*****************************************************************************
* www.FindStat.org - The Combinatorial Statistic Finder *
* *
* Copyright (C) 2019 The FindStatCrew <info@findstat.org> *
* *
* This information is distributed in the hope that it will be useful, *
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. *
*****************************************************************************
-----------------------------------------------------------------------------
Statistic identifier: St000086
-----------------------------------------------------------------------------
Collection: Graphs
-----------------------------------------------------------------------------
Description: The number of subgraphs.
Given a graph $G$, this is the number of graphs $H$ such that $H \hookrightarrow G$.
-----------------------------------------------------------------------------
References:
-----------------------------------------------------------------------------
Code:
def statistic(G):
return sum(1 for g in graphs(G.num_verts()) if G.subgraph_search(g) is not None)
-----------------------------------------------------------------------------
Statistic values:
([],1) => 1
([],2) => 1
([(0,1)],2) => 2
([],3) => 1
([(1,2)],3) => 2
([(0,2),(1,2)],3) => 3
([(0,1),(0,2),(1,2)],3) => 4
([],4) => 1
([(2,3)],4) => 2
([(1,3),(2,3)],4) => 3
([(0,3),(1,3),(2,3)],4) => 4
([(0,3),(1,2)],4) => 3
([(0,3),(1,2),(2,3)],4) => 5
([(1,2),(1,3),(2,3)],4) => 4
([(0,3),(1,2),(1,3),(2,3)],4) => 8
([(0,2),(0,3),(1,2),(1,3)],4) => 6
([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 10
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 11
([],5) => 1
([(3,4)],5) => 2
([(2,4),(3,4)],5) => 3
([(1,4),(2,4),(3,4)],5) => 4
([(0,4),(1,4),(2,4),(3,4)],5) => 5
([(1,4),(2,3)],5) => 3
([(1,4),(2,3),(3,4)],5) => 5
([(0,1),(2,4),(3,4)],5) => 5
([(2,3),(2,4),(3,4)],5) => 4
([(0,4),(1,4),(2,3),(3,4)],5) => 8
([(1,4),(2,3),(2,4),(3,4)],5) => 8
([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 12
([(1,3),(1,4),(2,3),(2,4)],5) => 6
([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 11
([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 10
([(0,4),(1,3),(2,3),(2,4),(3,4)],5) => 12
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 18
([(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) => 7
([(0,1),(2,3),(2,4),(3,4)],5) => 7
([(0,3),(1,2),(1,4),(2,4),(3,4)],5) => 13
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5) => 16
([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => 8
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5) => 18
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => 25
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5) => 18
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 11
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 23
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 31
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5) => 22
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) => 28
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 33
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 34
([],6) => 1
([(4,5)],6) => 2
([(3,5),(4,5)],6) => 3
([(2,5),(3,5),(4,5)],6) => 4
([(1,5),(2,5),(3,5),(4,5)],6) => 5
([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 6
([(2,5),(3,4)],6) => 3
([(2,5),(3,4),(4,5)],6) => 5
([(1,2),(3,5),(4,5)],6) => 5
([(3,4),(3,5),(4,5)],6) => 4
([(1,5),(2,5),(3,4),(4,5)],6) => 8
([(0,1),(2,5),(3,5),(4,5)],6) => 7
([(2,5),(3,4),(3,5),(4,5)],6) => 8
([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 11
([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 12
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 16
([(2,4),(2,5),(3,4),(3,5)],6) => 6
([(0,5),(1,5),(2,4),(3,4)],6) => 6
([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 11
([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 12
([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 10
([(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 12
([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 10
([(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) => 18
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 20
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 28
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 12
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 15
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 20
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 20
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 26
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 34
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 21
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 36
([(0,5),(1,4),(2,3)],6) => 4
([(1,5),(2,4),(3,4),(3,5)],6) => 7
([(0,1),(2,5),(3,4),(4,5)],6) => 8
([(1,2),(3,4),(3,5),(4,5)],6) => 7
([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 12
([(1,4),(2,3),(2,5),(3,5),(4,5)],6) => 13
([(0,1),(2,5),(3,4),(3,5),(4,5)],6) => 14
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 22
([(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) => 26
([(1,4),(1,5),(2,3),(2,5),(3,4)],6) => 8
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 18
([(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) => 18
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 18
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6) => 16
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 37
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 37
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => 25
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => 49
([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 11
([(0,1),(2,4),(2,5),(3,4),(3,5)],6) => 10
([(0,5),(1,5),(2,3),(2,4),(3,4)],6) => 9
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => 18
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6) => 22
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6) => 23
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 18
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6) => 19
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6) => 33
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6) => 35
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 34
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 49
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 11
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 30
([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 23
([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 37
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 24
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6) => 50
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 45
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 53
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 47
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => 74
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 50
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 31
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 43
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 71
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 58
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 87
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 22
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 22
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 49
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 28
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 58
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6) => 12
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6) => 22
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6) => 32
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 29
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 29
([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 35
([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 55
([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 56
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 47
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 71
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 25
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 45
([(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) => 63
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 97
([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 70
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 33
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 72
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 88
([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => 78
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 57
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 98
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 114
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 26
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 74
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 86
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 103
([(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) => 118
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6) => 10
([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6) => 33
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6) => 26
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 20
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 48
([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 43
([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 61
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6) => 40
([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6) => 70
([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 68
([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 71
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 67
([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 106
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 73
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 112
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],6) => 44
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 41
([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 68
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 76
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6) => 48
([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 91
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 91
([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 126
([(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) => 141
([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 96
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 85
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 127
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 82
([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 34
([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 94
([(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) => 137
([(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) => 152
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 100
([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 104
([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 108
([(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) => 142
([(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) => 101
([(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) => 149
([(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) => 155
([(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) => 156
-----------------------------------------------------------------------------
Created: Jun 13, 2013 at 10:34 by Travis Scrimshaw
-----------------------------------------------------------------------------
Last Updated: Feb 17, 2015 at 18:10 by Martin Rubey