New Graph
[4, 5, 1, 3, 1, 4], [2, 4, 5, 6, 3, 1]
π =
[6, 3, 5, 6, 4, 3]
POSSIBLE RANKS
1 x 27
3 x 9
BASE DETERMINANT
161757
/
1048576, 0.1542634964,
NullSpace of Δ
{1, 2, 3, 4, 5, 6}
Nullspace of A
` det(A) = ` 1/32
1
.
Coloring, {}
[4, 5, 1, 3, 1, 4], [2, 4, 5, 6, 3, 1]
R : 2 vs 4
{{1, 3, 4}}
B : 2 vs 6
{{3, 5}, {1, 2, 4, 6}}
NOT 1/2-SYNC'D
, NOT SYNC'D
The kernel has rank
3
Sandwich
2
.
Coloring, {2}
[4, 4, 1, 3, 1, 4], [2, 5, 5, 6, 3, 1]
R : 3 vs 3
{{1, 3, 4}}
B : 5 vs 5
{{3, 5}}
1/2-SYNC'D
RB-SYNC'D
3
.
Coloring, {3}
[4, 5, 5, 3, 1, 4], [2, 4, 1, 6, 3, 1]
R : 4 vs 4
{{1, 3, 4, 5}}
B : 5 vs 5
{{1, 2, 4, 6}}
1/2-SYNC'D
RB-SYNC'D
4
.
Coloring, {4}
[4, 5, 1, 6, 1, 4], [2, 4, 5, 3, 3, 1]
R : 4 vs 4
{{4, 6}}
B : 5 vs 5
{{3, 5}}
1/2-SYNC'D
RB-SYNC'D
5
.
Coloring, {5}
[4, 5, 1, 3, 3, 4], [2, 4, 5, 6, 1, 1]
R : 4 vs 4
{{1, 3, 4}}
B : 5 vs 5
{{1, 2, 4, 6}}
1/2-SYNC'D
RB-SYNC'D
6
.
Coloring, {6}
[4, 5, 1, 3, 1, 1], [2, 4, 5, 6, 3, 4]
R : 4 vs 4
{{1, 3, 4}}
B : 3 vs 5
{{3, 5}, {4, 6}}
1/2-SYNC'D
RB-SYNC'D
7
.
Coloring, {2, 3}
[4, 4, 5, 3, 1, 4], [2, 5, 1, 6, 3, 1]
R : 4 vs 4
{{1, 3, 4, 5}}
B : 5 vs 5
{{1, 2, 3, 5}}
1/2-SYNC'D
RB-SYNC'D
8
.
Coloring, {2, 4}
[4, 4, 1, 6, 1, 4], [2, 5, 5, 3, 3, 1]
R : 3 vs 3
{{4, 6}}
B : 4 vs 4
{{3, 5}}
1/2-SYNC'D
RB-SYNC'D
9
.
Coloring, {2, 5}
[4, 4, 1, 3, 3, 4], [2, 5, 5, 6, 1, 1]
R : 3 vs 3
{{1, 3, 4}}
B : 4 vs 4
{{1, 2, 5}}
1/2-SYNC'D
RB-SYNC'D
10
.
Coloring, {2, 6}
[4, 4, 1, 3, 1, 1], [2, 5, 5, 6, 3, 4]
R : 3 vs 3
{{1, 3, 4}}
B : 3 vs 5
{{3, 5}, {4, 6}}
1/2-SYNC'D
RB-SYNC'D
11
.
Coloring, {3, 4}
[4, 5, 5, 6, 1, 4], [2, 4, 1, 3, 3, 1]
R : 4 vs 4
{{4, 6}}
B : 4 vs 4
{{1, 2, 3, 4}}
1/2-SYNC'D
RB-SYNC'D
12
.
Coloring, {3, 5}
[4, 5, 5, 3, 3, 4], [2, 4, 1, 6, 1, 1]
R : 3 vs 3
{{3, 5}}
B : 4 vs 4
{{1, 2, 4, 6}}
1/2-SYNC'D
RB-SYNC'D
13
.
Coloring, {3, 6}
[4, 5, 5, 3, 1, 1], [2, 4, 1, 6, 3, 4]
R : 4 vs 4
{{1, 3, 4, 5}}
B : 5 vs 5
{{4, 6}}
1/2-SYNC'D
RB-SYNC'D
14
.
Coloring, {4, 5}
[4, 5, 1, 6, 3, 4], [2, 4, 5, 3, 1, 1]
R : 5 vs 5
{{4, 6}}
B : 5 vs 5
{{1, 2, 3, 4, 5}}
1/2-SYNC'D
RB-SYNC'D
15
.
Coloring, {4, 6}
[4, 5, 1, 6, 1, 1], [2, 4, 5, 3, 3, 4]
R : 4 vs 4
{{1, 4, 6}}
B : 4 vs 4
{{3, 5}}
1/2-SYNC'D
RB-SYNC'D
16
.
Coloring, {5, 6}
[4, 5, 1, 3, 3, 1], [2, 4, 5, 6, 1, 4]
R : 4 vs 4
{{1, 3, 4}}
B : 5 vs 5
{{4, 6}}
1/2-SYNC'D
RB-SYNC'D
17
.
Coloring, {2, 3, 4}
[4, 4, 5, 6, 1, 4], [2, 5, 1, 3, 3, 1]
R : 4 vs 4
{{4, 6}}
B : 4 vs 4
{{1, 2, 3, 5}}
1/2-SYNC'D
RB-SYNC'D
18
.
