New Graph

[2, 1A, 2, 19, 17, E, 1A, 1C, F, 19, E, A, 16, 13, 7, C, 19, C, F, 3, A, 19, 

  1E, 14, 15, 9, 2, 5, 2, 5, 6, 1F], [17, 4, 12, 18, 1, 8, 1E, 1A, 4, 20, A, 

  B, 9, C, 1C, 1, 13, 1D, 10, D, 18, 3, 3, 11, 1F, 1E, A, 7, 19, 1B, 5, 8]

π = [186789298, 291537278, 188617540, 223594603, 329159142, 109288918, 120479600, 115182146, 155651928, 242150748, 55249338, 110498676, 47704344, 82269128, 122245418, 44419454, 95408688, 94308770, 88838908, 95408688, 158040149, 23852172, 257974220, 190817376, 316080298, 263599512, 160513333, 118713782, 47154385, 321026666, 218577836, 121075374]

POSSIBLE RANKS

1 x 4996227716
2 x 2498113858
4 x 1249056929
17 x 293895748
23 x 217227292
31 x 161168636
34 x 146947874
46 x 108613646
62 x 80584318
68 x 73473937
92 x 54306823
124 x 40292159
391 x 12778076
527 x 9480508
713 x 7007332
782 x 6389038
1054 x 4740254
1426 x 3503666
1564 x 3194519
2108 x 2370127
2852 x 1751833
12121 x 412196
24242 x 206098
48484 x 103049
NullSpace of Δ

{17, 20}, {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 19, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32}

Nullspace of A

[{1, 2, 3, 6, 7, 9, 11, 14, 15, 19, 24, 26, 27, 29, 31, 32},{4, 5, 8, 10, 12, 13, 16, 18, 21, 22, 23, 25, 28, 30}] `,` [{20},{17}]

1 . [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
"R", [2, 1A, 2, 19, 17, E, 1A, 1C, F, 19, E, A, 16, 13, 7, C, 19, C, F, 3, A, 19, 1E, 14, 15, 9, 2, 5, 2, 5, 6, 1F]
"B", [17, 4, 12, 18, 1, 8, 1E, 1A, 4, 20, A, B, 9, C, 1C, 1, 13, 1D, 10, D, 18, 3, 3, 11, 1F, 1E, A, 7, 19, 1B, 5, 8]
"Coloring", {}

Delta Rank with R : "tailcheck for rank 20"
Delta Rank with B : "tailcheck for rank 25"

2 . [1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
"R", [2, 4, 2, 19, 17, E, 1A, 1C, F, 19, E, A, 16, 13, 7, C, 19, C, F, 3, A, 19, 1E, 14, 15, 9, 2, 5, 2, 5, 6, 1F]
"B", [17, 1A, 12, 18, 1, 8, 1E, 1A, 4, 20, A, B, 9, C, 1C, 1, 13, 1D, 10, D, 18, 3, 3, 11, 1F, 1E, A, 7, 19, 1B, 5, 8]
"Coloring", {2}

Delta Rank with R : "tailcheck for rank 21"
Delta Rank with B : "tailcheck for rank 25"

3 . [1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
"R", [2, 1A, 12, 19, 17, E, 1A, 1C, F, 19, E, A, 16, 13, 7, C, 19, C, F, 3, A, 19, 1E, 14, 15, 9, 2, 5, 2, 5, 6, 1F]
"B", [17, 4, 2, 18, 1, 8, 1E, 1A, 4, 20, A, B, 9, C, 1C, 1, 13, 1D, 10, D, 18, 3, 3, 11, 1F, 1E, A, 7, 19, 1B, 5, 8]
"Coloring", {3}

Delta Rank with R : "tailcheck for rank 21"
Delta Rank with B : "tailcheck for rank 25"

4 . [1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
"R", [2, 1A, 2, 18, 17, E, 1A, 1C, F, 19, E, A, 16, 13, 7, C, 19, C, F, 3, A, 19, 1E, 14, 15, 9, 2, 5, 2, 5, 6, 1F]
"B", [17, 4, 12, 19, 1, 8, 1E, 1A, 4, 20, A, B, 9, C, 1C, 1, 13, 1D, 10, D, 18, 3, 3, 11, 1F, 1E, A, 7, 19, 1B, 5, 8]
"Coloring", {4}

