- FindStat

Identifier

St000303: Graphs ⟶ ℤ

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