- FindStat

Your data matches 263 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)

Matching statistic: St000258
(load all 3 compositions to match this statistic)

Mapping

Mp00154: Graphs —core⟶ Graphs
St000258: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

([],1)
 => ([],1)
 => 1
([],2)
 => ([],1)
 => 1
([(0,1)],2)
 => ([(0,1)],2)
 => 2
([],3)
 => ([],1)
 => 1
([(1,2)],3)
 => ([(0,1)],2)
 => 2
([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 2
([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([],4)
 => ([],1)
 => 1
([(2,3)],4)
 => ([(0,1)],2)
 => 2
([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 2
([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 2
([(0,3),(1,2)],4)
 => ([(0,1)],2)
 => 2
([(0,3),(1,2),(2,3)],4)
 => ([(0,1)],2)
 => 2
([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => 2
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([],5)
 => ([],1)
 => 1
([(3,4)],5)
 => ([(0,1)],2)
 => 2
([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(1,4),(2,3)],5)
 => ([(0,1)],2)
 => 2
([(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(0,1),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => 2
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => 2
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(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)
 => 3
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([],6)
 => ([],1)
 => 1
([(4,5)],6)
 => ([(0,1)],2)
 => 2
([(3,5),(4,5)],6)
 => ([(0,1)],2)
 => 2
([(2,5),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => 2

Description

The burning number of a graph. This is the minimum number of rounds needed to burn all vertices of a graph. In each round, the neighbours of all burned vertices are burnt. Additionally, an unburned vertex may be chosen to be burned.

Matching statistic: St000452
(load all 4 compositions to match this statistic)

Mapping

Mp00154: Graphs —core⟶ Graphs
St000452: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

([],1)
 => ([],1)
 => 1
([],2)
 => ([],1)
 => 1
([(0,1)],2)
 => ([(0,1)],2)
 => 2
([],3)
 => ([],1)
 => 1
([(1,2)],3)
 => ([(0,1)],2)
 => 2
([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 2
([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([],4)
 => ([],1)
 => 1
([(2,3)],4)
 => ([(0,1)],2)
 => 2
([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 2
([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 2
([(0,3),(1,2)],4)
 => ([(0,1)],2)
 => 2
([(0,3),(1,2),(2,3)],4)
 => ([(0,1)],2)
 => 2
([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => 2
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([],5)
 => ([],1)
 => 1
([(3,4)],5)
 => ([(0,1)],2)
 => 2
([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(1,4),(2,3)],5)
 => ([(0,1)],2)
 => 2
([(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(0,1),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => 2
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => 2
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(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)
 => 3
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([],6)
 => ([],1)
 => 1
([(4,5)],6)
 => ([(0,1)],2)
 => 2
([(3,5),(4,5)],6)
 => ([(0,1)],2)
 => 2
([(2,5),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => 2

Description

The number of distinct eigenvalues of a graph.

Matching statistic: St000453
(load all 5 compositions to match this statistic)

Mapping

Mp00154: Graphs —core⟶ Graphs
St000453: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

([],1)
 => ([],1)
 => 1
([],2)
 => ([],1)
 => 1
([(0,1)],2)
 => ([(0,1)],2)
 => 2
([],3)
 => ([],1)
 => 1
([(1,2)],3)
 => ([(0,1)],2)
 => 2
([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 2
([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([],4)
 => ([],1)
 => 1
([(2,3)],4)
 => ([(0,1)],2)
 => 2
([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 2
([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 2
([(0,3),(1,2)],4)
 => ([(0,1)],2)
 => 2
([(0,3),(1,2),(2,3)],4)
 => ([(0,1)],2)
 => 2
([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => 2
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([],5)
 => ([],1)
 => 1
([(3,4)],5)
 => ([(0,1)],2)
 => 2
([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(1,4),(2,3)],5)
 => ([(0,1)],2)
 => 2
([(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(0,1),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => 2
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => 2
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(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)
 => 3
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([],6)
 => ([],1)
 => 1
([(4,5)],6)
 => ([(0,1)],2)
 => 2
([(3,5),(4,5)],6)
 => ([(0,1)],2)
 => 2
([(2,5),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => 2

Description

The number of distinct Laplacian eigenvalues of a graph.

