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* Copyright (C) 2019 The FindStatCrew <info@findstat.org> *
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Statistic identifier: St000303
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Collection: Graphs
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Description: The determinant of the product of the incidence matrix and its transpose of a graph divided by $4$.
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References:
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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
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Created: Nov 26, 2015 at 12:13 by Christian Stump
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Last Updated: Nov 26, 2015 at 12:13 by Christian Stump