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Identifier
Values
=>
Cc0020;cc-rep
([],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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Description
The determinant of the product of the incidence matrix and its transpose of a graph divided by $4$.
Code
def statistic(G):
    inc_mat = G.incidence_matrix()
    return ZZ((inc_mat*inc_mat.transpose()).determinant()/4)
Created
Nov 26, 2015 at 12:13 by Christian Stump
Updated
Nov 26, 2015 at 12:13 by Christian Stump