Values
=>
Cc0020;cc-rep
([],1)=>1
([],2)=>1
([(0,1)],2)=>2
([],3)=>1
([(1,2)],3)=>2
([(0,2),(1,2)],3)=>4
([(0,1),(0,2),(1,2)],3)=>8
([],4)=>1
([(2,3)],4)=>2
([(1,3),(2,3)],4)=>4
([(0,3),(1,3),(2,3)],4)=>8
([(0,3),(1,2)],4)=>4
([(0,3),(1,2),(2,3)],4)=>8
([(1,2),(1,3),(2,3)],4)=>8
([(0,3),(1,2),(1,3),(2,3)],4)=>16
([(0,2),(0,3),(1,2),(1,3)],4)=>16
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>32
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>64
([],5)=>1
([(3,4)],5)=>2
([(2,4),(3,4)],5)=>4
([(1,4),(2,4),(3,4)],5)=>8
([(0,4),(1,4),(2,4),(3,4)],5)=>16
([(1,4),(2,3)],5)=>4
([(1,4),(2,3),(3,4)],5)=>8
([(0,1),(2,4),(3,4)],5)=>8
([(2,3),(2,4),(3,4)],5)=>8
([(0,4),(1,4),(2,3),(3,4)],5)=>16
([(1,4),(2,3),(2,4),(3,4)],5)=>16
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>32
([(1,3),(1,4),(2,3),(2,4)],5)=>16
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)=>32
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>32
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>32
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>64
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>64
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>128
([(0,4),(1,3),(2,3),(2,4)],5)=>16
([(0,1),(2,3),(2,4),(3,4)],5)=>16
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)=>32
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)=>64
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)=>32
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>64
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)=>128
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)=>64
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>64
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>128
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>256
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)=>128
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)=>256
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>512
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>1024
([],6)=>1
([(4,5)],6)=>2
([(3,5),(4,5)],6)=>4
([(2,5),(3,5),(4,5)],6)=>8
([(1,5),(2,5),(3,5),(4,5)],6)=>16
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>32
([(2,5),(3,4)],6)=>4
([(2,5),(3,4),(4,5)],6)=>8
([(1,2),(3,5),(4,5)],6)=>8
([(3,4),(3,5),(4,5)],6)=>8
([(1,5),(2,5),(3,4),(4,5)],6)=>16
([(0,1),(2,5),(3,5),(4,5)],6)=>16
([(2,5),(3,4),(3,5),(4,5)],6)=>16
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>32
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>32
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>64
([(2,4),(2,5),(3,4),(3,5)],6)=>16
([(0,5),(1,5),(2,4),(3,4)],6)=>16
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>32
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>32
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>32
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>32
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)=>32
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>64
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>64
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>64
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>128
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>64
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>64
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>128
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>128
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>128
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>256
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>256
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>512
([(0,5),(1,4),(2,3)],6)=>8
([(1,5),(2,4),(3,4),(3,5)],6)=>16
([(0,1),(2,5),(3,4),(4,5)],6)=>16
([(1,2),(3,4),(3,5),(4,5)],6)=>16
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>32
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>32
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)=>32
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>64
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>64
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>128
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)=>32
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>64
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>64
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)=>64
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>64
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)=>64
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>128
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>128
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>128
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>256
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>32
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)=>32
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)=>32
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)=>64
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)=>64
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)=>64
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>64
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>64
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)=>128
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)=>128
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>128
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>256
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>64
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>128
([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>128
([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>256
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>128
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)=>256
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>256
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>256
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>256
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>512
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>256
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>256
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>256
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>512
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>512
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1024
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>128
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>128
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>256
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>256
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>512
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)=>64
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)=>128
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)=>128
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>128
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>128
([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>128
([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>256
([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>256
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>256
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>512
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)=>256
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>256
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>512
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>512
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1024
([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>512
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>512
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>512
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1024
([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>512
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>512
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1024
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2048
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>512
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1024
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>1024
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>2048
([(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)=>4096
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)=>64
([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)=>128
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)=>128
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>128
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>256
([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>256
([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>512
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)=>256
([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>512
([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>512
([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>512
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>512
([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1024
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>1024
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2048
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],6)=>256
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>256
([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>512
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>1024
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)=>512
([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1024
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>1024
([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2048
([(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)=>4096
([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>1024
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1024
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2048
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1024
([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1024
([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2048
([(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)=>4096
([(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)=>8192
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>2048
([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>2048
([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2048
([(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)=>4096
([(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)=>4096
([(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)=>8192
([(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)=>16384
([(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)=>32768
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Description
The number of spanning subgraphs of a graph.
This is the number of subsets of the edge set of the graph, or the evaluation of the Tutte polynomial at $x=y=2$.
This is the number of subsets of the edge set of the graph, or the evaluation of the Tutte polynomial at $x=y=2$.
Code
def statistic(x):
return 2^x.num_edges()
def statistic_alternative(g):
return g.tutte_polynomial().subs(x=Integer(2),y=Integer(2))
Created
Dec 23, 2015 at 09:06 by Martin Rubey
Updated
Dec 23, 2015 at 09:06 by Martin Rubey
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