Your data matches 129 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000273
(load all 4 compositions to match this statistic)
Mapping
St000273: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => 1 = 2 - 1
([],2)
 => 2 = 3 - 1
([(0,1)],2)
 => 1 = 2 - 1
([],3)
 => 3 = 4 - 1
([(1,2)],3)
 => 2 = 3 - 1
([(0,2),(1,2)],3)
 => 1 = 2 - 1
([(0,1),(0,2),(1,2)],3)
 => 1 = 2 - 1
([],4)
 => 4 = 5 - 1
([(2,3)],4)
 => 3 = 4 - 1
([(1,3),(2,3)],4)
 => 2 = 3 - 1
([(0,3),(1,3),(2,3)],4)
 => 1 = 2 - 1
([(0,3),(1,2)],4)
 => 2 = 3 - 1
([(0,3),(1,2),(2,3)],4)
 => 2 = 3 - 1
([(1,2),(1,3),(2,3)],4)
 => 2 = 3 - 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => 1 = 2 - 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => 2 = 3 - 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1 = 2 - 1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1 = 2 - 1
([],5)
 => 5 = 6 - 1
([(3,4)],5)
 => 4 = 5 - 1
([(2,4),(3,4)],5)
 => 3 = 4 - 1
([(1,4),(2,4),(3,4)],5)
 => 2 = 3 - 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(1,4),(2,3)],5)
 => 3 = 4 - 1
([(1,4),(2,3),(3,4)],5)
 => 3 = 4 - 1
([(0,1),(2,4),(3,4)],5)
 => 2 = 3 - 1
([(2,3),(2,4),(3,4)],5)
 => 3 = 4 - 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => 2 = 3 - 1
([(1,4),(2,3),(2,4),(3,4)],5)
 => 2 = 3 - 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => 3 = 4 - 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 2 = 3 - 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2 = 3 - 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 2 = 3 - 1
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 2 = 3 - 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => 2 = 3 - 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => 2 = 3 - 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 2 = 3 - 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 2 = 3 - 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 2 = 3 - 1
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => 2 = 3 - 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2 = 3 - 1
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => 2 = 3 - 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 1 = 2 - 1
Description
The domination number of a graph. The domination number of a graph is given by the minimum size of a dominating set of vertices. A dominating set of vertices is a subset of the vertex set of such that every vertex is either in this subset or adjacent to an element of this subset.
Matching statistic: St001316
(load all 8 compositions to match this statistic)
Mapping
St001316: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => 1 = 2 - 1
([],2)
 => 1 = 2 - 1
([(0,1)],2)
 => 2 = 3 - 1
([],3)
 => 1 = 2 - 1
([(1,2)],3)
 => 1 = 2 - 1
([(0,2),(1,2)],3)
 => 2 = 3 - 1
([(0,1),(0,2),(1,2)],3)
 => 3 = 4 - 1
([],4)
 => 1 = 2 - 1
([(2,3)],4)
 => 1 = 2 - 1
([(1,3),(2,3)],4)
 => 1 = 2 - 1
([(0,3),(1,3),(2,3)],4)
 => 2 = 3 - 1
([(0,3),(1,2)],4)
 => 2 = 3 - 1
([(0,3),(1,2),(2,3)],4)
 => 2 = 3 - 1
([(1,2),(1,3),(2,3)],4)
 => 1 = 2 - 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => 2 = 3 - 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => 2 = 3 - 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 3 = 4 - 1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4 = 5 - 1
([],5)
 => 1 = 2 - 1
([(3,4)],5)
 => 1 = 2 - 1
([(2,4),(3,4)],5)
 => 1 = 2 - 1
([(1,4),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => 2 = 3 - 1
([(1,4),(2,3)],5)
 => 1 = 2 - 1
([(1,4),(2,3),(3,4)],5)
 => 1 = 2 - 1
([(0,1),(2,4),(3,4)],5)
 => 2 = 3 - 1
([(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => 2 = 3 - 1
([(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2 = 3 - 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => 1 = 2 - 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 2 = 3 - 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 2 = 3 - 1
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2 = 3 - 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 2 = 3 - 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3 = 4 - 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => 2 = 3 - 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => 2 = 3 - 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 2 = 3 - 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => 3 = 4 - 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 2 = 3 - 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 2 = 3 - 1
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => 3 = 4 - 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => 2 = 3 - 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2 = 3 - 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3 = 4 - 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => 2 = 3 - 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 3 = 4 - 1
Description
The domatic number of a graph. This is the maximal size of a partition of the vertices into dominating sets.
