New Graph

[2, 9, B, 10, 1A, 11, 20, 7, 1, B, 3, B, 17, 6, 1D, 1A, 19, 20, 10, 13, 9, 1F, 

  D, 9, 13, 1E, C, 1F, 5, 10, 16, 16], [1E, 1E, 1D, 1, 3, 18, 5, 10, 6, 17, 

  1D, 14, 1F, 15, 1B, A, 1C, 19, 18, 12, 4, D, A, F, B, 8, E, 6, 1, A, 13, 17]

π = [2812824, 1406412, 3603887, 30228, 2538633, 764568, 698928, 1397856, 1217082, 5407227, 4669141, 120912, 2736573, 120912, 483648, 3052791, 382284, 30228, 1170024, 60456, 60456, 1218957, 4254189, 967296, 206256, 2795712, 241824, 191142, 4378338, 3507474, 2073336, 364578]

POSSIBLE RANKS

1 x 52964172
2 x 26482086
3 x 17654724
4 x 13241043
6 x 8827362
9 x 5884908
12 x 4413681
18 x 2942454
19 x 2787588
27 x 1961636
36 x 1471227
38 x 1393794
53 x 999324
54 x 980818
57 x 929196
76 x 696897
106 x 499662
108 x 490409
114 x 464598
159 x 333108
171 x 309732
212 x 249831
228 x 232299
318 x 166554
342 x 154866
477 x 111036
487 x 108756
513 x 103244
636 x 83277
684 x 77433
954 x 55518
974 x 54378
1007 x 52596
1026 x 51622
1431 x 37012
1461 x 36252
1908 x 27759
1948 x 27189
2014 x 26298
2052 x 25811
2862 x 18506
2922 x 18126
3021 x 17532
4028 x 13149
4383 x 12084
5724 x 9253
5844 x 9063
6042 x 8766
NullSpace of Δ

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

Nullspace of A

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

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

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

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

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

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

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

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

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

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

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

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

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

Delta Rank with R : "tailcheck for rank 20"
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, 9, B, 10, 1A, 11, 20, 7, 6, B, 3, B, 17, 6, 1D, 1A, 19, 20, 10, 13, 9, 1F, D, 9, 13, 1E, C, 1F, 5, 10, 16, 16]
"B", [1E, 1E, 1D, 1, 3, 18, 5, 10, 1, 17, 1D, 14, 1F, 15, 1B, A, 1C, 19, 18, 12, 4, D, A, F, B, 8, E, 6, 1, A, 13, 17]
"Coloring", {9}

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

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

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

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

Delta Rank with R : "tailcheck for rank 22"
Delta Rank with B : "tailcheck for rank 23"

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

Delta Rank with R : "tailcheck for rank 20"
Delta Rank with B : "tailcheck for rank 23"

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

Delta Rank with R : "tailcheck for rank 21"
Delta Rank with B : "tailcheck for rank 23"

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

Delta Rank with R : "tailcheck for rank 21"
Delta Rank with B : "tailcheck for rank 23"

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

Delta Rank with R : "tailcheck for rank 22"
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, 9, B, 10, 1A, 11, 20, 7, 1, B, 3, B, 17, 6, 1D, 1A, 1C, 20, 10, 13, 9, 1F, D, 9, 13, 1E, C, 1F, 5, 10, 16, 16]
"B", [1E, 1E, 1D, 1, 3, 18, 5, 10, 6, 17, 1D, 14, 1F, 15, 1B, A, 19, 19, 18, 12, 4, D, A, F, B, 8, E, 6, 1, A, 13, 17]
"Coloring", {17}

Delta Rank with R : "tailcheck for rank 21"
Delta Rank with B : "tailcheck for rank 23"

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

Delta Rank with R : "tailcheck for rank 22"
Delta Rank with B : "tailcheck for rank 24"

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

Delta Rank with R : "tailcheck for rank 22"
Delta Rank with B : "tailcheck for rank 23"

SUMMARY

Graph Type
CC

ν(A)
3

ν(Δ)
3

π
[2812824, 1406412, 3603887, 30228, 2538633, 764568, 698928, 1397856, 1217082, 5407227, 4669141, 120912, 2736573, 120912, 483648, 3052791, 382284, 30228, 1170024, 60456, 60456, 1218957, 4254189, 967296, 206256, 2795712, 241824, 191142, 4378338, 3507474, 2073336, 364578]

Dbly Stoch
false

SUMMARY
Graph Type		CC
ν(A)		3
ν(Δ)		3
π		[2812824, 1406412, 3603887, 30228, 2538633, 764568, 698928, 1397856, 1217082, 5407227, 4669141, 120912, 2736573, 120912, 483648, 3052791, 382284, 30228, 1170024, 60456, 60456, 1218957, 4254189, 967296, 206256, 2795712, 241824, 191142, 4378338, 3507474, 2073336, 364578]
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