***************************************************************************** * 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: St000096 ----------------------------------------------------------------------------- Collection: Graphs ----------------------------------------------------------------------------- Description: The number of spanning trees of a graph. A subgraph $H \subseteq G$ is a spanning tree if $V(H)=V(G)$ and $H$ is a tree (i.e. $H$ is connected and contains no cycles). ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: def statistic(g): return g.spanning_trees_count() ----------------------------------------------------------------------------- Statistic values: ([],1) => 1 ([],2) => 0 ([(0,1)],2) => 1 ([],3) => 0 ([(1,2)],3) => 0 ([(0,2),(1,2)],3) => 1 ([(0,1),(0,2),(1,2)],3) => 3 ([],4) => 0 ([(2,3)],4) => 0 ([(1,3),(2,3)],4) => 0 ([(0,3),(1,3),(2,3)],4) => 1 ([(0,3),(1,2)],4) => 0 ([(0,3),(1,2),(2,3)],4) => 1 ([(1,2),(1,3),(2,3)],4) => 0 ([(0,3),(1,2),(1,3),(2,3)],4) => 3 ([(0,2),(0,3),(1,2),(1,3)],4) => 4 ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 8 ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 16 ([],5) => 0 ([(3,4)],5) => 0 ([(2,4),(3,4)],5) => 0 ([(1,4),(2,4),(3,4)],5) => 0 ([(0,4),(1,4),(2,4),(3,4)],5) => 1 ([(1,4),(2,3)],5) => 0 ([(1,4),(2,3),(3,4)],5) => 0 ([(0,1),(2,4),(3,4)],5) => 0 ([(2,3),(2,4),(3,4)],5) => 0 ([(0,4),(1,4),(2,3),(3,4)],5) => 1 ([(1,4),(2,3),(2,4),(3,4)],5) => 0 ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 3 ([(1,3),(1,4),(2,3),(2,4)],5) => 0 ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 4 ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 0 ([(0,4),(1,3),(2,3),(2,4),(3,4)],5) => 3 ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 8 ([(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) => 1 ([(0,1),(2,3),(2,4),(3,4)],5) => 0 ([(0,3),(1,2),(1,4),(2,4),(3,4)],5) => 3 ([(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) => 5 ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5) => 11 ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => 21 ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5) => 8 ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 0 ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 16 ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 40 ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5) => 24 ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) => 45 ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 75 ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 125 ([],6) => 0 ([(4,5)],6) => 0 ([(3,5),(4,5)],6) => 0 ([(2,5),(3,5),(4,5)],6) => 0 ([(1,5),(2,5),(3,5),(4,5)],6) => 0 ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 1 ([(2,5),(3,4)],6) => 0 ([(2,5),(3,4),(4,5)],6) => 0 ([(1,2),(3,5),(4,5)],6) => 0 ([(3,4),(3,5),(4,5)],6) => 0 ([(1,5),(2,5),(3,4),(4,5)],6) => 0 ([(0,1),(2,5),(3,5),(4,5)],6) => 0 ([(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 1 ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3 ([(2,4),(2,5),(3,4),(3,5)],6) => 0 ([(0,5),(1,5),(2,4),(3,4)],6) => 0 ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 0 ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 1 ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 0 ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 1 ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 4 ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 3 ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8 ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 0 ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 4 ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 12 ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8 ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 20 ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 32 ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 48 ([(0,5),(1,4),(2,3)],6) => 0 ([(1,5),(2,4),(3,4),(3,5)],6) => 0 ([(0,1),(2,5),(3,4),(4,5)],6) => 0 ([(1,2),(3,4),(3,5),(4,5)],6) => 0 ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 1 ([(1,4),(2,3),(2,5),(3,5),(4,5)],6) => 0 ([(0,1),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 3 ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 0 ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 9 ([(1,4),(1,5),(2,3),(2,5),(3,4)],6) => 0 ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 4 ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 0 ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => 5 ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 0 ([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6) => 3 ([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 11 ([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 8 ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => 21 ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 1 ([(0,1),(2,4),(2,5),(3,4),(3,5)],6) => 0 ([(0,5),(1,5),(2,3),(2,4),(3,4)],6) => 0 ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => 4 ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6) => 3 ([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6) => 3 ([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6) => 3 ([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6) => 12 ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6) => 8 ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 9 ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 24 ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 8 ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(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) => 16 ([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6) => 32 ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 20 ([(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) => 28 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => 52 ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 24 ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 16 ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 40 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 64 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 96 ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 12 ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 0 ([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 24 ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 0 ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 45 ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6) => 6 ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6) => 15 ([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6) => 11 ([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 14 ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 8 ([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 11 ([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 29 ([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 21 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 30 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 55 ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 36 ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 24 ([(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) => 60 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 111 ([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 45 ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 40 ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 75 ([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => 61 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 54 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 99 ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 180 ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 81 ([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 135 ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 120 ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 216 ([(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) => 324 ([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6) => 0 ([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6) => 8 ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6) => 9 ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 24 ([(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) => 48 ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6) => 30 ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6) => 64 ([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 40 ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 55 ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 56 ([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 104 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 128 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 192 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],6) => 35 ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 32 ([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 66 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 121 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6) => 75 ([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 130 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 114 ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 209 ([(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) => 336 ([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 115 ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 100 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 185 ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 75 ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 125 ([(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) => 300 ([(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) => 540 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 224 ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 200 ([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 225 ([(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) => 360 ([(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) => 384 ([(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) => 576 ([(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) => 864 ([(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) => 1296 ----------------------------------------------------------------------------- Created: Jun 13, 2013 at 16:35 by Chris Berg ----------------------------------------------------------------------------- Last Updated: Dec 17, 2015 at 19:10 by Matthew Donahue