Matching statistic: St001322
(load all 4 compositions to match this statistic)
Mapping
St001322: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => 1 = 2 - 1
([],2)
 => 2 = 3 - 1
([(0,1)],2)
 => 1 = 2 - 1
([],3)
 => 3 = 4 - 1
([(1,2)],3)
 => 2 = 3 - 1
([(0,2),(1,2)],3)
 => 1 = 2 - 1
([(0,1),(0,2),(1,2)],3)
 => 1 = 2 - 1
([],4)
 => 4 = 5 - 1
([(2,3)],4)
 => 3 = 4 - 1
([(1,3),(2,3)],4)
 => 2 = 3 - 1
([(0,3),(1,3),(2,3)],4)
 => 1 = 2 - 1
([(0,3),(1,2)],4)
 => 2 = 3 - 1
([(0,3),(1,2),(2,3)],4)
 => 2 = 3 - 1
([(1,2),(1,3),(2,3)],4)
 => 2 = 3 - 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => 1 = 2 - 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => 2 = 3 - 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1 = 2 - 1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1 = 2 - 1
([],5)
 => 5 = 6 - 1
([(3,4)],5)
 => 4 = 5 - 1
([(2,4),(3,4)],5)
 => 3 = 4 - 1
([(1,4),(2,4),(3,4)],5)
 => 2 = 3 - 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(1,4),(2,3)],5)
 => 3 = 4 - 1
([(1,4),(2,3),(3,4)],5)
 => 3 = 4 - 1
([(0,1),(2,4),(3,4)],5)
 => 2 = 3 - 1
([(2,3),(2,4),(3,4)],5)
 => 3 = 4 - 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => 2 = 3 - 1
([(1,4),(2,3),(2,4),(3,4)],5)
 => 2 = 3 - 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => 3 = 4 - 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 2 = 3 - 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2 = 3 - 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 2 = 3 - 1
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 2 = 3 - 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => 2 = 3 - 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => 2 = 3 - 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 2 = 3 - 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 2 = 3 - 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 2 = 3 - 1
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => 2 = 3 - 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2 = 3 - 1
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => 2 = 3 - 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 1 = 2 - 1
Description
The size of a minimal independent dominating set in a graph.
Matching statistic: St001339
(load all 4 compositions to match this statistic)
Mapping
St001339: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => 1 = 2 - 1
([],2)
 => 2 = 3 - 1
([(0,1)],2)
 => 1 = 2 - 1
([],3)
 => 3 = 4 - 1
([(1,2)],3)
 => 2 = 3 - 1
([(0,2),(1,2)],3)
 => 1 = 2 - 1
([(0,1),(0,2),(1,2)],3)
 => 1 = 2 - 1
([],4)
 => 4 = 5 - 1
([(2,3)],4)
 => 3 = 4 - 1
([(1,3),(2,3)],4)
 => 2 = 3 - 1
([(0,3),(1,3),(2,3)],4)
 => 1 = 2 - 1
([(0,3),(1,2)],4)
 => 2 = 3 - 1
([(0,3),(1,2),(2,3)],4)
 => 2 = 3 - 1
([(1,2),(1,3),(2,3)],4)
 => 2 = 3 - 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => 1 = 2 - 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => 2 = 3 - 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1 = 2 - 1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1 = 2 - 1
([],5)
 => 5 = 6 - 1
([(3,4)],5)
 => 4 = 5 - 1
([(2,4),(3,4)],5)
 => 3 = 4 - 1
([(1,4),(2,4),(3,4)],5)
 => 2 = 3 - 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(1,4),(2,3)],5)
 => 3 = 4 - 1
([(1,4),(2,3),(3,4)],5)
 => 3 = 4 - 1
([(0,1),(2,4),(3,4)],5)
 => 2 = 3 - 1
([(2,3),(2,4),(3,4)],5)
 => 3 = 4 - 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => 2 = 3 - 1
([(1,4),(2,3),(2,4),(3,4)],5)
 => 2 = 3 - 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => 3 = 4 - 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 2 = 3 - 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2 = 3 - 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 2 = 3 - 1
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 2 = 3 - 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => 2 = 3 - 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => 2 = 3 - 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 2 = 3 - 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 2 = 3 - 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 2 = 3 - 1
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => 2 = 3 - 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2 = 3 - 1
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => 2 = 3 - 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 1 = 2 - 1
Description
The irredundance number of a graph. A set $S$ of vertices is irredundant, if there is no vertex in $S$, whose closed neighbourhood is contained in the union of the closed neighbourhoods of the other vertices of $S$. The irredundance number is the smallest size of a maximal irredundant set.
