Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St000466
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Mapping
St000466: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => 0
([(0,1)],2)
 => 1
([(0,2),(1,2)],3)
 => 6
([(0,1),(0,2),(1,2)],3)
 => 12
([(0,3),(1,3),(2,3)],4)
 => 15
([(0,3),(1,2),(2,3)],4)
 => 19
([(0,3),(1,2),(1,3),(2,3)],4)
 => 27
([(0,2),(0,3),(1,2),(1,3)],4)
 => 32
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 41
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 54
([(0,4),(1,4),(2,4),(3,4)],5)
 => 28
([(0,4),(1,4),(2,3),(3,4)],5)
 => 36
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 46
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 57
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 50
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 66
([(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)
 => 88
([(0,4),(1,3),(2,3),(2,4)],5)
 => 44
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 58
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => 72
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 60
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 77
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => 93
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => 72
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 85
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 113
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => 99
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 120
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 138
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 160
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 45
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => 57
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 69
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => 73
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => 61
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => 86
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => 77
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 95
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => 94
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 115
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 99
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 123
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 144
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 153
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => 69
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => 85
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => 101
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => 90
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => 95
Description
The Gutman (or modified Schultz) index of a connected graph. This is $$\sum_{\{u,v\}\subseteq V} d(u)d(v)d(u,v)$$ where $d(u)$ is the degree of vertex $u$ and $d(u,v)$ is the distance between vertices $u$ and $v$. For trees on $n$ vertices, the modified Schultz index is related to the Wiener index via $S^\ast(T)=4W(T)-(n-1)(2n-1)$ [1].