Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St000361
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Mapping
St000361: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => 0
([],2)
 => 0
([(0,1)],2)
 => 1
([],3)
 => 0
([(1,2)],3)
 => 1
([(0,2),(1,2)],3)
 => 4
([(0,1),(0,2),(1,2)],3)
 => 12
([],4)
 => 0
([(2,3)],4)
 => 1
([(1,3),(2,3)],4)
 => 4
([(0,3),(1,3),(2,3)],4)
 => 9
([(0,3),(1,2)],4)
 => 2
([(0,3),(1,2),(2,3)],4)
 => 8
([(1,2),(1,3),(2,3)],4)
 => 12
([(0,3),(1,2),(1,3),(2,3)],4)
 => 19
([(0,2),(0,3),(1,2),(1,3)],4)
 => 16
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 33
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 54
([],5)
 => 0
([(3,4)],5)
 => 1
([(2,4),(3,4)],5)
 => 4
([(1,4),(2,4),(3,4)],5)
 => 9
([(0,4),(1,4),(2,4),(3,4)],5)
 => 16
([(1,4),(2,3)],5)
 => 2
([(1,4),(2,3),(3,4)],5)
 => 8
([(0,1),(2,4),(3,4)],5)
 => 5
([(2,3),(2,4),(3,4)],5)
 => 12
([(0,4),(1,4),(2,3),(3,4)],5)
 => 14
([(1,4),(2,3),(2,4),(3,4)],5)
 => 19
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 28
([(1,3),(1,4),(2,3),(2,4)],5)
 => 16
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 23
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 33
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 27
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 44
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 36
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 64
([(0,4),(1,3),(2,3),(2,4)],5)
 => 12
([(0,1),(2,3),(2,4),(3,4)],5)
 => 13
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 24
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => 40
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 20
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 37
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => 61
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => 42
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 54
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 67
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 89
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => 57
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 84
Description
The second Zagreb index of a graph. This is $$ \sum_{\{u,v\}\in E(G)} d(u)d(v) $$ where $d(u)$ is the degree of the vertex $u$. Closely related is the Randić index of a graph without isolated vertices, which is $$ \sum_{\{u,v\}\in E(G)} \frac{1}{\sqrt{d(u)d(v)}}. $$