Coloring, {2, 3, 5}
[4, 4, 5, 3, 3, 4], [2, 5, 1, 6, 1, 1]
R : 3 vs 3
{{3, 5}}
B : 4 vs 4
{{1, 2, 5}}
1/2-SYNC'D
RB-SYNC'D
19
.
Coloring, {2, 3, 6}
[4, 4, 5, 3, 1, 1], [2, 5, 1, 6, 3, 4]
R : 4 vs 4
{{1, 3, 4, 5}}
B : 4 vs 6
{{1, 2, 3, 5}, {4, 6}}
1/2-SYNC'D
RB-SYNC'D
20,
20
.
Coloring, {2, 4, 5}
[4, 4, 1, 6, 3, 4], [2, 5, 5, 3, 1, 1]
R : 4 vs 4
{{4, 6}}
B : 4 vs 4
{{1, 2, 5}}
1/2-SYNC'D
RB-SYNC'D
21
.
Coloring, {2, 4, 6}
[4, 4, 1, 6, 1, 1], [2, 5, 5, 3, 3, 4]
R : 3 vs 3
{{1, 4, 6}}
B : 3 vs 4
{{3, 5}}
1/2-SYNC'D
RB-SYNC'D
22
.
Coloring, {2, 5, 6}
[4, 4, 1, 3, 3, 1], [2, 5, 5, 6, 1, 4]
R : 3 vs 3
{{1, 3, 4}}
B : 4 vs 5
{{1, 2, 5}, {4, 6}}
1/2-SYNC'D
RB-SYNC'D
23
.
Coloring, {3, 4, 5}
[4, 5, 5, 6, 3, 4], [2, 4, 1, 3, 1, 1]
R : 2 vs 4
{{3, 5}, {4, 6}}
B : 4 vs 4
{{1, 2, 3, 4}}
1/2-SYNC'D
RB-SYNC'D
24
.
Coloring, {3, 4, 6}
[4, 5, 5, 6, 1, 1], [2, 4, 1, 3, 3, 4]
R : 4 vs 4
{{1, 4, 6}}
B : 4 vs 4
{{1, 2, 3, 4}}
1/2-SYNC'D
RB-SYNC'D
25
.
Coloring, {3, 5, 6}
[4, 5, 5, 3, 3, 1], [2, 4, 1, 6, 1, 4]
R : 4 vs 4
{{3, 5}}
B : 4 vs 4
{{4, 6}}
1/2-SYNC'D
RB-SYNC'D
26
.
Coloring, {4, 5, 6}
[4, 5, 1, 6, 3, 1], [2, 4, 5, 3, 1, 4]
R : 5 vs 5
{{1, 4, 6}}
B : 5 vs 5
{{1, 2, 3, 4, 5}}
1/2-SYNC'D
RB-SYNC'D
27
.
Coloring, {2, 3, 4, 5}
[4, 4, 5, 6, 3, 4], [2, 5, 1, 3, 1, 1]
R : 2 vs 4
{{3, 5}, {4, 6}}
B : 4 vs 4
{{1, 2, 5}}
1/2-SYNC'D
RB-SYNC'D
28
.
Coloring, {2, 3, 4, 6}
[4, 4, 5, 6, 1, 1], [2, 5, 1, 3, 3, 4]
R : 4 vs 4
{{1, 4, 6}}
B : 5 vs 5
{{1, 2, 3, 5}}
1/2-SYNC'D
RB-SYNC'D
29
.
Coloring, {2, 3, 5, 6}
[4, 4, 5, 3, 3, 1], [2, 5, 1, 6, 1, 4]
R : 4 vs 4
{{3, 5}}
B : 4 vs 5
{{1, 2, 5}, {4, 6}}
1/2-SYNC'D
RB-SYNC'D
30
.
Coloring, {2, 4, 5, 6}
[4, 4, 1, 6, 3, 1], [2, 5, 5, 3, 1, 4]
R : 4 vs 4
{{1, 4, 6}}
B : 5 vs 5
{{1, 2, 5}}
1/2-SYNC'D
RB-SYNC'D
31
.
Coloring, {3, 4, 5, 6}
[4, 5, 5, 6, 3, 1], [2, 4, 1, 3, 1, 4]
R : 4 vs 5
{{1, 4, 6}, {3, 5}}
B : 4 vs 4
{{1, 2, 3, 4}}
1/2-SYNC'D
RB-SYNC'D
32
.
Coloring, {2, 3, 4, 5, 6}
[4, 4, 5, 6, 3, 1], [2, 5, 1, 3, 1, 4]
R : 4 vs 5
{{3, 5}, {1, 4, 6}}
B : 3 vs 5
{{1, 2, 5}}
1/2-SYNC'D
| SUMMARY |
|---|
| Graph Type |
| NOT CC |
|---|
| ν(A) |
|
0
|
|---|
| ν(Δ) |
|
1
|
|---|
| π |
|
[6, 3, 5, 6, 4, 3]
|
|---|
| Dbly Stoch |
| false |
|---|
| SYNC'D | SC'D !RK'D |
τ-RANK'D | R/B RANK'D | NOT SYNC'D |
Total Runs | 2n-1 |
|---|
|
31
|
0
|
31
|
30
|
1
|
32
|
32
|