***************************************************************************** * 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: St000302 ----------------------------------------------------------------------------- Collection: Graphs ----------------------------------------------------------------------------- Description: The determinant of the distance matrix of a connected graph. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: def statistic(G): return G.distance_matrix().det() ----------------------------------------------------------------------------- Statistic values: ([],1) => 0 ([(0,1)],2) => -1 ([(0,2),(1,2)],3) => 4 ([(0,1),(0,2),(1,2)],3) => 2 ([(0,3),(1,3),(2,3)],4) => -12 ([(0,3),(1,2),(2,3)],4) => -12 ([(0,3),(1,2),(1,3),(2,3)],4) => -7 ([(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) => -3 ([(0,4),(1,4),(2,4),(3,4)],5) => 32 ([(0,4),(1,4),(2,3),(3,4)],5) => 32 ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 20 ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 0 ([(0,4),(1,3),(2,3),(2,4),(3,4)],5) => 20 ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 12 ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => -16 ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 8 ([(0,4),(1,3),(2,3),(2,4)],5) => 32 ([(0,3),(1,2),(1,4),(2,4),(3,4)],5) => 20 ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5) => 12 ([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => 6 ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5) => 0 ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => 6 ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5) => 12 ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 10 ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6 ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5) => -4 ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) => 0 ([(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) => 4 ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => -80 ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => -80 ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => -52 ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => -80 ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => -80 ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 0 ([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => -52 ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => -32 ([(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) => 48 ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => -32 ([(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) => 64 ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => -16 ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => -80 ([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => -52 ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => -33 ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 0 ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => -17 ([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6) => -52 ([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 0 ([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => -32 ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => -17 ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => -80 ([(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) => -52 ([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6) => -52 ([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6) => -52 ([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6) => 0 ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6) => -32 ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => -33 ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => -20 ([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => -32 ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => -28 ([(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) => 28 ([(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) => -17 ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => -8 ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 12 ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => -28 ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => -17 ([(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) => -12 ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 48 ([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 12 ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 0 ([(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) => 0 ([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => -9 ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => -32 ([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 0 ([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => -17 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 0 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => -9 ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 48 ([(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) => 28 ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 12 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4 ([(0,5),(1,2),(1,3),(1,4),(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) => -17 ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => -12 ([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => 7 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => -8 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => -9 ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => -8 ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 112 ([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 44 ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 16 ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 16 ([(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 ([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6) => -32 ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6) => -33 ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => -20 ([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => -28 ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => -17 ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6) => 0 ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6) => 7 ([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => -17 ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => -9 ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => -8 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 12 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => -9 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],6) => 7 ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => -5 ([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 0 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => -5 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6) => 0 ([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 0 ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0 ([(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) => -5 ([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 7 ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => -9 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => -5 ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => -12 ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => -13 ([(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) => -8 ([(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 ([(0,3),(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) => 8 ([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 15 ([(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) => 4 ([(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) => 0 ([(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) => 0 ([(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) => -4 ([(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) => -5 ----------------------------------------------------------------------------- Created: Nov 26, 2015 at 12:07 by Christian Stump ----------------------------------------------------------------------------- Last Updated: Nov 26, 2015 at 12:07 by Christian Stump