Values
=>
Cc0020;cc-rep
([],1)=>1
([],2)=>4
([(0,1)],2)=>2
([],3)=>27
([(1,2)],3)=>6
([(0,2),(1,2)],3)=>6
([(0,1),(0,2),(1,2)],3)=>6
([],4)=>256
([(2,3)],4)=>32
([(1,3),(2,3)],4)=>24
([(0,3),(1,3),(2,3)],4)=>30
([(0,3),(1,2)],4)=>16
([(0,3),(1,2),(2,3)],4)=>16
([(1,2),(1,3),(2,3)],4)=>24
([(0,3),(1,2),(1,3),(2,3)],4)=>14
([(0,2),(0,3),(1,2),(1,3)],4)=>32
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>16
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>24
([],5)=>3125
([(3,4)],5)=>250
([(2,4),(3,4)],5)=>150
([(1,4),(2,4),(3,4)],5)=>150
([(0,4),(1,4),(2,4),(3,4)],5)=>260
([(1,4),(2,3)],5)=>80
([(1,4),(2,3),(3,4)],5)=>80
([(0,1),(2,4),(3,4)],5)=>48
([(2,3),(2,4),(3,4)],5)=>150
([(0,4),(1,4),(2,3),(3,4)],5)=>60
([(1,4),(2,3),(2,4),(3,4)],5)=>70
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>48
([(1,3),(1,4),(2,3),(2,4)],5)=>160
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)=>94
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>80
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>42
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>50
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>180
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>66
([(0,4),(1,3),(2,3),(2,4)],5)=>42
([(0,1),(2,3),(2,4),(3,4)],5)=>48
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)=>32
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)=>32
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)=>10
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>28
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)=>36
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)=>44
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>120
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>78
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>52
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)=>48
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)=>64
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>60
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>120
([],6)=>46656
([(4,5)],6)=>2592
([(3,5),(4,5)],6)=>1296
([(2,5),(3,5),(4,5)],6)=>1080
([(1,5),(2,5),(3,5),(4,5)],6)=>1560
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>3130
([(2,5),(3,4)],6)=>576
([(2,5),(3,4),(4,5)],6)=>576
([(1,2),(3,5),(4,5)],6)=>288
([(3,4),(3,5),(4,5)],6)=>1296
([(1,5),(2,5),(3,4),(4,5)],6)=>360
([(0,1),(2,5),(3,5),(4,5)],6)=>256
([(2,5),(3,4),(3,5),(4,5)],6)=>504
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>374
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>288
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>282
([(2,4),(2,5),(3,4),(3,5)],6)=>1152
([(0,5),(1,5),(2,4),(3,4)],6)=>144
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>564
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>166
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>576
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>252
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)=>234
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>440
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>300
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>162
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>220
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>1080
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>316
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>680
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>396
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>192
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>282
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>1280
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>528
([(0,5),(1,4),(2,3)],6)=>216
([(1,5),(2,4),(3,4),(3,5)],6)=>252
([(0,1),(2,5),(3,4),(4,5)],6)=>144
([(1,2),(3,4),(3,5),(4,5)],6)=>288
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>156
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>192
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)=>140
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>104
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>192
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>112
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)=>60
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>296
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>168
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)=>22
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>264
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)=>162
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>99
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>153
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>216
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>136
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>104
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)=>340
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)=>108
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)=>234
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)=>74
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)=>101
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>192
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>86
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)=>76
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)=>130
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>86
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>88
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>864
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>152
([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>468
([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>312
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>24
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)=>84
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>174
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>119
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>112
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>114
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>164
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>312
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>292
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>198
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>200
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>144
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>522
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>288
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>174
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>384
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>256
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)=>132
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)=>362
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)=>96
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>44
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>144
([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>75
([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>99
([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>113
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>58
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>82
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)=>768
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>144
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>120
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>180
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>168
([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>220
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>360
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>194
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>244
([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>117
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>84
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>130
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>168
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>232
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)=>144
([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)=>120
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)=>56
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>336
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>72
([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>246
([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>156
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)=>40
([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>70
([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>180
([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>74
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>196
([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>110
([(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)=>112
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],6)=>52
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>52
([(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)=>10
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)=>36
([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>70
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>124
([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>90
([(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)=>124
([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>152
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>150
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>228
([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>720
([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>504
([(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)=>372
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>176
([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>240
([(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)=>384
([(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)=>208
([(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)=>288
([(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)=>720
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Description
The number of endomorphisms of a graph.
An endomorphism of a graph $(V, E)$ is a map $f: V\to V$ such that for any edge $(u,v)\in E$ also $\big(f(u), f(v)\big)\in E$.
An endomorphism of a graph $(V, E)$ is a map $f: V\to V$ such that for any edge $(u,v)\in E$ also $\big(f(u), f(v)\big)\in E$.
Code
def statistic(G):
G = G.relabel(inplace=False)
n = G.num_verts()
endomorphisms = 0
for f in cartesian_product([list(range(n)) for _ in range(n)]):
if all(G.has_edge(f[u], f[v]) for u, v in G.edges(labels=False)):
endomorphisms += 1
return endomorphisms
Created
Jun 06, 2022 at 18:38 by Martin Rubey
Updated
Jun 06, 2022 at 18:38 by Martin Rubey
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