***************************************************************************** * 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: St001834 ----------------------------------------------------------------------------- Collection: Graphs ----------------------------------------------------------------------------- Description: The number of non-isomorphic minors of a graph. A minor of a graph $G$ is a graph obtained from $G$ by repeatedly deleting or contracting edges, or removing isolated vertices. This statistic records the total number of (non-empty) non-isomorphic minors of a graph. ----------------------------------------------------------------------------- References: [1] [[wikipedia:Graph_minor]] ----------------------------------------------------------------------------- Code: # extremely naive and slow code def statistic(G): l = 0 for n in range(G.num_verts()+1): for H in graphs(n): try: m = G.minor(H) l += 1 except ValueError: pass return l ----------------------------------------------------------------------------- Statistic values: ([],1) => 2 ([],2) => 3 ([(0,1)],2) => 4 ([],3) => 4 ([(1,2)],3) => 6 ([(0,2),(1,2)],3) => 7 ([(0,1),(0,2),(1,2)],3) => 8 ([],4) => 5 ([(2,3)],4) => 8 ([(1,3),(2,3)],4) => 10 ([(0,3),(1,3),(2,3)],4) => 11 ([(0,3),(1,2)],4) => 9 ([(0,3),(1,2),(2,3)],4) => 12 ([(1,2),(1,3),(2,3)],4) => 12 ([(0,3),(1,2),(1,3),(2,3)],4) => 16 ([(0,2),(0,3),(1,2),(1,3)],4) => 14 ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 18 ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 19 ([],5) => 6 ([(3,4)],5) => 10 ([(2,4),(3,4)],5) => 13 ([(1,4),(2,4),(3,4)],5) => 15 ([(0,4),(1,4),(2,4),(3,4)],5) => 16 ([(1,4),(2,3)],5) => 12 ([(1,4),(2,3),(3,4)],5) => 17 ([(0,1),(2,4),(3,4)],5) => 16 ([(2,3),(2,4),(3,4)],5) => 16 ([(0,4),(1,4),(2,3),(3,4)],5) => 21 ([(1,4),(2,3),(2,4),(3,4)],5) => 24 ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 28 ([(1,3),(1,4),(2,3),(2,4)],5) => 21 ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 28 ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 28 ([(0,4),(1,3),(2,3),(2,4),(3,4)],5) => 28 ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 36 ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 30 ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 38 ([(0,4),(1,3),(2,3),(2,4)],5) => 19 ([(0,1),(2,3),(2,4),(3,4)],5) => 20 ([(0,3),(1,2),(1,4),(2,4),(3,4)],5) => 29 ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5) => 32 ([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => 22 ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5) => 36 ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => 43 ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5) => 36 ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 30 ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 42 ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 50 ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5) => 41 ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) => 47 ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 52 ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 53 ----------------------------------------------------------------------------- Created: Sep 14, 2022 at 22:34 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Sep 14, 2022 at 22:34 by Martin Rubey