- FindStat

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Identifier

St000571: Graphs ⟶ ℤ

Values

([],1) => 0

([],2) => 0

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

([],3) => 0

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

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

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

([],4) => 0

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

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

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

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

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

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

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

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

([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 70

([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 108

([],5) => 0

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

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

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

([(0,4),(1,4),(2,4),(3,4)],5) => 68

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

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

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

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

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

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

([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 82

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

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

([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 70

([(0,4),(1,3),(2,3),(2,4),(3,4)],5) => 64

([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 108

([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 78

([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 152

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

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

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

([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5) => 96

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

([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5) => 78

([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => 134

([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5) => 90

([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 108

([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 146

([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 190

([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5) => 116

([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) => 172

([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 246

([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 320

([],6) => 0

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

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

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

([(1,5),(2,5),(3,5),(4,5)],6) => 68

([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 130

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

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

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

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

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

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

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

([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 76

([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 82

([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 144

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

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

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

([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 46

([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 70

([(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 64

([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 58

([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 90

([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 108

([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 102

([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 170

([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 78

([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 72

([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 116

([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 152

([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 146

([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 214

([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 160

([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 282

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

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

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

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

([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 46

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

([(0,1),(2,5),(3,4),(3,5),(4,5)],6) => 46

([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 90

([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 96

([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 158

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

([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 72

([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 78

([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => 60

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Description

The F-index (or forgotten topological index) of a graph.
This is
$$\sum_{v \in V(G)} d^3(v) = \sum_{\{u,v\}\in E(G)} \big(d^2(u)+d^2(v)\big)$$
where $d(u)$ is the degree of the vertex $u$.

References

[1] Furtula, B., Gutman, I. A forgotten topological index MathSciNet:3317408
[2] Amin, R., Abu Nayeem, S. M. On the F-index and F-coindex of the line graphs of the subdivision graphs arXiv:1608.01503

Code

def statistic(G):
    return sum( d^3 for d in G.degree_iterator() )

def statistic_alt(G):
    return sum( G.degree(i)^2 + G.degree(j)^2 for (i,j) in G.edges(labels=False) )

Created

Aug 10, 2016 at 11:21 by Christian Stump

Updated

Aug 10, 2016 at 15:42 by Christian Stump