Delta Rank with R : "tailcheck for rank 21"
Delta Rank with B : "tailcheck for rank 25"

5 . [1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
"R", [2, 1A, 2, 19, 1, E, 1A, 1C, F, 19, E, A, 16, 13, 7, C, 19, C, F, 3, A, 19, 1E, 14, 15, 9, 2, 5, 2, 5, 6, 1F]
"B", [17, 4, 12, 18, 17, 8, 1E, 1A, 4, 20, A, B, 9, C, 1C, 1, 13, 1D, 10, D, 18, 3, 3, 11, 1F, 1E, A, 7, 19, 1B, 5, 8]
"Coloring", {5}

Delta Rank with R : "tailcheck for rank 20"
Delta Rank with B : "tailcheck for rank 25"

6 . [1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
"R", [2, 1A, 2, 19, 17, 8, 1A, 1C, F, 19, E, A, 16, 13, 7, C, 19, C, F, 3, A, 19, 1E, 14, 15, 9, 2, 5, 2, 5, 6, 1F]
"B", [17, 4, 12, 18, 1, E, 1E, 1A, 4, 20, A, B, 9, C, 1C, 1, 13, 1D, 10, D, 18, 3, 3, 11, 1F, 1E, A, 7, 19, 1B, 5, 8]
"Coloring", {6}

Delta Rank with R : "tailcheck for rank 21"
Delta Rank with B : "tailcheck for rank 26"

7 . [1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
"R", [2, 1A, 2, 19, 17, E, 1E, 1C, F, 19, E, A, 16, 13, 7, C, 19, C, F, 3, A, 19, 1E, 14, 15, 9, 2, 5, 2, 5, 6, 1F]
"B", [17, 4, 12, 18, 1, 8, 1A, 1A, 4, 20, A, B, 9, C, 1C, 1, 13, 1D, 10, D, 18, 3, 3, 11, 1F, 1E, A, 7, 19, 1B, 5, 8]
"Coloring", {7}

Delta Rank with R : "tailcheck for rank 20"
Delta Rank with B : "tailcheck for rank 25"

8 . [1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
"R", [2, 1A, 2, 19, 17, E, 1A, 1A, F, 19, E, A, 16, 13, 7, C, 19, C, F, 3, A, 19, 1E, 14, 15, 9, 2, 5, 2, 5, 6, 1F]
"B", [17, 4, 12, 18, 1, 8, 1E, 1C, 4, 20, A, B, 9, C, 1C, 1, 13, 1D, 10, D, 18, 3, 3, 11, 1F, 1E, A, 7, 19, 1B, 5, 8]
"Coloring", {8}

Delta Rank with R : "tailcheck for rank 19"
Delta Rank with B : "tailcheck for rank 24"

9 . [1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
"R", [2, 1A, 2, 19, 17, E, 1A, 1C, 4, 19, E, A, 16, 13, 7, C, 19, C, F, 3, A, 19, 1E, 14, 15, 9, 2, 5, 2, 5, 6, 1F]
"B", [17, 4, 12, 18, 1, 8, 1E, 1A, F, 20, A, B, 9, C, 1C, 1, 13, 1D, 10, D, 18, 3, 3, 11, 1F, 1E, A, 7, 19, 1B, 5, 8]
"Coloring", {9}

Delta Rank with R : "tailcheck for rank 21"
Delta Rank with B : "tailcheck for rank 26"

10 . [1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
"R", [2, 1A, 2, 19, 17, E, 1A, 1C, F, 20, E, A, 16, 13, 7, C, 19, C, F, 3, A, 19, 1E, 14, 15, 9, 2, 5, 2, 5, 6, 1F]
"B", [17, 4, 12, 18, 1, 8, 1E, 1A, 4, 19, A, B, 9, C, 1C, 1, 13, 1D, 10, D, 18, 3, 3, 11, 1F, 1E, A, 7, 19, 1B, 5, 8]
"Coloring", {10}