Matching statistic: St001829
(load all 4 compositions to match this statistic)
Mapping
St001829: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => 1 = 2 - 1
([],2)
 => 2 = 3 - 1
([(0,1)],2)
 => 1 = 2 - 1
([],3)
 => 3 = 4 - 1
([(1,2)],3)
 => 2 = 3 - 1
([(0,2),(1,2)],3)
 => 1 = 2 - 1
([(0,1),(0,2),(1,2)],3)
 => 1 = 2 - 1
([],4)
 => 4 = 5 - 1
([(2,3)],4)
 => 3 = 4 - 1
([(1,3),(2,3)],4)
 => 2 = 3 - 1
([(0,3),(1,3),(2,3)],4)
 => 1 = 2 - 1
([(0,3),(1,2)],4)
 => 2 = 3 - 1
([(0,3),(1,2),(2,3)],4)
 => 2 = 3 - 1
([(1,2),(1,3),(2,3)],4)
 => 2 = 3 - 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => 1 = 2 - 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => 2 = 3 - 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1 = 2 - 1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1 = 2 - 1
([],5)
 => 5 = 6 - 1
([(3,4)],5)
 => 4 = 5 - 1
([(2,4),(3,4)],5)
 => 3 = 4 - 1
([(1,4),(2,4),(3,4)],5)
 => 2 = 3 - 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(1,4),(2,3)],5)
 => 3 = 4 - 1
([(1,4),(2,3),(3,4)],5)
 => 3 = 4 - 1
([(0,1),(2,4),(3,4)],5)
 => 2 = 3 - 1
([(2,3),(2,4),(3,4)],5)
 => 3 = 4 - 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => 2 = 3 - 1
([(1,4),(2,3),(2,4),(3,4)],5)
 => 2 = 3 - 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => 3 = 4 - 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 2 = 3 - 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2 = 3 - 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 2 = 3 - 1
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 2 = 3 - 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => 2 = 3 - 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => 2 = 3 - 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 2 = 3 - 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 2 = 3 - 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 2 = 3 - 1
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => 2 = 3 - 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2 = 3 - 1
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => 2 = 3 - 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 1 = 2 - 1
Description
The common independence number of a graph. The common independence number of a graph $G$ is the greatest integer $r$ such that every vertex of $G$ belongs to some independent set $X$ of vertices of cardinality at least $r$.
