Spanning Run

R

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

B

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

pi

[4, 1, 3, 4, 2, 2]

indegrees

[3, 1, 2, 4, 1, 1]

Friedman weight

16

det

2831/16384, .1727905273

nullspace of Delta

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

nullspace of A

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

spanNum

80

Data

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

Summary

Spanning Vector: [40, 10, 30, 40, 20, 20]

Unicycle Frequency Length Value
{1, 3} 12 2 24
{4, 6} 10 2 20
{1, 3, 4} 8 3 24
{1, 4, 5} 8 3 24
{3, 4, 6} 7 3 21
{1, 3, 4, 5, 6} 2 5 10
{1, 2, 4, 5} 4 4 16
{1, 2, 5} 5 3 15
{1, 2, 3, 4, 5, 6} 1 6 6

Twice No. of Spanning In-Trees = 160