***************************************************************************** * 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: St000299 ----------------------------------------------------------------------------- Collection: Graphs ----------------------------------------------------------------------------- Description: The number of nonisomorphic vertex-induced subtrees. ----------------------------------------------------------------------------- References: [1] Mubayi, D., Verstraete, J. The number of trees in a graph [[arXiv:1511.07274]] ----------------------------------------------------------------------------- Code: def statistic(G): V = G.vertices() indSubG = set() for subV in Subsets(V): subG = G.subgraph(subV) if subG.is_tree(): indSubG.add(subG.canonical_label().copy(immutable=True)) return len(indSubG) ----------------------------------------------------------------------------- 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) => 2 ([],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) => 2 ([(0,3),(1,2),(2,3)],4) => 4 ([(1,2),(1,3),(2,3)],4) => 2 ([(0,3),(1,2),(1,3),(2,3)],4) => 3 ([(0,2),(0,3),(1,2),(1,3)],4) => 3 ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3 ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2 ([],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) => 2 ([(1,4),(2,3),(3,4)],5) => 4 ([(0,1),(2,4),(3,4)],5) => 3 ([(2,3),(2,4),(3,4)],5) => 2 ([(0,4),(1,4),(2,3),(3,4)],5) => 6 ([(1,4),(2,3),(2,4),(3,4)],5) => 3 ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 4 ([(1,3),(1,4),(2,3),(2,4)],5) => 3 ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 5 ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3 ([(0,4),(1,3),(2,3),(2,4),(3,4)],5) => 4 ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4 ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 4 ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4 ([(0,4),(1,3),(2,3),(2,4)],5) => 5 ([(0,1),(2,3),(2,4),(3,4)],5) => 2 ([(0,3),(1,2),(1,4),(2,4),(3,4)],5) => 4 ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5) => 3 ([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => 4 ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5) => 4 ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => 4 ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5) => 4 ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2 ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3 ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3 ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5) => 3 ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) => 3 ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3 ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2 ([],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) => 2 ([(2,5),(3,4),(4,5)],6) => 4 ([(1,2),(3,5),(4,5)],6) => 3 ([(3,4),(3,5),(4,5)],6) => 2 ([(1,5),(2,5),(3,4),(4,5)],6) => 6 ([(0,1),(2,5),(3,5),(4,5)],6) => 4 ([(2,5),(3,4),(3,5),(4,5)],6) => 3 ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 8 ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 4 ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 5 ([(2,4),(2,5),(3,4),(3,5)],6) => 3 ([(0,5),(1,5),(2,4),(3,4)],6) => 3 ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 5 ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 8 ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3 ([(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 4 ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 7 ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 7 ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4 ([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 6 ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5 ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4 ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 6 ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 6 ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4 ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5 ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5 ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 5 ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5 ([(0,5),(1,4),(2,3)],6) => 2 ([(1,5),(2,4),(3,4),(3,5)],6) => 5 ([(0,1),(2,5),(3,4),(4,5)],6) => 4 ([(1,2),(3,4),(3,5),(4,5)],6) => 2 ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 8 ([(1,4),(2,3),(2,5),(3,5),(4,5)],6) => 4 ([(0,1),(2,5),(3,4),(3,5),(4,5)],6) => 3 ([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 6 ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 3 ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 4 ([(1,4),(1,5),(2,3),(2,5),(3,4)],6) => 4 ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 6 ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 4 ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => 7 ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 4 ([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6) => 4 ([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 6 ([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6 ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => 4 ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => 5 ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 6 ([(0,1),(2,4),(2,5),(3,4),(3,5)],6) => 3 ([(0,5),(1,5),(2,3),(2,4),(3,4)],6) => 3 ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => 7 ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6) => 5 ([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6) => 5 ([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3 ([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6) => 6 ([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6) => 5 ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6) => 6 ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 4 ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4 ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2 ([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 6 ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3 ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4 ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 6 ([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6) => 6 ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6 ([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 6 ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => 6 ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 5 ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3 ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4 ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 4 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4 ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 6 ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 3 ([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 5 ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 3 ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 4 ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6) => 5 ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6) => 6 ([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6) => 5 ([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 5 ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 5 ([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 7 ([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6 ([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 5 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 5 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 6 ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 5 ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 5 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 5 ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5 ([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5 ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3 ([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4 ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4 ([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => 5 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 4 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5 ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4 ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 4 ([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4 ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 4 ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 4 ([(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) => 4 ([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6) => 2 ([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6) => 5 ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6) => 4 ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2 ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 4 ([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4 ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3 ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6) => 4 ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6) => 4 ([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4 ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4 ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4 ([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 3 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],6) => 5 ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 4 ([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 4 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 4 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6) => 4 ([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 4 ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4 ([(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) => 4 ([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 4 ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4 ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4 ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2 ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 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) => 3 ([(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) => 3 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 4 ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 3 ([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3 ([(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) => 3 ([(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) => 3 ([(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) => 3 ([(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) => 3 ([(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) => 2 ----------------------------------------------------------------------------- Created: Nov 24, 2015 at 17:41 by Christian Stump ----------------------------------------------------------------------------- Last Updated: Nov 25, 2015 at 11:11 by Christian Stump