Matching statistic: St000093
(load all 3 compositions to match this statistic)
Mapping
Mp00250: Graphs —clique graph⟶ Graphs
St000093: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => ([],1)
 => 1 = 2 - 1
([],2)
 => ([],2)
 => 2 = 3 - 1
([(0,1)],2)
 => ([],1)
 => 1 = 2 - 1
([],3)
 => ([],3)
 => 3 = 4 - 1
([(1,2)],3)
 => ([],2)
 => 2 = 3 - 1
([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,1),(0,2),(1,2)],3)
 => ([],1)
 => 1 = 2 - 1
([],4)
 => ([],4)
 => 4 = 5 - 1
([(2,3)],4)
 => ([],3)
 => 3 = 4 - 1
([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => 2 = 3 - 1
([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 1 = 2 - 1
([(0,3),(1,2)],4)
 => ([],2)
 => 2 = 3 - 1
([(0,3),(1,2),(2,3)],4)
 => ([(0,2),(1,2)],3)
 => 2 = 3 - 1
([(1,2),(1,3),(2,3)],4)
 => ([],2)
 => 2 = 3 - 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2 = 3 - 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],1)
 => 1 = 2 - 1
([],5)
 => ([],5)
 => 5 = 6 - 1
([(3,4)],5)
 => ([],4)
 => 4 = 5 - 1
([(2,4),(3,4)],5)
 => ([(2,3)],4)
 => 3 = 4 - 1
([(1,4),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => 2 = 3 - 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1 = 2 - 1
([(1,4),(2,3)],5)
 => ([],3)
 => 3 = 4 - 1
([(1,4),(2,3),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => 3 = 4 - 1
([(0,1),(2,4),(3,4)],5)
 => ([(1,2)],3)
 => 2 = 3 - 1
([(2,3),(2,4),(3,4)],5)
 => ([],3)
 => 3 = 4 - 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 2 = 3 - 1
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2)],3)
 => 2 = 3 - 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 1 = 2 - 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => 3 = 4 - 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 2 = 3 - 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2)],3)
 => 2 = 3 - 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => 2 = 3 - 1
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 1 = 2 - 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => 2 = 3 - 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 1 = 2 - 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,3),(1,2),(2,3)],4)
 => 2 = 3 - 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => 2 = 3 - 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => 2 = 3 - 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 2 = 3 - 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2 = 3 - 1
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 1 = 2 - 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => 2 = 3 - 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => 2 = 3 - 1
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2 = 3 - 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1 = 2 - 1
Description
The cardinality of a maximal independent set of vertices of a graph. An independent set of a graph is a set of pairwise non-adjacent vertices. A maximum independent set is an independent set of maximum cardinality. This statistic is also called the independence number or stability number $\alpha(G)$ of $G$.
Matching statistic: St000774
(load all 2 compositions to match this statistic)
Mapping
Mp00250: Graphs —clique graph⟶ Graphs
St000774: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => ([],1)
 => 1 = 2 - 1
([],2)
 => ([],2)
 => 2 = 3 - 1
([(0,1)],2)
 => ([],1)
 => 1 = 2 - 1
([],3)
 => ([],3)
 => 3 = 4 - 1
([(1,2)],3)
 => ([],2)
 => 2 = 3 - 1
([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,1),(0,2),(1,2)],3)
 => ([],1)
 => 1 = 2 - 1
([],4)
 => ([],4)
 => 4 = 5 - 1
([(2,3)],4)
 => ([],3)
 => 3 = 4 - 1
([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => 2 = 3 - 1
([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 2 = 3 - 1
([(0,3),(1,2)],4)
 => ([],2)
 => 2 = 3 - 1
([(0,3),(1,2),(2,3)],4)
 => ([(0,2),(1,2)],3)
 => 1 = 2 - 1
([(1,2),(1,3),(2,3)],4)
 => ([],2)
 => 2 = 3 - 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2 = 3 - 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],1)
 => 1 = 2 - 1
([],5)
 => ([],5)
 => 5 = 6 - 1
([(3,4)],5)
 => ([],4)
 => 4 = 5 - 1
([(2,4),(3,4)],5)
 => ([(2,3)],4)
 => 3 = 4 - 1
([(1,4),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => 2 = 3 - 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 3 = 4 - 1
([(1,4),(2,3)],5)
 => ([],3)
 => 3 = 4 - 1
([(1,4),(2,3),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => 2 = 3 - 1
([(0,1),(2,4),(3,4)],5)
 => ([(1,2)],3)
 => 2 = 3 - 1
([(2,3),(2,4),(3,4)],5)
 => ([],3)
 => 3 = 4 - 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1 = 2 - 1
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2)],3)
 => 2 = 3 - 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2 = 3 - 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => 2 = 3 - 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2)],3)
 => 2 = 3 - 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => 1 = 2 - 1
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2 = 3 - 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => 2 = 3 - 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2 = 3 - 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,3),(1,2),(2,3)],4)
 => 1 = 2 - 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => 2 = 3 - 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => 1 = 2 - 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 2 = 3 - 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2 = 3 - 1
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2 = 3 - 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => 1 = 2 - 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => 2 = 3 - 1
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2 = 3 - 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 3 = 4 - 1
Description
The maximal multiplicity of a Laplacian eigenvalue in a graph.
