25200-40140t+25520t2-8325t3+1475t4-135t5+5t6)/6!
5000t10/(1-t)9(362880-663696t+509004t2-214676t3+54649t4-8624t5+826t6-44t7+t8)/8!

Data for graphs with 6 essential vertices

sparse6 nameimageadjacency matrixdegree sequence
:Ek?EAIPJpicture of the graph :Ek?EAIPJ
000210
000102
000021
210000
102000
021000
[3, 3, 3, 3, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104777(4t+3t2)/(1-t)7
20031227(3t2+3t3-3t5)/(1-t)3(-30+9t+3t2)/2!
300016(t3+2t4+6t5+4t6-t7)/(1-t)4(-276+294t-102t2+12t3)/3!
400000(3t6+3t7-3t9)/(1-t)6(17640-13878t+3795t2-345t3-15t4+3t5)/5!
500000(3t9+3t10)/(1-t)7(241920-254304t+110184t2-25200t3+3210t4-216t5+6t6)/6!
600000t12/(1-t)9(6652800-7893840t+4028156t2-1155420t3+203889t4-22680t5+1554t6-60t7+t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Ek@EAI@Jpicture of the graph :Ek@EAI@J
000111
000201
000021
120000
102000
111000
[3, 3, 3, 3, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104777(4t+3t2)/(1-t)7
20031123(3t2+2t3-t4-2t5+t6)/(1-t)3(-6+t+3t2)/2!
300002(2t4+8t5+2t6-4t7)/(1-t)4(156+28t-48t2+8t3)/3!
400000(t6+5t7+2t8-6t9)/(1-t)6(31560-24662t+6945t2-780t3+15t4+2t5)/5!
500000(2t9+4t10)/(1-t)7(282240-289968t+122604t2-27330t3+3390t4-222t5+6t6)/6!
600000t12/(1-t)9(6652800-7893840t+4028156t2-1155420t3+203889t4-22680t5+1554t6-60t7+t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:Ek@I@I@Jpicture of the graph :Ek@I@I@J
000111
000111
000111
111000
111000
111000
[3, 3, 3, 3, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
1044444t/(1-t)4
2000819(8t3+3t4-2t5)/(1-t)2-17+9t
300001(t4+7t5+12t6)/(1-t)3(330-162t+20t2)/2!
40000015t8/(1-t)5(12600-9570t+2685t2-330t3+15t4)/4!
5000006t10/(1-t)7(362880-361296t+147444t2-31590t3+3750t4-234t5+6t6)/6!
600000t12/(1-t)9(6652800-7893840t+4028156t2-1155420t3+203889t4-22680t5+1554t6-60t7+t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:EgGEQI@Npicture of the graph :EgGEQI@N
001101
000111
100020
110001
012000
110100
[3, 3, 3, 3, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104666(4t+2t2)/(1-t)6
20021022(2t2+4t3-2t4-4t5+t6)/(1-t)3(-32+15t+t2)/2!
300002(2t4+6t5+3t6-5t7)/(1-t)4(264-51t-27t2+6t3)/3!
400000(6t7+3t8-8t9)/(1-t)6(41880-33026t+9555t2-1175t3+45t4+t5)/5!
500000(t9+5t10)/(1-t)7(322560-325632t+135024t2-29460t3+3570t4-228t5+6t6)/6!
600000t12/(1-t)9(6652800-7893840t+4028156t2-1155420t3+203889t4-22680t5+1554t6-60t7+t8)/8!

sparse6 nameimageadjacency matrixdegree sequence
:EgGE@IQNpicture of the graph :EgGE@IQN
001110
000111
100011
110001
111000
011100
[3, 3, 3, 3, 3, 3]

Betti numbers βi(Bk(Γ)):

i\k01234Poincaré seriesstable polynomial value
0111111/(1-t)1
104555(4t+t2)/(1-t)5
2001919(t2+7t3+2t4-t5)/(1-t)2-17+9t
300000(9t5+2t6-9t7)/(1-t)4(744-338t+30t2+2t3)/3!
400000(2t7+13t8)/(1-t)5(11640-8978t+2565t2-322t3+15t4)/4!
5000006t10/(1-t)7(362880-361296t+147444t2-31590t3+3750t4-234t5+6t6)/6!
600000t12/(1-t)9(6652800-7893840t+4028156t2-1155420t3+203889t4-22680t5+1554t6-60t7+t8)/8!