Spanning Run

R

[4, 3, 1, 2, 1]

B

[3, 4, 5, 3, 3]

pi

[3, 1, 4, 2, 2]

indegrees

[2, 1, 4, 2, 1]

Friedman weight

12

det

153/1024, .1494140625

nullspace of Delta

{1, 2, 3, 4, 5}

nullspace of A

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

spanNum

36

Data

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

Summary

Spanning Vector: [18, 6, 24, 12, 12]

Unicycle	Frequency	Length	Value
{1, 2, 3, 4}	2	4	8
{3, 5}	6	2	12
{2, 4}	3	2	6
{1, 2, 3, 4, 5}	1	5	5
{1, 3}	6	2	12
{1, 3, 4}	4	3	12
{1, 3, 5}	3	3	9
{1, 3, 4, 5}	2	4	8

Twice No. of Spanning In-Trees = 72