Matching statistic: St000786
(load all 3 compositions to match this statistic)
Mapping
Mp00250: Graphs —clique graph⟶ Graphs
St000786: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => ([],1)
 => 1 = 2 - 1
([],2)
 => ([],2)
 => 2 = 3 - 1
([(0,1)],2)
 => ([],1)
 => 1 = 2 - 1
([],3)
 => ([],3)
 => 3 = 4 - 1
([(1,2)],3)
 => ([],2)
 => 2 = 3 - 1
([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,1),(0,2),(1,2)],3)
 => ([],1)
 => 1 = 2 - 1
([],4)
 => ([],4)
 => 4 = 5 - 1
([(2,3)],4)
 => ([],3)
 => 3 = 4 - 1
([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => 2 = 3 - 1
([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 1 = 2 - 1
([(0,3),(1,2)],4)
 => ([],2)
 => 2 = 3 - 1
([(0,3),(1,2),(2,3)],4)
 => ([(0,2),(1,2)],3)
 => 2 = 3 - 1
([(1,2),(1,3),(2,3)],4)
 => ([],2)
 => 2 = 3 - 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2 = 3 - 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],1)
 => 1 = 2 - 1
([],5)
 => ([],5)
 => 5 = 6 - 1
([(3,4)],5)
 => ([],4)
 => 4 = 5 - 1
([(2,4),(3,4)],5)
 => ([(2,3)],4)
 => 3 = 4 - 1
([(1,4),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => 2 = 3 - 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1 = 2 - 1
([(1,4),(2,3)],5)
 => ([],3)
 => 3 = 4 - 1
([(1,4),(2,3),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => 3 = 4 - 1
([(0,1),(2,4),(3,4)],5)
 => ([(1,2)],3)
 => 2 = 3 - 1
([(2,3),(2,4),(3,4)],5)
 => ([],3)
 => 3 = 4 - 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 2 = 3 - 1
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2)],3)
 => 2 = 3 - 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 1 = 2 - 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => 3 = 4 - 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 2 = 3 - 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2)],3)
 => 2 = 3 - 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => 2 = 3 - 1
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 1 = 2 - 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => 2 = 3 - 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 1 = 2 - 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,3),(1,2),(2,3)],4)
 => 2 = 3 - 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => 2 = 3 - 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => 2 = 3 - 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 2 = 3 - 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2 = 3 - 1
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 1 = 2 - 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => 2 = 3 - 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => 2 = 3 - 1
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2 = 3 - 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1 = 2 - 1
Description
The maximal number of occurrences of a colour in a proper colouring of a graph. To any proper colouring with the minimal number of colours possible we associate the integer partition recording how often each colour is used. This statistic records the largest part occurring in any of these partitions. For example, the graph on six vertices consisting of a square together with two attached triangles - ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6) in the list of values - is three-colourable and admits two colouring schemes, $[2,2,2]$ and $[3,2,1]$. Therefore, the statistic on this graph is $3$.
Matching statistic: St001340
Mapping
Mp00259: Graphs —vertex addition⟶ Graphs
St001340: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => ([],2)
 => 1 = 2 - 1
([],2)
 => ([],3)
 => 2 = 3 - 1
([(0,1)],2)
 => ([(1,2)],3)
 => 1 = 2 - 1
([],3)
 => ([],4)
 => 3 = 4 - 1
([(1,2)],3)
 => ([(2,3)],4)
 => 2 = 3 - 1
([(0,2),(1,2)],3)
 => ([(1,3),(2,3)],4)
 => 1 = 2 - 1
([(0,1),(0,2),(1,2)],3)
 => ([(1,2),(1,3),(2,3)],4)
 => 1 = 2 - 1
([],4)
 => ([],5)
 => 4 = 5 - 1
([(2,3)],4)
 => ([(3,4)],5)
 => 3 = 4 - 1
([(1,3),(2,3)],4)
 => ([(2,4),(3,4)],5)
 => 2 = 3 - 1
([(0,3),(1,3),(2,3)],4)
 => ([(1,4),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,3),(1,2)],4)
 => ([(1,4),(2,3)],5)
 => 2 = 3 - 1
([(0,3),(1,2),(2,3)],4)
 => ([(1,4),(2,3),(3,4)],5)
 => 2 = 3 - 1
([(1,2),(1,3),(2,3)],4)
 => ([(2,3),(2,4),(3,4)],5)
 => 2 = 3 - 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => 2 = 3 - 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 2 - 1
([],5)
 => ([],6)
 => 5 = 6 - 1
([(3,4)],5)
 => ([(4,5)],6)
 => 4 = 5 - 1
([(2,4),(3,4)],5)
 => ([(3,5),(4,5)],6)
 => 3 = 4 - 1
([(1,4),(2,4),(3,4)],5)
 => ([(2,5),(3,5),(4,5)],6)
 => 2 = 3 - 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => 1 = 2 - 1
([(1,4),(2,3)],5)
 => ([(2,5),(3,4)],6)
 => 3 = 4 - 1
([(1,4),(2,3),(3,4)],5)
 => ([(2,5),(3,4),(4,5)],6)
