***************************************************************************** * www.FindStat.org - The Combinatorial Statistic Finder * * * * Copyright (C) 2019 The FindStatCrew * * * * 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