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Statistic identifier: St000343
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Collection: Graphs
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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 $x=y=2$.
-----------------------------------------------------------------------------
References:
-----------------------------------------------------------------------------
Code:
def statistic(x):
return 2^x.num_edges()
def statistic_alternative(g):
return g.tutte_polynomial().subs(x=Integer(2),y=Integer(2))
-----------------------------------------------------------------------------
Statistic values:
([],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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Created: Dec 23, 2015 at 09:06 by Martin Rubey
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Last Updated: Dec 23, 2015 at 09:06 by Martin Rubey