 => 3 = 4 - 1
([(0,1),(2,4),(3,4)],5)
 => ([(1,2),(3,5),(4,5)],6)
 => 2 = 3 - 1
([(2,3),(2,4),(3,4)],5)
 => ([(3,4),(3,5),(4,5)],6)
 => 3 = 4 - 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(1,5),(2,5),(3,4),(4,5)],6)
 => 2 = 3 - 1
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(2,5),(3,4),(3,5),(4,5)],6)
 => 2 = 3 - 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 2 - 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(2,4),(2,5),(3,4),(3,5)],6)
 => 3 = 4 - 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => 2 = 3 - 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2 = 3 - 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => 2 = 3 - 1
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 2 - 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 2 = 3 - 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 2 - 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 2 = 3 - 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(3,4),(3,5),(4,5)],6)
 => 2 = 3 - 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => 2 = 3 - 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => 1 = 2 - 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => 2 = 3 - 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => 2 = 3 - 1
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 2 - 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => 2 = 3 - 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2 = 3 - 1
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 2 - 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 2 - 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => 2 = 3 - 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 1 = 2 - 1
Description
The cardinality of a minimal non-edge isolating set of a graph. Let $\mathcal F$ be a set of graphs. A set of vertices $S$ is $\mathcal F$-isolating, if the subgraph induced by the vertices in the complement of the closed neighbourhood of $S$ does not contain any graph in $\mathcal F$. This statistic returns the cardinality of the smallest isolating set when $\mathcal F$ contains only the graph with two isolated vertices.
Matching statistic: St001674
Mapping
Mp00250: Graphs —clique graph⟶ Graphs
Mp00203: Graphs —cone⟶ Graphs
St001674: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => ([],1)
 => ([(0,1)],2)
 => 2
([],2)
 => ([],2)
 => ([(0,2),(1,2)],3)
 => 3
([(0,1)],2)
 => ([],1)
 => ([(0,1)],2)
 => 2
([],3)
 => ([],3)
 => ([(0,3),(1,3),(2,3)],4)
 => 4
([(1,2)],3)
 => ([],2)
 => ([(0,2),(1,2)],3)
 => 3
([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,1),(0,2),(1,2)],3)
 => ([],1)
 => ([(0,1)],2)
 => 2
([],4)
 => ([],4)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 5
([(2,3)],4)
 => ([],3)
 => ([(0,3),(1,3),(2,3)],4)
 => 4
([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 3
([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,3),(1,2)],4)
 => ([],2)
 => ([(0,2),(1,2)],3)
 => 3
([(0,3),(1,2),(2,3)],4)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 3
([(1,2),(1,3),(2,3)],4)
 => ([],2)
 => ([(0,2),(1,2)],3)
 => 3
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 3
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],1)
 => ([(0,1)],2)
 => 2
([],5)
 => ([],5)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 6
([(3,4)],5)
 => ([],4)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 5
([(2,4),(3,4)],5)
 => ([(2,3)],4)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 4
([(1,4),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(1,4),(2,3)],5)
 => ([],3)
 => ([(0,3),(1,3),(2,3)],4)
 => 4
([(1,4),(2,3),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4
([(0,1),(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 3
([(2,3),(2,4),(3,4)],5)
 => ([],3)
 => ([(0,3),(1,3),(2,3)],4)
 => 4
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 3
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 4
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 3
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 3
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => 3
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => ([(0,2),(1,2)],3)
 => 3
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 3
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => 3
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 3
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 3
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => ([(0,2),(1,2)],3)
 => 3
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 3
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
Description
The number of vertices of the largest induced star graph in the graph.
