New Graph

[6, 3, 14, 2, C, D, 13, 1B, 19, 2, 1A, B, 19, 7, A, 3, 10, 19, 7, 10, 1A, F, 

  11, 1, 8, 19, 6], [4, 18, 8, 5, 13, 17, 15, 3, A, 18, 13, A, 16, 15, 9, 15, 

  12, 2, 1B, 18, E, 19, 1, 17, 11, 4, 10]

π = [518151, 421036, 994626, 464144, 232072, 533088, 350782, 775614, 33318, 107995, 58018, 116036, 266544, 381128, 66636, 792602, 539866, 269933, 320436, 497313, 762256, 133272, 523130, 513172, 556602, 410137, 548025]

POSSIBLE RANKS

1 x 11185932
2 x 5592966
3 x 3728644
4 x 2796483
6 x 1864322
12 x 932161
17 x 657996
34 x 328998
51 x 219332
68 x 164499
102 x 109666
204 x 54833
NullSpace of Δ

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

Nullspace of A

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

Delta Rank with R : "tailcheck for rank 18"
Delta Rank with B : "tailcheck for rank 19"

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

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

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

Delta Rank with R : "tailcheck for rank 17"
Delta Rank with B : "tailcheck for rank 19"

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

Delta Rank with R : "tailcheck for rank 19"
Delta Rank with B : "tailcheck for rank 18"

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

Delta Rank with R : "tailcheck for rank 17"
Delta Rank with B : "tailcheck for rank 20"

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

Delta Rank with R : "tailcheck for rank 18"
Delta Rank with B : "tailcheck for rank 20"

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

Delta Rank with R : "tailcheck for rank 18"
Delta Rank with B : "tailcheck for rank 19"

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

Delta Rank with R : "tailcheck for rank 17"
Delta Rank with B : "tailcheck for rank 18"

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

Delta Rank with R : "tailcheck for rank 18"
Delta Rank with B : "tailcheck for rank 19"

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

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

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

Delta Rank with R : "tailcheck for rank 18"
Delta Rank with B : "tailcheck for rank 20"

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

Delta Rank with R : "tailcheck for rank 17"
Delta Rank with B : "tailcheck for rank 20"

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

Delta Rank with R : "tailcheck for rank 19"
Delta Rank with B : "tailcheck for rank 18"

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

Delta Rank with R : "tailcheck for rank 19"
Delta Rank with B : "tailcheck for rank 20"

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

Delta Rank with R : "tailcheck for rank 18"
Delta Rank with B : "tailcheck for rank 18"

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

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

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

Delta Rank with R : "tailcheck for rank 19"
Delta Rank with B : "tailcheck for rank 18"

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

Delta Rank with R : "tailcheck for rank 18"
Delta Rank with B : "tailcheck for rank 18"

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

Delta Rank with R : "tailcheck for rank 18"
Delta Rank with B : "tailcheck for rank 19"

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

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

SUMMARY

Graph Type
CC

ν(A)
2

ν(Δ)
2

π
[518151, 421036, 994626, 464144, 232072, 533088, 350782, 775614, 33318, 107995, 58018, 116036, 266544, 381128, 66636, 792602, 539866, 269933, 320436, 497313, 762256, 133272, 523130, 513172, 556602, 410137, 548025]

Dbly Stoch
false

SUMMARY
Graph Type		CC
ν(A)		2
ν(Δ)		2
π		[518151, 421036, 994626, 464144, 232072, 533088, 350782, 775614, 33318, 107995, 58018, 116036, 266544, 381128, 66636, 792602, 539866, 269933, 320436, 497313, 762256, 133272, 523130, 513172, 556602, 410137, 548025]
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 67108864