Delta Rank with R : "tailcheck for rank 21"
Delta Rank with B : "tailcheck for rank 24"

11 . [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
"R", [2, 1A, 2, 19, 17, E, 1A, 1C, F, 19, A, A, 16, 13, 7, C, 19, C, F, 3, A, 19, 1E, 14, 15, 9, 2, 5, 2, 5, 6, 1F]
"B", [17, 4, 12, 18, 1, 8, 1E, 1A, 4, 20, E, B, 9, C, 1C, 1, 13, 1D, 10, D, 18, 3, 3, 11, 1F, 1E, A, 7, 19, 1B, 5, 8]
"Coloring", {11}

Delta Rank with R : "tailcheck for rank 20"
Delta Rank with B : "tailcheck for rank 26"

12 . [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
"R", [2, 1A, 2, 19, 17, E, 1A, 1C, F, 19, E, B, 16, 13, 7, C, 19, C, F, 3, A, 19, 1E, 14, 15, 9, 2, 5, 2, 5, 6, 1F]
"B", [17, 4, 12, 18, 1, 8, 1E, 1A, 4, 20, A, A, 9, C, 1C, 1, 13, 1D, 10, D, 18, 3, 3, 11, 1F, 1E, A, 7, 19, 1B, 5, 8]
"Coloring", {12}

Delta Rank with R : "tailcheck for rank 21"
Delta Rank with B : "tailcheck for rank 24"

13 . [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
"R", [2, 1A, 2, 19, 17, E, 1A, 1C, F, 19, E, A, 9, 13, 7, C, 19, C, F, 3, A, 19, 1E, 14, 15, 9, 2, 5, 2, 5, 6, 1F]
"B", [17, 4, 12, 18, 1, 8, 1E, 1A, 4, 20, A, B, 16, C, 1C, 1, 13, 1D, 10, D, 18, 3, 3, 11, 1F, 1E, A, 7, 19, 1B, 5, 8]
"Coloring", {13}

Delta Rank with R : "tailcheck for rank 19"
Delta Rank with B : "tailcheck for rank 25"

14 . [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
"R", [2, 1A, 2, 19, 17, E, 1A, 1C, F, 19, E, A, 16, C, 7, C, 19, C, F, 3, A, 19, 1E, 14, 15, 9, 2, 5, 2, 5, 6, 1F]
"B", [17, 4, 12, 18, 1, 8, 1E, 1A, 4, 20, A, B, 9, 13, 1C, 1, 13, 1D, 10, D, 18, 3, 3, 11, 1F, 1E, A, 7, 19, 1B, 5, 8]
"Coloring", {14}

Delta Rank with R : "tailcheck for rank 19"
Delta Rank with B : "tailcheck for rank 24"

15 . [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
"R", [2, 1A, 2, 19, 17, E, 1A, 1C, F, 19, E, A, 16, 13, 1C, C, 19, C, F, 3, A, 19, 1E, 14, 15, 9, 2, 5, 2, 5, 6, 1F]
"B", [17, 4, 12, 18, 1, 8, 1E, 1A, 4, 20, A, B, 9, C, 7, 1, 13, 1D, 10, D, 18, 3, 3, 11, 1F, 1E, A, 7, 19, 1B, 5, 8]
"Coloring", {15}

Delta Rank with R : "tailcheck for rank 19"
Delta Rank with B : "tailcheck for rank 24"

16 . [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
"R", [2, 1A, 2, 19, 17, E, 1A, 1C, F, 19, E, A, 16, 13, 7, 1, 19, C, F, 3, A, 19, 1E, 14, 15, 9, 2, 5, 2, 5, 6, 1F]
"B", [17, 4, 12, 18, 1, 8, 1E, 1A, 4, 20, A, B, 9, C, 1C, C, 13, 1D, 10, D, 18, 3, 3, 11, 1F, 1E, A, 7, 19, 1B, 5, 8]
"Coloring", {16}

Delta Rank with R : "tailcheck for rank 21"
Delta Rank with B : "tailcheck for rank 25"

