***************************************************************************** * 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: St000303 ----------------------------------------------------------------------------- Collection: Graphs ----------------------------------------------------------------------------- Description: The determinant of the product of the incidence matrix and its transpose of a graph divided by $4$. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: def statistic(G): inc_mat = G.incidence_matrix() return ZZ((inc_mat*inc_mat.transpose()).determinant()/4) ----------------------------------------------------------------------------- Statistic values: ([],1) => 0 ([],2) => 0 ([(0,1)],2) => 0 ([],3) => 0 ([(1,2)],3) => 0 ([(0,2),(1,2)],3) => 0 ([(0,1),(0,2),(1,2)],3) => 1 ([],4) => 0 ([(2,3)],4) => 0 ([(1,3),(2,3)],4) => 0 ([(0,3),(1,3),(2,3)],4) => 0 ([(0,3),(1,2)],4) => 0 ([(0,3),(1,2),(2,3)],4) => 0 ([(1,2),(1,3),(2,3)],4) => 0 ([(0,3),(1,2),(1,3),(2,3)],4) => 1 ([(0,2),(0,3),(1,2),(1,3)],4) => 0 ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 4 ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 12 ([],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) => 0 ([(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) => 0 ([(1,4),(2,3),(2,4),(3,4)],5) => 0 ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 1 ([(1,3),(1,4),(2,3),(2,4)],5) => 0 ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 0 ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 0 ([(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) => 4 ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 0 ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 12 ([(0,4),(1,3),(2,3),(2,4)],5) => 0 ([(0,1),(2,3),(2,4),(3,4)],5) => 0 ([(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) => 6 ([(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) => 4 ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => 15 ([(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) => 0 ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 12 ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 36 ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5) => 12 ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) => 36 ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 81 ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 162 ([],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) => 0 ([(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) => 0 ([(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) => 1 ([(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) => 0 ([(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) => 0 ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 0 ([(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) => 1 ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4 ([(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) => 0 ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 0 ([(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) => 4 ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 12 ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 0 ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 32 ([(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) => 0 ([(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) => 1 ([(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) => 6 ([(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) => 0 ([(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) => 1 ([(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) => 1 ([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 4 ([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4 ([(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) => 15 ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 0 ([(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) => 0 ([(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) => 0 ([(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) => 4 ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6) => 4 ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 6 ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 20 ([(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) => 4 ([(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) => 12 ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 4 ([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6) => 12 ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 12 ([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 15 ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 16 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => 44 ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 12 ([(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) => 12 ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 36 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 32 ([(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) => 0 ([(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) => 12 ([(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) => 36 ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6) => 0 ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6) => 0 ([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6) => 4 ([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 6 ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 4 ([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 4 ([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 15 ([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 15 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 20 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 50 ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 0 ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 12 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 36 ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 36 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 105 ([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 36 ([(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) => 36 ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 81 ([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => 44 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 50 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 105 ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 216 ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 0 ([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 81 ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 96 ([(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) => 432 ([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6) => 4 ([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6) => 4 ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6) => 10 ([(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) => 12 ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 56 ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6) => 24 ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6) => 56 ([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 36 ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 54 ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 44 ([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 120 ([(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) => 256 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],6) => 15 ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 20 ([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 50 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 125 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6) => 54 ([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 120 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 120 ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 250 ([(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) => 480 ([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 105 ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 108 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 234 ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 81 ([(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) => 162 ([(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) => 432 ([(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 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 256 ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 216 ([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 234 ([(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) => 480 ([(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) => 512 ([(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) => 896 ([(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) => 1536 ([(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) => 2560 ----------------------------------------------------------------------------- Created: Nov 26, 2015 at 12:13 by Christian Stump ----------------------------------------------------------------------------- Last Updated: Nov 26, 2015 at 12:13 by Christian Stump