Spanning Run

R

[2, 4, 4, 2, 6, 5]

B

[3, 6, 5, 3, 1, 4]

pi

[1, 2, 2, 3, 2, 2]

indegrees

[1, 2, 2, 3, 2, 2]

Friedman weight

12

det

231/2048, .1127929688

nullspace of Delta

{2, 3}, {1, 4, 5, 6}

nullspace of A

[{3},{2}] `,` [{5, 6},{1, 4}]

spanNum

72

Data

Coloring R-cycles B-cycles Sync'd/Not Sync'd R/B/Delta Ranking
1. {} {{5, 6}, {2, 4}} {{1, 3, 5}} notsyncd, [2, 4, 4, 2, 6, 5], [3, 6, 5, 3, 1, 4] 1:4 , 1:3 , 3:4
2. {2} {{5, 6}} {{1, 3, 5}} syncd, [2, 6, 4, 2, 6, 5], [3, 4, 5, 3, 1, 4] 1:2 , 3:3 , 4:4
3. {3} {{2, 4}, {5, 6}} {{3, 4}} notsyncd, [2, 4, 5, 2, 6, 5], [3, 6, 4, 3, 1, 4] 2:4 , 1:2 , 2:4
4. {4} {{3, 4}, {5, 6}} {{2, 4, 6}, {1, 3, 5}} notsyncd, [2, 4, 4, 3, 6, 5], [3, 6, 5, 2, 1, 4] 1:4 , 3:6 , 3:4
5. {5} {{2, 4}} {{3, 4, 5, 6}} notsyncd, [2, 4, 4, 2, 1, 5], [3, 6, 5, 3, 6, 4] 1:2 , 2:4 , 2:4
6. {6} {{2, 4}} {{1, 3, 5}} syncd, [2, 4, 4, 2, 6, 4], [3, 6, 5, 3, 1, 5] 1:2 , 3:3 , 4:4
7. {2, 3} {{5, 6}} {{3, 4}} syncd, [2, 6, 5, 2, 6, 5], [3, 4, 4, 3, 1, 4] 2:2 , 2:2 , 4:4
8. {2, 4} {{3, 4}, {5, 6}} {{1, 3, 5}, {2, 4}} syncd, [2, 6, 4, 3, 6, 5], [3, 4, 5, 2, 1, 4] 2:4 , 4:5 , 4:4
9. {2, 5} {{1, 2, 5, 6}} {{3, 4, 5, 6}} syncd, [2, 6, 4, 2, 1, 5], [3, 4, 5, 3, 6, 4] 3:4 , 3:4 , 4:4
10. {2, 6} {{2, 4, 6}} {{1, 3, 5}} notsyncd, [2, 6, 4, 2, 6, 4], [3, 4, 5, 3, 1, 5] 1:3 , 1:3 , 2:4
11. {3, 4} {{5, 6}} {{2, 4, 6}} syncd, [2, 4, 5, 3, 6, 5], [3, 6, 4, 2, 1, 4] 1:2 , 3:3 , 4:4
12. {3, 5} {{2, 4}} {{3, 4}} syncd, [2, 4, 5, 2, 1, 5], [3, 6, 4, 3, 6, 4] 2:2 , 2:2 , 4:4
13. {3, 6} {{2, 4}} {{3, 4}} syncd, [2, 4, 5, 2, 6, 4], [3, 6, 4, 3, 1, 5] 1:2 , 1:2 , 4:4
14. {4, 5} {{3, 4}} {{2, 4, 6}} syncd, [2, 4, 4, 3, 1, 5], [3, 6, 5, 2, 6, 4] 1:2 , 3:3 , 4:4
15. {4, 6} {{3, 4}} {{1, 3, 5}} syncd, [2, 4, 4, 3, 6, 4], [3, 6, 5, 2, 1, 5] 1:2 , 3:3 , 4:4
16. {5, 6} {{2, 4}} {{5, 6}} syncd, [2, 4, 4, 2, 1, 4], [3, 6, 5, 3, 6, 5] 2:2 , 2:2 , 4:4
