Values
=>
Cc0020;cc-rep
([],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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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).
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).
Code
def statistic(g):
return g.spanning_trees_count()
Created
Jun 13, 2013 at 16:35 by Chris Berg
Updated
Dec 17, 2015 at 19:10 by Matthew Donahue
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