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Identifier

St001441: Graphs ⟶ ℤ

Values

([],1) => 1

([],2) => 2

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

([],3) => 3

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

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

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

([],4) => 4

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

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

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

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

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

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

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

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

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

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

([],5) => 5

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

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

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

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

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

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

([(0,1),(2,4),(3,4)],5) => 9

([(2,3),(2,4),(3,4)],5) => 9

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

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

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

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

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

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

([(0,4),(1,3),(2,3),(2,4),(3,4)],5) => 19

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

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

([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 27

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

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

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

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

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

([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5) => 24

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

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

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

([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 24

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

([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5) => 27

([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) => 29

([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 30

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

([],6) => 6

([(4,5)],6) => 7

([(3,5),(4,5)],6) => 9

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

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

([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 37

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

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

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

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

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

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

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

([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 30

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

([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 38

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

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

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

([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 24

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

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

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

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

([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 24

([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 32

([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 40

([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 27

([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 32

([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 42

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

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

([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 44

([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 51

([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 52

([(0,5),(1,4),(2,3)],6) => 9

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

([(0,1),(2,5),(3,4),(4,5)],6) => 13

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

([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 25

([(1,4),(2,3),(2,5),(3,5),(4,5)],6) => 19

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

([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 31

([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 23

([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 39

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

([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 33

([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 25

([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => 33

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$F_{1} = q$

$F_{2} = q^{2} + q^{3}$

$F_{3} = q^{3} + q^{4} + q^{6} + q^{7}$

$F_{4} = q^{4} + q^{5} + q^{6} + q^{7} + q^{8} + q^{10} + q^{11} + q^{12} + q^{13} + q^{14} + q^{15}$

$F_{5} = q^{5} + q^{6} + q^{7} + q^{8} + 2\ q^{9} + q^{10} + q^{11} + q^{12} + q^{13} + q^{14} + 2\ q^{15} + q^{16} + q^{17} + q^{18} + q^{19} + q^{20} + 3\ q^{21} + 2\ q^{22} + q^{23} + 2\ q^{24} + 2\ q^{26} + 2\ q^{27} + q^{28} + q^{29} + q^{30} + q^{31}$

$F_{6} = q^{6} + q^{7} + q^{8} + 2\ q^{9} + 2\ q^{10} + q^{11} + 2\ q^{12} + 3\ q^{13} + 3\ q^{14} + 2\ q^{15} + 3\ q^{16} + 2\ q^{17} + 2\ q^{18} + q^{19} + q^{20} + 2\ q^{21} + 3\ q^{22} + 2\ q^{23} + 2\ q^{24} + 4\ q^{25} + 3\ q^{27} + 3\ q^{28} + 3\ q^{29} + 4\ q^{30} + 4\ q^{31} + 3\ q^{32} + 5\ q^{33} + q^{34} + q^{35} + 3\ q^{36} + 6\ q^{37} + 2\ q^{38} + 3\ q^{39} + 3\ q^{40} + 5\ q^{41} + 6\ q^{42} + 6\ q^{43} + q^{44} + 3\ q^{45} + 5\ q^{46} + 4\ q^{47} + 3\ q^{48} + 4\ q^{49} + 2\ q^{50} + 4\ q^{51} + 4\ q^{52} + 4\ q^{53} + 4\ q^{54} + 3\ q^{55} + 3\ q^{56} + 2\ q^{57} + 2\ q^{58} + 2\ q^{59} + 2\ q^{60} + q^{61} + q^{62} + q^{63}$

Description

The number of non-empty connected induced subgraphs of a graph.
More precisely, this is the number of non-empty subsets of the set of vertices of a graph, such that the induced subgraph is connected.

Code

def statistic(G):
    return sum(1 for V in subsets(G.vertices()) if V and G.subgraph(vertices=V).is_connected())

Created

Jul 03, 2019 at 23:38 by Martin Rubey

Updated

Jul 04, 2019 at 15:45 by Martin Rubey