17 . [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
"R", [2, 1A, 2, 19, 17, E, 1A, 1C, F, 19, E, A, 16, 13, 7, C, 13, C, F, 3, A, 19, 1E, 14, 15, 9, 2, 5, 2, 5, 6, 1F]
"B", [17, 4, 12, 18, 1, 8, 1E, 1A, 4, 20, A, B, 9, C, 1C, 1, 19, 1D, 10, D, 18, 3, 3, 11, 1F, 1E, A, 7, 19, 1B, 5, 8]
"Coloring", {17}

Delta Rank with R : "tailcheck for rank 20"
Delta Rank with B : "tailcheck for rank 24"

18 . [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
"R", [2, 1A, 2, 19, 17, E, 1A, 1C, F, 19, E, A, 16, 13, 7, C, 19, 1D, F, 3, A, 19, 1E, 14, 15, 9, 2, 5, 2, 5, 6, 1F]
"B", [17, 4, 12, 18, 1, 8, 1E, 1A, 4, 20, A, B, 9, C, 1C, 1, 13, C, 10, D, 18, 3, 3, 11, 1F, 1E, A, 7, 19, 1B, 5, 8]
"Coloring", {18}

Delta Rank with R : "tailcheck for rank 21"
Delta Rank with B : "tailcheck for rank 24"

19 . [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
"R", [2, 1A, 2, 19, 17, E, 1A, 1C, F, 19, E, A, 16, 13, 7, C, 19, C, 10, 3, A, 19, 1E, 14, 15, 9, 2, 5, 2, 5, 6, 1F]
"B", [17, 4, 12, 18, 1, 8, 1E, 1A, 4, 20, A, B, 9, C, 1C, 1, 13, 1D, F, D, 18, 3, 3, 11, 1F, 1E, A, 7, 19, 1B, 5, 8]
"Coloring", {19}

Delta Rank with R : "tailcheck for rank 21"
Delta Rank with B : "tailcheck for rank 25"

20 . [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
"R", [2, 1A, 2, 19, 17, E, 1A, 1C, F, 19, E, A, 16, 13, 7, C, 19, C, F, D, A, 19, 1E, 14, 15, 9, 2, 5, 2, 5, 6, 1F]
"B", [17, 4, 12, 18, 1, 8, 1E, 1A, 4, 20, A, B, 9, C, 1C, 1, 13, 1D, 10, 3, 18, 3, 3, 11, 1F, 1E, A, 7, 19, 1B, 5, 8]
"Coloring", {20}

Delta Rank with R : "tailcheck for rank 20"
Delta Rank with B : "tailcheck for rank 24"

SUMMARY

Graph Type
CC

ν(A)
2

ν(Δ)
2

π
[186789298, 291537278, 188617540, 223594603, 329159142, 109288918, 120479600, 115182146, 155651928, 242150748, 55249338, 110498676, 47704344, 82269128, 122245418, 44419454, 95408688, 94308770, 88838908, 95408688, 158040149, 23852172, 257974220, 190817376, 316080298, 263599512, 160513333, 118713782, 47154385, 321026666, 218577836, 121075374]

Dbly Stoch
false

SUMMARY
Graph Type		CC
ν(A)		2
ν(Δ)		2
π		[186789298, 291537278, 188617540, 223594603, 329159142, 109288918, 120479600, 115182146, 155651928, 242150748, 55249338, 110498676, 47704344, 82269128, 122245418, 44419454, 95408688, 94308770, 88838908, 95408688, 158040149, 23852172, 257974220, 190817376, 316080298, 263599512, 160513333, 118713782, 47154385, 321026666, 218577836, 121075374]
Dbly Stoch		false

SANDWICH
Total 0

No . Coloring Rank

SANDWICH		Total 0
No .	Coloring	Rank

RT GROUPS
Total 0

No . Coloring Rank Solv

RT GROUPS		Total 0
No .	Coloring	Rank	Solv

RANK'D SYNC'D NOT RANK'D τ-RANK'D NOT SYNC'D Total Runs 2^n-1
0 0 0 0 20 2147483648