***************************************************************************** * 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: St000087 ----------------------------------------------------------------------------- Collection: Graphs ----------------------------------------------------------------------------- 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 $H$. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- 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) ----------------------------------------------------------------------------- Statistic 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 ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 19 ([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6) => 14 ([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 20 ([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 21 ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => 18 ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => 18 ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 14 ([(0,1),(2,4),(2,5),(3,4),(3,5)],6) => 13 ([(0,5),(1,5),(2,3),(2,4),(3,4)],6) => 15 ([(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) => 19 ([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6) => 20 ([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 16 ([(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) => 20 ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6) => 21 ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 19 ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 18 ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 12 ([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 19 ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 17 ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 16 ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 15 ([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6) => 19 ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 19 ([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 21 ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 18 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => 19 ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 21 ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 18 ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 17 ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 20 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 16 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 16 ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 16 ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 18 ([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 19 ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 15 ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 16 ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6) => 11 ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6) => 14 ([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6) => 17 ([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 17 ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 18 ([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 22 ([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 22 ([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 20 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 17 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 18 ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 13 ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 20 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 19 ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 19 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 19 ([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 20 ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 15 ([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 19 ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 18 ([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => 20 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 14 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 18 ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 17 ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 9 ([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 15 ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 17 ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 13 ([(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) => 12 ([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6) => 9 ([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6) => 19 ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6) => 13 ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 11 ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 16 ([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 16 ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 14 ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6) => 14 ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6) => 18 ([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 17 ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 15 ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 16 ([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 18 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 13 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 13 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],6) => 17 ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 15 ([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 16 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 12 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6) => 11 ([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 14 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 16 ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 16 ([(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) => 14 ([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 18 ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 14 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 17 ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 16 ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 10 ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 13 ([(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) => 14 ([(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) => 13 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 14 ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 15 ([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 13 ([(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) => 15 ([(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) => 9 ([(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) => 11 ([(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) => 10 ([(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) => 6 ----------------------------------------------------------------------------- Created: Jun 13, 2013 at 11:19 by Travis Scrimshaw ----------------------------------------------------------------------------- Last Updated: Dec 17, 2015 at 06:40 by Matthew Donahue