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Statistic identifier: St000096
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Collection: Graphs
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Description: The number of spanning trees of a graph.
A subgraph $H \subseteq G$ is a spanning tree if $V(H)=V(G)$ and $H$ is a tree (i.e. $H$ is connected and contains no cycles).
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References:
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Code:
def statistic(g):
return g.spanning_trees_count()
-----------------------------------------------------------------------------
Statistic values:
([],1) => 1
([],2) => 0
([(0,1)],2) => 1
([],3) => 0
([(1,2)],3) => 0
([(0,2),(1,2)],3) => 1
([(0,1),(0,2),(1,2)],3) => 3
([],4) => 0
([(2,3)],4) => 0
([(1,3),(2,3)],4) => 0
([(0,3),(1,3),(2,3)],4) => 1
([(0,3),(1,2)],4) => 0
([(0,3),(1,2),(2,3)],4) => 1
([(1,2),(1,3),(2,3)],4) => 0
([(0,3),(1,2),(1,3),(2,3)],4) => 3
([(0,2),(0,3),(1,2),(1,3)],4) => 4
([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 8
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 16
([],5) => 0
([(3,4)],5) => 0
([(2,4),(3,4)],5) => 0
([(1,4),(2,4),(3,4)],5) => 0
([(0,4),(1,4),(2,4),(3,4)],5) => 1
([(1,4),(2,3)],5) => 0
([(1,4),(2,3),(3,4)],5) => 0
([(0,1),(2,4),(3,4)],5) => 0
([(2,3),(2,4),(3,4)],5) => 0
([(0,4),(1,4),(2,3),(3,4)],5) => 1
([(1,4),(2,3),(2,4),(3,4)],5) => 0
([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 3
([(1,3),(1,4),(2,3),(2,4)],5) => 0
([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 4
([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 0
([(0,4),(1,3),(2,3),(2,4),(3,4)],5) => 3
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 8
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 12
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 20
([(0,4),(1,3),(2,3),(2,4)],5) => 1
([(0,1),(2,3),(2,4),(3,4)],5) => 0
([(0,3),(1,2),(1,4),(2,4),(3,4)],5) => 3
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5) => 9
([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => 5
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5) => 11
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => 21
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5) => 8
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 0
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 16
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 40
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5) => 24
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) => 45
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 75
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 125
([],6) => 0
([(4,5)],6) => 0
([(3,5),(4,5)],6) => 0
([(2,5),(3,5),(4,5)],6) => 0
([(1,5),(2,5),(3,5),(4,5)],6) => 0
([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 1
([(2,5),(3,4)],6) => 0
([(2,5),(3,4),(4,5)],6) => 0
([(1,2),(3,5),(4,5)],6) => 0
([(3,4),(3,5),(4,5)],6) => 0
([(1,5),(2,5),(3,4),(4,5)],6) => 0
([(0,1),(2,5),(3,5),(4,5)],6) => 0
([(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 1
([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
([(2,4),(2,5),(3,4),(3,5)],6) => 0
([(0,5),(1,5),(2,4),(3,4)],6) => 0
([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 0
([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 0
([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 1
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 4
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 3
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 0
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 4
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 12
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 20
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 32
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 48
([(0,5),(1,4),(2,3)],6) => 0
([(1,5),(2,4),(3,4),(3,5)],6) => 0
([(0,1),(2,5),(3,4),(4,5)],6) => 0
([(1,2),(3,4),(3,5),(4,5)],6) => 0
([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 1
([(1,4),(2,3),(2,5),(3,5),(4,5)],6) => 0
([(0,1),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 3
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 0
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 9
([(1,4),(1,5),(2,3),(2,5),(3,4)],6) => 0
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 4
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 0
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => 5
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 0
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6) => 3
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 11
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => 21
([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 1
([(0,1),(2,4),(2,5),(3,4),(3,5)],6) => 0
([(0,5),(1,5),(2,3),(2,4),(3,4)],6) => 0
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => 4
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6) => 3
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6) => 3
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6) => 3
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6) => 12
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6) => 8
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 9
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 24
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 8
([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 16
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 16
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6) => 32
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 20
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 21
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 28
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => 52
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 24
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 16
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 40
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 64
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 96
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 12
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 0
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 24
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 0
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 45
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6) => 6
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6) => 15
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6) => 11
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 14
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 8
([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 11
([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 29
([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 21
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 30
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 55
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 36
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 24
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 69
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 60
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 111
([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 45
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 40
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 75
([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => 61
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 54
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 99
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 180
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 81
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 135
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 120
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 216
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 324
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6) => 0
([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6) => 8
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6) => 9
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 24
([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 16
([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 48
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6) => 30
([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6) => 64
([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 40
([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 55
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 56
([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 104
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 128
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 192
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],6) => 35
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 32
([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 66
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 121
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6) => 75
([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 130
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 114
([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 209
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 336
([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 115
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 100
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 185
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 75
([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 125
([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 300
([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 540
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 224
([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 200
([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 225
([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 360
([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 384
([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 576
([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 864
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1296
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Created: Jun 13, 2013 at 16:35 by Chris Berg
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Last Updated: Dec 17, 2015 at 19:10 by Matthew Donahue