Spanning Run

R

[5, 5, 1, 5, 2]

B

[3, 4, 5, 2, 1]

pi

[2, 2, 1, 1, 3]

indegrees

[2, 2, 1, 1, 4]

Friedman weight

9

det

351/4096, .8569335938e-1

nullspace of Delta

{1, 2, 3, 4, 5}

nullspace of A

` det(A) = ` -1/16

spanNum

27

Data

Coloring	R-cycles	B-cycles	Sync'd/Not Sync'd	R/B/Delta Ranking
1. {}	{{2, 5}}	{{1, 3, 5}, {2, 4}}	syncd, [5, 5, 1, 5, 2], [3, 4, 5, 2, 1]	2:2 , 4:5 , 4:4
2. {2}	{{2, 4, 5}}	{{1, 3, 5}}	notsyncd, [5, 4, 1, 5, 2], [3, 5, 5, 2, 1]	1:3 , 1:3 , 2:4
3. {3}	{{2, 5}}	{{1, 3}, {2, 4}}	syncd, [5, 5, 5, 5, 2], [3, 4, 1, 2, 1]	2:2 , 2:4 , 3:4
4. {4}	{{2, 5}}	{{1, 3, 5}}	syncd, [5, 5, 1, 2, 2], [3, 4, 5, 5, 1]	2:2 , 3:3 , 4:4
5. {5}	{{1, 5}}	{{2, 4}}	syncd, [5, 5, 1, 5, 1], [3, 4, 5, 2, 2]	2:2 , 2:2 , 4:4
6. {2, 3}	{{2, 4, 5}}	{{1, 3}}	syncd, [5, 4, 5, 5, 2], [3, 5, 1, 2, 1]	3:3 , 2:2 , 4:4
7. {2, 4}	{{2, 4}}	{{1, 3, 5}}	syncd, [5, 4, 1, 2, 2], [3, 5, 5, 5, 1]	2:2 , 3:3 , 4:4
8. {2, 5}	{{1, 5}}	{{2, 5}}	syncd, [5, 4, 1, 5, 1], [3, 5, 5, 2, 2]	2:2 , 2:2 , 4:4
9. {3, 4}	{{2, 5}}	{{1, 3}}	syncd, [5, 5, 5, 2, 2], [3, 4, 1, 5, 1]	2:2 , 2:2 , 4:4
10. {3, 5}	{{1, 5}}	{{1, 3}, {2, 4}}	syncd, [5, 5, 5, 5, 1], [3, 4, 1, 2, 2]	2:2 , 2:4 , 3:4
11. {4, 5}	{{1, 5}}	{{2, 4, 5}}	syncd, [5, 5, 1, 2, 1], [3, 4, 5, 5, 2]	2:2 , 3:3 , 4:4
12. {2, 3, 4}	{{2, 4}}	{{1, 3}}	syncd, [5, 4, 5, 2, 2], [3, 5, 1, 5, 1]	2:2 , 2:2 , 4:4
13. {2, 3, 5}	{{1, 5}}	{{2, 5}, {1, 3}}	syncd, [5, 4, 5, 5, 1], [3, 5, 1, 2, 2]	2:2 , 2:4 , 4:4
14. {2, 4, 5}	{{1, 5}, {2, 4}}	{{2, 5}}	syncd, [5, 4, 1, 2, 1], [3, 5, 5, 5, 2]	2:4 , 2:2 , 4:4
15. {3, 4, 5}	{{1, 5}}	{{1, 3}, {2, 4, 5}}	syncd, [5, 5, 5, 2, 1], [3, 4, 1, 5, 2]	2:2 , 4:5 , 4:4
16. {2, 3, 4, 5}	{{1, 5}, {2, 4}}	{{2, 5}, {1, 3}}	notsyncd, [5, 4, 5, 2, 1], [3, 5, 1, 5, 2]	2:4 , 2:4 , 2:4

Summary

Spanning Vector: [12, 12, 6, 6, 18]

Unicycle	Frequency	Length	Value
{2, 5}	6	2	12
{2, 4, 5}	3	3	9
{1, 3, 5}	3	3	9
{1, 5}	6	2	12
{2, 4}	3	2	6
{1, 3}	3	2	6

Twice No. of Spanning In-Trees = 54