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University of South Carolina at Columbia
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Partitioning the Labeled Spanning Trees of an Arbitrary Graph into Isomorphism Classes
Paper
Source Code (ver. 1.0)
Isomorphism Classes of Spanning Trees of Selected Graphs
Spanning Trees of Complete Graphs
2
3
4
5
6
7
8
9
10
1
1
3
1
16
2
125
3
1,296
6
16,807
11
262,144
23
4,782,969
47
100,000,000
106
Spanning Trees of Complete Bipartite Graphs
1
2
3
4
5
6
7
8
9
10
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
---
4
1
12
2
32
2
80
3
192
3
448
4
1,024
4
2,304
5
5,120
5
3
---
---
81
3
432
7
2,025
10
8,748
14
35,721
19
139,968
24
531,441
30
1,968,300
37
4
---
---
---
4,096
9
32,000
28
221,184
45
1,404,928
73
8,388,608
105
5
---
---
---
---
390,625
37
4,050,000
132
6
---
---
---
---
---
60,466,176
168
Spanning Trees of Hypercubes
1
2
3
4
5
1
1
4
1
384
6
Spanning Trees of Other Graphs
Petersen Graph
2000
20
Tetrahedron
16
2
Cube
384
6
Octahedron
384
5
Dodecahedron
Icosaahedron
5,184,000
434