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Statistic identifier: St001802
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Collection: Graphs
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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 $\big(f(u), f(v)\big)\in E$.
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References:
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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
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Statistic values:
([],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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Created: Jun 06, 2022 at 18:38 by Martin Rubey
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Last Updated: Jun 06, 2022 at 18:38 by Martin Rubey