The following 119 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St000097The order of the largest clique of the graph. St000381The largest part of an integer composition. St000382The first part of an integer composition. St000808The number of up steps of the associated bargraph. St001337The upper domination number of a graph. St001338The upper irredundance number of a graph. St000326The position of the first one in a binary word after appending a 1 at the end. St000297The number of leading ones in a binary word. St000617The number of global maxima of a Dyck path. St001235The global dimension of the corresponding Comp-Nakayama algebra. St001330The hat guessing number of a graph. St001654The monophonic hull number of a graph. St001656The monophonic position number of a graph. St000993The multiplicity of the largest part of an integer partition. St001038The minimal height of a column in the parallelogram polyomino associated with the Dyck path. St001323The independence gap of a graph. St000733The row containing the largest entry of a standard tableau. St000745The index of the last row whose first entry is the row number in a standard Young tableau. St001024Maximum of dominant dimensions of the simple modules in the Nakayama algebra corresponding to the Dyck path. St001184Number of indecomposable injective modules with grade at least 1 in the corresponding Nakayama algebra. St001481The minimal height of a peak of a Dyck path. St000674The number of hills of a Dyck path. St000741The Colin de Verdière graph invariant. St001233The number of indecomposable 2-dimensional modules with projective dimension one. St000120The number of left tunnels of a Dyck path. St001008Number of indecomposable injective modules with projective dimension 1 in the Nakayama algebra corresponding to the Dyck path. St001264The smallest index i such that the i-th simple module has projective dimension equal to the global dimension of the corresponding Nakayama algebra. St001265The maximal i such that the i-th simple module has projective dimension equal to the global dimension in the corresponding Nakayama algebra. St000689The maximal n such that the minimal generator-cogenerator module in the LNakayama algebra of a Dyck path is n-rigid. St001803The maximal overlap of the cylindrical tableau associated with a tableau. St000454The largest eigenvalue of a graph if it is integral. St001200The number of simple modules in $eAe$ with projective dimension at most 2 in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St000771The largest multiplicity of a distance Laplacian eigenvalue in a connected graph. St001526The Loewy length of the Auslander-Reiten translate of the regular module as a bimodule of the Nakayama algebra corresponding to the Dyck path. St001000Number of indecomposable modules with projective dimension equal to the global dimension in the Nakayama algebra corresponding to the Dyck path. St000443The number of long tunnels of a Dyck path. St001060The distinguishing index of a graph. St001187The number of simple modules with grade at least one in the corresponding Nakayama algebra. St001224Let X be the direct sum of all simple modules of the corresponding Nakayama algebra. St000772The multiplicity of the largest distance Laplacian eigenvalue in a connected graph. St000260The radius of a connected graph. St000777The number of distinct eigenvalues of the distance Laplacian of a connected graph. St000259The diameter of a connected graph. St001118The acyclic chromatic index of a graph. St001704The size of the largest multi-subset-intersection of the deck of a graph with the deck of another graph. St001515The vector space dimension of the socle of the first syzygy module of the regular module (as a bimodule). St001613The binary logarithm of the size of the center of a lattice. St001881The number of factors of a lattice as a Cartesian product of lattices. St001198The number of simple modules in the algebra $eAe$ with projective dimension at most 1 in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001206The maximal dimension of an indecomposable projective $eAe$-module (that is the height of the corresponding Dyck path) of the corresponding Nakayama algebra with minimal faithful projective-injective module $eA$. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St001570The minimal number of edges to add to make a graph Hamiltonian. St000264The girth of a graph, which is not a tree. St000014The number of parking functions supported by a Dyck path. St000063The number of linear extensions of a certain poset defined for an integer partition. St000108The number of partitions contained in the given partition. St000144The pyramid weight of the Dyck path. St000294The number of distinct factors of a binary word. St000380Half of the maximal perimeter of a rectangle fitting into the diagram of an integer partition. St000393The number of strictly increasing runs in a binary word. St000395The sum of the heights of the peaks of a Dyck path. St000439The position of the first down step of a Dyck path. St000518The number of distinct subsequences in a binary word. St000532The total number of rook placements on a Ferrers board. St000543The size of the conjugacy class of a binary word. St000626The minimal period of a binary word. St000806The semiperimeter of the associated bargraph. St000969We make a CNakayama algebra out of the LNakayama