***************************************************************************** * 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: St000286 ----------------------------------------------------------------------------- Collection: Graphs ----------------------------------------------------------------------------- Description: The number of connected components of the complement of a graph. The complement of a graph is the graph on the same vertex set with complementary edges. ----------------------------------------------------------------------------- References: [1] Triangle read by rows: T(n,m) = number of unlabeled graphs on n nodes with m connected components, m = 1,2,...,n. [[OEIS:A201922]] ----------------------------------------------------------------------------- Code: def statistic(G): return len(G.complement().connected_components()) ----------------------------------------------------------------------------- Statistic values: ([],1) => 1 ([],2) => 1 ([(0,1)],2) => 2 ([],3) => 1 ([(1,2)],3) => 1 ([(0,2),(1,2)],3) => 2 ([(0,1),(0,2),(1,2)],3) => 3 ([],4) => 1 ([(2,3)],4) => 1 ([(1,3),(2,3)],4) => 1 ([(0,3),(1,3),(2,3)],4) => 2 ([(0,3),(1,2)],4) => 1 ([(0,3),(1,2),(2,3)],4) => 1 ([(1,2),(1,3),(2,3)],4) => 1 ([(0,3),(1,2),(1,3),(2,3)],4) => 2 ([(0,2),(0,3),(1,2),(1,3)],4) => 2 ([(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) => 4 ([],5) => 1 ([(3,4)],5) => 1 ([(2,4),(3,4)],5) => 1 ([(1,4),(2,4),(3,4)],5) => 1 ([(0,4),(1,4),(2,4),(3,4)],5) => 2 ([(1,4),(2,3)],5) => 1 ([(1,4),(2,3),(3,4)],5) => 1 ([(0,1),(2,4),(3,4)],5) => 1 ([(2,3),(2,4),(3,4)],5) => 1 ([(0,4),(1,4),(2,3),(3,4)],5) => 1 ([(1,4),(2,3),(2,4),(3,4)],5) => 1 ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2 ([(1,3),(1,4),(2,3),(2,4)],5) => 1 ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 1 ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1 ([(0,4),(1,3),(2,3),(2,4),(3,4)],5) => 1 ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2 ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 2 ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3 ([(0,4),(1,3),(2,3),(2,4)],5) => 1 ([(0,1),(2,3),(2,4),(3,4)],5) => 1 ([(0,3),(1,2),(1,4),(2,4),(3,4)],5) => 1 ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5) => 2 ([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => 1 ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5) => 1 ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => 2 ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5) => 1 ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1 ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2 ([(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) => 2 ([(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) => 4 ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 5 ([],6) => 1 ([(4,5)],6) => 1 ([(3,5),(4,5)],6) => 1 ([(2,5),(3,5),(4,5)],6) => 1 ([(1,5),(2,5),(3,5),(4,5)],6) => 1 ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2 ([(2,5),(3,4)],6) => 1 ([(2,5),(3,4),(4,5)],6) => 1 ([(1,2),(3,5),(4,5)],6) => 1 ([(3,4),(3,5),(4,5)],6) => 1 ([(1,5),(2,5),(3,4),(4,5)],6) => 1 ([(0,1),(2,5),(3,5),(4,5)],6) => 1 ([(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 1 ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 2 ([(2,4),(2,5),(3,4),(3,5)],6) => 1 ([(0,5),(1,5),(2,4),(3,4)],6) => 1 ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 1 ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 1 ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 1 ([(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) => 1 ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 1 ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2 ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 1 ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 1 ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 1 ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2 ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 2 ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3 ([(0,5),(1,4),(2,3)],6) => 1 ([(1,5),(2,4),(3,4),(3,5)],6) => 1 ([(0,1),(2,5),(3,4),(4,5)],6) => 1 ([(1,2),(3,4),(3,5),(4,5)],6) => 1 ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 1 ([(1,4),(2,3),(2,5),(3,5),(4,5)],6) => 1 ([(0,1),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 1 ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 1 ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 2 ([(1,4),(1,5),(2,3),(2,5),(3,4)],6) => 1 ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 1 ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 1 ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => 1 ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 1 ([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6) => 1 ([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 1 ([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => 2 ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 1 ([(0,1),(2,4),(2,5),(3,4),(3,5)],6) => 1 ([(0,5),(1,5),(2,3),(2,4),(3,4)],6) => 1 ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => 1 ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6) => 1 ([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6) => 1 ([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6) => 1 ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6) => 1 ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2 ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 1 ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2 ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 1 ([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6) => 1 ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 1 ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => 2 ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 1 ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 2 ([(0,4),(0,5),(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),(3,5),(4,5)],6) => 1 ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 1 ([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 1 ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 1 ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 2 ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6) => 1 ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6) => 1 ([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6) => 1 ([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 1 ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 1 ([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 1 ([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 1 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 1 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 2 ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 1 ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 1 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 1 ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2 ([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2 ([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 1 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2 ([(0,4),(0,5),(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),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 2 ([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2 ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 2 ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 3 ([(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) => 1 ([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6) => 1 ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6) => 1 ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 1 ([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2 ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6) => 1 ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6) => 1 ([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 2 ([(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) => 1 ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 1 ([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 1 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 2 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6) => 1 ([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 1 ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2 ([(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) => 3 ([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 1 ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2 ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1 ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2 ([(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) => 4 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 2 ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 2 ([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2 ([(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) => 4 ([(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) => 5 ([(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: Oct 30, 2015 at 17:23 by Alexander Engström ----------------------------------------------------------------------------- Last Updated: Oct 30, 2015 at 17:28 by Christian Stump