Your data matches 1 statistic following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001374
(load all 2 compositions to match this statistic)
Mapping
St001374: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => 0
([],2)
 => 0
([(0,1)],2)
 => 0
([],3)
 => 0
([(1,2)],3)
 => 0
([(0,2),(1,2)],3)
 => 2
([(0,1),(0,2),(1,2)],3)
 => 0
([],4)
 => 0
([(2,3)],4)
 => 0
([(1,3),(2,3)],4)
 => 2
([(0,3),(1,3),(2,3)],4)
 => 6
([(0,3),(1,2)],4)
 => 0
([(0,3),(1,2),(2,3)],4)
 => 6
([(1,2),(1,3),(2,3)],4)
 => 0
([(0,3),(1,2),(1,3),(2,3)],4)
 => 5
([(0,2),(0,3),(1,2),(1,3)],4)
 => 8
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 0
([],5)
 => 0
([(3,4)],5)
 => 0
([(2,4),(3,4)],5)
 => 2
([(1,4),(2,4),(3,4)],5)
 => 6
([(0,4),(1,4),(2,4),(3,4)],5)
 => 12
([(1,4),(2,3)],5)
 => 0
([(1,4),(2,3),(3,4)],5)
 => 6
([(0,1),(2,4),(3,4)],5)
 => 2
([(2,3),(2,4),(3,4)],5)
 => 0
([(0,4),(1,4),(2,3),(3,4)],5)
 => 12
([(1,4),(2,3),(2,4),(3,4)],5)
 => 5
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 12
([(1,3),(1,4),(2,3),(2,4)],5)
 => 8
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 16
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 12
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 12
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 18
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 12
([(0,4),(1,3),(2,3),(2,4)],5)
 => 12
([(0,1),(2,3),(2,4),(3,4)],5)
 => 0
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 12
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => 12
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 10
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 14
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => 12
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => 13
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 0
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 9
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 10
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => 16
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 12
Description
The Padmakar-Ivan index of a graph. For an edge $e=(u, v)$, let $n_{e, u}$ be the number of edges in a graph $G$ induced by the set of vertices $\{w: d(u, w) < d(v, w)\}$, where $d(u,v)$ denotes the distance between $u$ and $v$. Then the PI-index of $G$ is $$\sum_{e=(u,v)} n_{e, u} + n_{e, v}.$$