algebra (corresponding to the Dyck path) $[c_0,c_1,...,c_{n-1}]$ by adding $c_0$ to $c_{n-1}$. St000998Number of indecomposable projective modules with injective dimension smaller than or equal to the dominant dimension in the Nakayama algebra corresponding to the Dyck path. St001012Number of simple modules with projective dimension at most 2 in the Nakayama algebra corresponding to the Dyck path. St001018Sum of projective dimension of the indecomposable injective modules of the Nakayama algebra corresponding to the Dyck path. St001020Sum of the codominant dimensions of the non-projective indecomposable injective modules of the Nakayama algebra corresponding to the Dyck path. St001023Number of simple modules with projective dimension at most 3 in the Nakayama algebra corresponding to the Dyck path. St001028Number of simple modules with injective dimension equal to the dominant dimension in the Nakayama algebra corresponding to the Dyck path. St001039The maximal height of a column in the parallelogram polyomino associated with a Dyck path. St001065Number of indecomposable reflexive modules in the corresponding Nakayama algebra. St001166Number of indecomposable projective non-injective modules with dominant dimension equal to the global dimension plus the number of indecomposable projective injective modules in the corresponding Nakayama algebra. St001170Number of indecomposable injective modules whose socle has projective dimension at most g-1 when g denotes the global dimension in the corresponding Nakayama algebra. St001179Number of indecomposable injective modules with projective dimension at most 2 in the corresponding Nakayama algebra. St001180Number of indecomposable injective modules with projective dimension at most 1. St001183The maximum of $projdim(S)+injdim(S)$ over all simple modules in the Nakayama algebra corresponding to the Dyck path. St001190Number of simple modules with projective dimension at most 4 in the corresponding Nakayama algebra. St001211The number of simple modules in the corresponding Nakayama algebra that have vanishing second Ext-group with the regular module. St001226The number of integers i such that the radical of the i-th indecomposable projective module has vanishing first extension group with the Jacobson radical J in the corresponding Nakayama algebra. St001237The number of simple modules with injective dimension at most one or dominant dimension at least one. St001240The number of indecomposable modules e_i J^2 that have injective dimension at most one in the corresponding Nakayama algebra St001258Gives the maximum of injective plus projective dimension of an indecomposable module over the corresponding Nakayama algebra. St001267The length of the Lyndon factorization of the binary word. St001290The first natural number n such that the tensor product of n copies of D(A) is zero for the corresponding Nakayama algebra A. St001291The number of indecomposable summands of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path. St001365The number of lattice paths of the same length weakly above the path given by a binary word. St001400The total number of Littlewood-Richardson tableaux of given shape. St001437The flex of a binary word. St001492The number of simple modules that do not appear in the socle of the regular module or have no nontrivial selfextensions with the regular module in the corresponding Nakayama algebra. St001504The sum of all indegrees of vertices with indegree at least two in the resolution quiver of a Nakayama algebra corresponding to the Dyck path. St001505The number of elements generated by the Dyck path as a map in the full transformation monoid. St001650The order of Ringel's homological bijection associated to the linear Nakayama algebra corresponding to the Dyck path. St001814The number of partitions interlacing the given partition. St001621The number of atoms of a lattice. St001545The second Elser number of a connected graph. St001630The global dimension of the incidence algebra of the lattice over the rational numbers. St001878The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L. St000642The size of the smallest orbit of antichains under Panyushev complementation. St000939The number of characters of the symmetric group whose value on the partition is positive. St000515The number of invariant set partitions when acting with a permutation of given cycle type. St000937The number of positive values of the symmetric group character corresponding to the partition. St000438The position of the last up step in a Dyck path. St000514The number of invariant simple graphs when acting with a permutation of given cycle type. St000422The energy of a graph, if it is integral. St001644The dimension of a graph. St001875The number of simple modules with projective dimension at most 1. St000455The second largest eigenvalue of a graph if it is integral. St001816Eigenvalues of the top-to-random operator acting on a simple module. St001645The pebbling number of a connected graph. St001651The Frankl number of a lattice. St001879The number of indecomposable summands of the top of the first syzygy of the dual of the regular module in the incidence algebra of the lattice. St000302The determinant of the distance matrix of a connected graph. St000466The Gutman (or modified Schultz) index of a connected graph. St000467The hyper-Wiener index of a connected graph.