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Identifier
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).
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