Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St000464
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Mapping
St000464: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([(0,1)],2)
 => 2
([(0,2),(1,2)],3)
 => 10
([(0,1),(0,2),(1,2)],3)
 => 12
([(0,3),(1,3),(2,3)],4)
 => 24
([(0,3),(1,2),(2,3)],4)
 => 28
([(0,3),(1,2),(1,3),(2,3)],4)
 => 30
([(0,2),(0,3),(1,2),(1,3)],4)
 => 32
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 34
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 36
([(0,4),(1,4),(2,4),(3,4)],5)
 => 44
([(0,4),(1,4),(2,3),(3,4)],5)
 => 52
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 54
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 61
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 58
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 62
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 66
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 68
([(0,4),(1,3),(2,3),(2,4)],5)
 => 60
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 64
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => 64
([(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)
 => 66
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => 70
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => 67
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 68
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 74
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => 72
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 76
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 78
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 80
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 70
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => 82
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 84
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => 98
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => 86
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => 96
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => 92
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 96
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => 104
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 106
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 100
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 106
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 112
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 114
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => 94
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => 98
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => 98
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => 100
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => 100
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => 96
Description
The 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 Schultz index is related to the Wiener index via $S(T)=4W(T)-n(n-1)$ [2].