New Graph

        [8, F, 6, 9, E, 9, E, 11, C, 11, C, 3, 2, 2, 5, 12, A, 3], 

          [12, 10, 2, F, 3, 5, 9, 4, 7, 12, 11, D, 12, 3, 3, 1, B, A]

 

 

π = [4728, 18912, 26070, 1182, 11541, 13035, 4739, 2364, 9478, 12570, 4978, 7228, 3614, 8140, 10047, 9456, 9956, 15184]

POSSIBLE RANKS

1 x 173222
2 x 86611
7 x 24746
14 x 12373
NullSpace of Δ

{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18}

Nullspace of A

[{3, 4, 6, 9, 11, 12, 16, 18},{1, 2, 5, 7, 8, 10, 13, 14, 15, 17}]

 

1 . [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
"R", [8, F, 6, 9, E, 9, E, 11, C, 11, C, 3, 2, 2, 5, 12, A, 3]
"B", [12, 10, 2, F, 3, 5, 9, 4, 7, 12, 11, D, 12, 3, 3, 1, B, A]
"Coloring", {}

Delta Rank with R :  "tailcheck for rank 12"
Delta Rank with B :  "tailcheck for rank 14"


2 . [1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
"R", [8, 10, 6, 9, E, 9, E, 11, C, 11, C, 3, 2, 2, 5, 12, A, 3]
"B", [12, F, 2, F, 3, 5, 9, 4, 7, 12, 11, D, 12, 3, 3, 1, B, A]
"Coloring", {2}

Delta Rank with R :  "tailcheck for rank 12"
Delta Rank with B :  "tailcheck for rank 13"


3 . [1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
"R", [8, F, 2, 9, E, 9, E, 11, C, 11, C, 3, 2, 2, 5, 12, A, 3]
"B", [12, 10, 6, F, 3, 5, 9, 4, 7, 12, 11, D, 12, 3, 3, 1, B, A]
"Coloring", {3}

Delta Rank with R :  "tailcheck for rank 11"
Delta Rank with B :  "tailcheck for rank 14"


4 . [1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
"R", [8, F, 6, F, E, 9, E, 11, C, 11, C, 3, 2, 2, 5, 12, A, 3]
"B", [12, 10, 2, 9, 3, 5, 9, 4, 7, 12, 11, D, 12, 3, 3, 1, B, A]
"Coloring", {4}

Delta Rank with R :  "tailcheck for rank 12"
Delta Rank with B :  "tailcheck for rank 13"


5 . [1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
"R", [8, F, 6, 9, 3, 9, E, 11, C, 11, C, 3, 2, 2, 5, 12, A, 3]
"B", [12, 10, 2, F, E, 5, 9, 4, 7, 12, 11, D, 12, 3, 3, 1, B, A]
"Coloring", {5}

Delta Rank with R :  "tailcheck for rank 12"
Delta Rank with B :  "tailcheck for rank 15"


6 . [1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
"R", [8, F, 6, 9, E, 5, E, 11, C, 11, C, 3, 2, 2, 5, 12, A, 3]
"B", [12, 10, 2, F, 3, 9, 9, 4, 7, 12, 11, D, 12, 3, 3, 1, B, A]
"Coloring", {6}

Delta Rank with R :  "tailcheck for rank 12"
Delta Rank with B :  "tailcheck for rank 13"


7 . [1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
"R", [8, F, 6, 9, E, 9, 9, 11, C, 11, C, 3, 2, 2, 5, 12, A, 3]
"B", [12, 10, 2, F, 3, 5, E, 4, 7, 12, 11, D, 12, 3, 3, 1, B, A]
"Coloring", {7}

Delta Rank with R :  "tailcheck for rank 12"
Delta Rank with B :  "tailcheck for rank 14"


8 . [1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
"R", [8, F, 6, 9, E, 9, E, 4, C, 11, C, 3, 2, 2, 5, 12, A, 3]
"B", [12, 10, 2, F, 3, 5, 9, 11, 7, 12, 11, D, 12, 3, 3, 1, B, A]
"Coloring", {8}

Delta Rank with R :  "tailcheck for rank 13"
Delta Rank with B :  "tailcheck for rank 13"


9 . [1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
"R", [8, F, 6, 9, E, 9, E, 11, 7, 11, C, 3, 2, 2, 5, 12, A, 3]
"B", [12, 10, 2, F, 3, 5, 9, 4, C, 12, 11, D, 12, 3, 3, 1, B, A]
"Coloring", {9}

Delta Rank with R :  "tailcheck for rank 13"
Delta Rank with B :  "tailcheck for rank 14"


10 . [1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1]
"R", [8, F, 6, 9, E, 9, E, 11, C, 12, C, 3, 2, 2, 5, 12, A, 3]
"B", [12, 10, 2, F, 3, 5, 9, 4, 7, 11, 11, D, 12, 3, 3, 1, B, A]
"Coloring", {10}

Delta Rank with R :  8 vs 12
Delta Rank with B :  "tailcheck for rank 14"


11 . [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1]
"R", [8, F, 6, 9, E, 9, E, 11, C, 11, 11, 3, 2, 2, 5, 12, A, 3]
"B", [12, 10, 2, F, 3, 5, 9, 4, 7, 12, C, D, 12, 3, 3, 1, B, A]
"Coloring", {11}

Delta Rank with R :  "tailcheck for rank 12"
Delta Rank with B :  "tailcheck for rank 14"


12 . [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1]
"R", [8, F, 6, 9, E, 9, E, 11, C, 11, C, D, 2, 2, 5, 12, A, 3]
"B", [12, 10, 2, F, 3, 5, 9, 4, 7, 12, 11, 3, 12, 3, 3, 1, B, A]
"Coloring", {12}

Delta Rank with R :  "tailcheck for rank 13"
Delta Rank with B :  "tailcheck for rank 13"


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

Delta Rank with R :  "tailcheck for rank 12"
Delta Rank with B :  "tailcheck for rank 14"


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

Delta Rank with R :  "tailcheck for rank 12"
Delta Rank with B :  "tailcheck for rank 14"


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

Delta Rank with R :  "tailcheck for rank 11"
Delta Rank with B :  "tailcheck for rank 14"


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

Delta Rank with R :  6 vs 12
Delta Rank with B :  "tailcheck for rank 13"


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

Delta Rank with R :  "tailcheck for rank 12"
Delta Rank with B :  "tailcheck for rank 13"


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

Delta Rank with R :  "tailcheck for rank 12"
Delta Rank with B :  "tailcheck for rank 13"


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

Delta Rank with R :  "tailcheck for rank 11"
Delta Rank with B :  "tailcheck for rank 13"


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

Delta Rank with R :  "tailcheck for rank 13"
Delta Rank with B :  "tailcheck for rank 13"


 
SUMMARY
Graph Type
CC
ν(A)
 1
ν(Δ)
 1
π
 [4728, 18912, 26070, 1182, 11541, 13035, 4739, 2364, 9478, 12570, 4978, 7228, 3614, 8140, 10047, 9456, 9956, 15184]
Dbly Stoch
false

 
SANDWICH
Total 0
No .ColoringRank

 
RT GROUPS
Total 0
No .ColoringRankSolv

 

RANK'DSYNC'D NOT RANK'D τ-RANK'DNOT SYNC'D Total Runs2n-1
0 0 0 0 20 131072