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Identifier

St000086: Graphs ⟶ ℤ

Values

([],1) => 1

([],2) => 1

([(0,1)],2) => 2

([],3) => 1

([(1,2)],3) => 2

([(0,2),(1,2)],3) => 3

([(0,1),(0,2),(1,2)],3) => 4

([],4) => 1

([(2,3)],4) => 2

([(1,3),(2,3)],4) => 3

([(0,3),(1,3),(2,3)],4) => 4

([(0,3),(1,2)],4) => 3

([(0,3),(1,2),(2,3)],4) => 5

([(1,2),(1,3),(2,3)],4) => 4

([(0,3),(1,2),(1,3),(2,3)],4) => 8

([(0,2),(0,3),(1,2),(1,3)],4) => 6

([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 10

([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 11

([],5) => 1

([(3,4)],5) => 2

([(2,4),(3,4)],5) => 3

([(1,4),(2,4),(3,4)],5) => 4

([(0,4),(1,4),(2,4),(3,4)],5) => 5

([(1,4),(2,3)],5) => 3

([(1,4),(2,3),(3,4)],5) => 5

([(0,1),(2,4),(3,4)],5) => 5

([(2,3),(2,4),(3,4)],5) => 4

([(0,4),(1,4),(2,3),(3,4)],5) => 8

([(1,4),(2,3),(2,4),(3,4)],5) => 8

([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 12

([(1,3),(1,4),(2,3),(2,4)],5) => 6

([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 11

([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 10

([(0,4),(1,3),(2,3),(2,4),(3,4)],5) => 12

([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 18

([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 12

([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 20

([(0,4),(1,3),(2,3),(2,4)],5) => 7

([(0,1),(2,3),(2,4),(3,4)],5) => 7

([(0,3),(1,2),(1,4),(2,4),(3,4)],5) => 13

([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5) => 16

([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => 8

([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5) => 18

([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => 25

([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5) => 18

([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 11

([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 23

([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 31

([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5) => 22

([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) => 28

([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 33

([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 34

([],6) => 1

([(4,5)],6) => 2

([(3,5),(4,5)],6) => 3

([(2,5),(3,5),(4,5)],6) => 4

([(1,5),(2,5),(3,5),(4,5)],6) => 5

([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 6

([(2,5),(3,4)],6) => 3

([(2,5),(3,4),(4,5)],6) => 5

([(1,2),(3,5),(4,5)],6) => 5

([(3,4),(3,5),(4,5)],6) => 4

([(1,5),(2,5),(3,4),(4,5)],6) => 8

([(0,1),(2,5),(3,5),(4,5)],6) => 7

([(2,5),(3,4),(3,5),(4,5)],6) => 8

([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 11

([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 12

([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 16

([(2,4),(2,5),(3,4),(3,5)],6) => 6

([(0,5),(1,5),(2,4),(3,4)],6) => 6

([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 11

([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 12

([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 10

([(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 12

([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 10

([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 17

([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 18

([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 20

([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 28

([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 12

([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 15

([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 20

([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 20

([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 26

([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 34

([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 21

([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 36

([(0,5),(1,4),(2,3)],6) => 4

([(1,5),(2,4),(3,4),(3,5)],6) => 7

([(0,1),(2,5),(3,4),(4,5)],6) => 8

([(1,2),(3,4),(3,5),(4,5)],6) => 7

([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 12

([(1,4),(2,3),(2,5),(3,5),(4,5)],6) => 13

([(0,1),(2,5),(3,4),(3,5),(4,5)],6) => 14

([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 22

([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 16

([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 26

([(1,4),(1,5),(2,3),(2,5),(3,4)],6) => 8

([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 18

([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 18

([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => 18

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Description

The number of subgraphs.
Given a graph $G$, this is the number of graphs $H$ such that $H \hookrightarrow G$.

Code

def statistic(G):
    return sum(1 for g in graphs(G.num_verts()) if G.subgraph_search(g) is not None)

Created

Jun 13, 2013 at 10:34 by Travis Scrimshaw

Updated

Feb 17, 2015 at 18:10 by Martin Rubey