17. {2, 3, 4} {{5, 6}} {{2, 4}} syncd, [2, 6, 5, 3, 6, 5], [3, 4, 4, 2, 1, 4] 2:2 , 2:2 , 3:4
18. {2, 3, 5} {{1, 2, 5, 6}} {{3, 4}} notsyncd, [2, 6, 5, 2, 1, 5], [3, 4, 4, 3, 6, 4] 2:4 , 1:2 , 2:4
19. {2, 3, 6} {{2, 4, 6}} {{3, 4}} syncd, [2, 6, 5, 2, 6, 4], [3, 4, 4, 3, 1, 5] 3:3 , 1:2 , 4:4
20. {2, 4, 5} {{3, 4}, {1, 2, 5, 6}} {{2, 4}} syncd, [2, 6, 4, 3, 1, 5], [3, 4, 5, 2, 6, 4] 4:6 , 1:2 , 4:4
21. {2, 4, 6} {{3, 4}} {{1, 3, 5}, {2, 4}} syncd, [2, 6, 4, 3, 6, 4], [3, 4, 5, 2, 1, 5] 2:2 , 4:5 , 4:4
22. {2, 5, 6} {{2, 4, 6}} {{5, 6}} syncd, [2, 6, 4, 2, 1, 4], [3, 4, 5, 3, 6, 5] 3:3 , 1:2 , 4:4
23. {3, 4, 5} {{1, 2, 3, 4, 5}} {{2, 4, 6}} syncd, [2, 4, 5, 3, 1, 5], [3, 6, 4, 2, 6, 4] 5:5 , 3:3 , 4:4
24. {3, 4, 6} {{3, 4, 5, 6}} {{1, 2, 3, 4, 5, 6}} syncd, [2, 4, 5, 3, 6, 4], [3, 6, 4, 2, 1, 5] 3:4 , 5:6 , 4:4
25. {3, 5, 6} {{2, 4}} {{3, 4}, {5, 6}} notsyncd, [2, 4, 5, 2, 1, 4], [3, 6, 4, 3, 6, 5] 1:2 , 2:4 , 2:4
26. {4, 5, 6} {{3, 4}} {{5, 6}} syncd, [2, 4, 4, 3, 1, 4], [3, 6, 5, 2, 6, 5] 2:2 , 2:2 , 4:4
27. {2, 3, 4, 5} {{1, 2, 5, 6}} {{2, 4}} syncd, [2, 6, 5, 3, 1, 5], [3, 4, 4, 2, 6, 4] 4:4 , 1:2 , 4:4
28. {2, 3, 4, 6} {{3, 4, 5, 6}} {{2, 4}} syncd, [2, 6, 5, 3, 6, 4], [3, 4, 4, 2, 1, 5] 4:4 , 1:2 , 4:4
29. {2, 3, 5, 6} {{2, 4, 6}} {{3, 4}, {5, 6}} notsyncd, [2, 6, 5, 2, 1, 4], [3, 4, 4, 3, 6, 5] 1:3 , 1:4 , 3:4
30. {2, 4, 5, 6} {{3, 4}} {{5, 6}, {2, 4}} syncd, [2, 6, 4, 3, 1, 4], [3, 4, 5, 2, 6, 5] 2:2 , 2:4 , 4:4
31. {3, 4, 5, 6} {{1, 2, 3, 4, 5}} {{5, 6}} syncd, [2, 4, 5, 3, 1, 4], [3, 6, 4, 2, 6, 5] 5:5 , 1:2 , 4:4
32. {2, 3, 4, 5, 6} {{1, 2, 3, 4, 5, 6}} {{5, 6}, {2, 4}} notsyncd, [2, 6, 5, 3, 1, 4], [3, 4, 4, 2, 6, 5] 4:6 , 1:4 , 3:4

Summary

Spanning Vector: [12, 24, 24, 36, 24, 24]

Unicycle Frequency Length Value
{1, 3, 5} 5 3 15
{5, 6} 8 2 16
{3, 4} 11 2 22
{2, 4} 10 2 20
{3, 4, 5, 6} 4 4 16
{1, 2, 5, 6} 3 4 12
{2, 4, 6} 7 3 21
{1, 2, 3, 4, 5} 2 5 10
{1, 2, 3, 4, 5, 6} 2 6 12

Twice No. of Spanning In-Trees = 144