Values
([],1) => 1
([],2) => 2
([(0,1)],2) => 2
([],3) => 3
([(1,2)],3) => 4
([(0,2),(1,2)],3) => 4
([(0,1),(0,2),(1,2)],3) => 3
([],4) => 4
([(2,3)],4) => 6
([(1,3),(2,3)],4) => 7
([(0,3),(1,3),(2,3)],4) => 6
([(0,3),(1,2)],4) => 5
([(0,3),(1,2),(2,3)],4) => 6
([(1,2),(1,3),(2,3)],4) => 6
([(0,3),(1,2),(1,3),(2,3)],4) => 7
([(0,2),(0,3),(1,2),(1,3)],4) => 5
([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 6
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4
([],5) => 5
([(3,4)],5) => 8
([(2,4),(3,4)],5) => 10
([(1,4),(2,4),(3,4)],5) => 10
([(0,4),(1,4),(2,4),(3,4)],5) => 8
([(1,4),(2,3)],5) => 8
([(1,4),(2,3),(3,4)],5) => 10
([(0,1),(2,4),(3,4)],5) => 10
([(2,3),(2,4),(3,4)],5) => 9
([(0,4),(1,4),(2,3),(3,4)],5) => 11
([(1,4),(2,3),(2,4),(3,4)],5) => 12
([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 11
([(1,3),(1,4),(2,3),(2,4)],5) => 9
([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 11
([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 11
([(0,4),(1,3),(2,3),(2,4),(3,4)],5) => 11
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 12
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 8
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 9
([(0,4),(1,3),(2,3),(2,4)],5) => 10
([(0,1),(2,3),(2,4),(3,4)],5) => 8
([(0,3),(1,2),(1,4),(2,4),(3,4)],5) => 11
([(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) => 7
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5) => 10
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => 10
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5) => 11
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 8
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 10
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 10
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5) => 10
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) => 8
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 8
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5
([],6) => 6
([(4,5)],6) => 10
([(3,5),(4,5)],6) => 13
([(2,5),(3,5),(4,5)],6) => 14
([(1,5),(2,5),(3,5),(4,5)],6) => 13
([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 10
([(2,5),(3,4)],6) => 11
([(2,5),(3,4),(4,5)],6) => 14
([(1,2),(3,5),(4,5)],6) => 15
([(3,4),(3,5),(4,5)],6) => 12
([(1,5),(2,5),(3,4),(4,5)],6) => 17
([(0,1),(2,5),(3,5),(4,5)],6) => 15
([(2,5),(3,4),(3,5),(4,5)],6) => 17
([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 16
([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 18
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 15
([(2,4),(2,5),(3,4),(3,5)],6) => 13
([(0,5),(1,5),(2,4),(3,4)],6) => 13
([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 18
([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 18
([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 16
([(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 18
([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 14
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 17
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 20
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 19
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 18
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 14
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 16
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 16
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 16
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 17
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 17
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 11
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 12
([(0,5),(1,4),(2,3)],6) => 9
([(1,5),(2,4),(3,4),(3,5)],6) => 16
([(0,1),(2,5),(3,4),(4,5)],6) => 14
([(1,2),(3,4),(3,5),(4,5)],6) => 13
([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 16
([(1,4),(2,3),(2,5),(3,5),(4,5)],6) => 19
([(0,1),(2,5),(3,4),(3,5),(4,5)],6) => 17
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 20
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 16
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 15
([(1,4),(1,5),(2,3),(2,5),(3,4)],6) => 12
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 15
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 18
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => 16
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Description
The number of induced subgraphs.
A subgraph $H \subseteq G$ is induced if $E(H)$ consists of all edges in $E(G)$ that connect the vertices of $H$.
A subgraph $H \subseteq G$ is induced if $E(H)$ consists of all edges in $E(G)$ that connect the vertices of $H$.
Code
def statistic(G):
return sum(1 for k in range(1, G.num_verts()+1) for g in graphs(k) if G.subgraph_search(g, True) is not None)
Created
Jun 13, 2013 at 11:19 by Travis Scrimshaw
Updated
Dec 17, 2015 at 06:40 by Matthew Donahue
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