Matching statistic: St000777
(load all 4 compositions to match this statistic)

Mapping

Mp00154: Graphs —core⟶ Graphs
St000777: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

([],1)
 => ([],1)
 => 1
([],2)
 => ([],1)
 => 1
([(0,1)],2)
 => ([(0,1)],2)
 => 2
([],3)
 => ([],1)
 => 1
([(1,2)],3)
 => ([(0,1)],2)
 => 2
([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 2
([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([],4)
 => ([],1)
 => 1
([(2,3)],4)
 => ([(0,1)],2)
 => 2
([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 2
([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 2
([(0,3),(1,2)],4)
 => ([(0,1)],2)
 => 2
([(0,3),(1,2),(2,3)],4)
 => ([(0,1)],2)
 => 2
([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => 2
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([],5)
 => ([],1)
 => 1
([(3,4)],5)
 => ([(0,1)],2)
 => 2
([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(1,4),(2,3)],5)
 => ([(0,1)],2)
 => 2
([(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(0,1),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => 2
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => 2
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(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)
 => 3
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([],6)
 => ([],1)
 => 1
([(4,5)],6)
 => ([(0,1)],2)
 => 2
([(3,5),(4,5)],6)
 => ([(0,1)],2)
 => 2
([(2,5),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => 2

Description

The number of distinct eigenvalues of the distance Laplacian of a connected graph.

Matching statistic: St000918
(load all 4 compositions to match this statistic)

Mapping

Mp00154: Graphs —core⟶ Graphs
St000918: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

([],1)
 => ([],1)
 => 1
([],2)
 => ([],1)
 => 1
([(0,1)],2)
 => ([(0,1)],2)
 => 2
([],3)
 => ([],1)
 => 1
([(1,2)],3)
 => ([(0,1)],2)
 => 2
([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 2
([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([],4)
 => ([],1)
 => 1
([(2,3)],4)
 => ([(0,1)],2)
 => 2
([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 2
([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 2
([(0,3),(1,2)],4)
 => ([(0,1)],2)
 => 2
([(0,3),(1,2),(2,3)],4)
 => ([(0,1)],2)
 => 2
([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => 2
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([],5)
 => ([],1)
 => 1
([(3,4)],5)
 => ([(0,1)],2)
 => 2
([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(1,4),(2,3)],5)
 => ([(0,1)],2)
 => 2
([(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(0,1),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => 2
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => 2
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(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)
 => 3
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([],6)
 => ([],1)
 => 1
([(4,5)],6)
 => ([(0,1)],2)
 => 2
([(3,5),(4,5)],6)
 => ([(0,1)],2)
 => 2
([(2,5),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => 2

Description

The 2-limited packing number of a graph. A subset

$B$ of the set of vertices of a graph is a

$k$ -limited packing set if its intersection with the (closed) neighbourhood of any vertex is at most

$k$ . The

$k$ -limited packing number is the largest number of vertices in a

$k$ -limited packing set.

Matching statistic: St001261
(load all 4 compositions to match this statistic)

Mapping

Mp00154: Graphs —core⟶ Graphs
St001261: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

([],1)
 => ([],1)
 => 1
([],2)
 => ([],1)
 => 1
([(0,1)],2)
 => ([(0,1)],2)
 => 2
([],3)
 => ([],1)
 => 1
([(1,2)],3)
 => ([(0,1)],2)
 => 2
([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 2
([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([],4)
 => ([],1)
 => 1
([(2,3)],4)
 => ([(0,1)],2)
 => 2
([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 2
([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 2
([(0,3),(1,2)],4)
 => ([(0,1)],2)
 => 2
([(0,3),(1,2),(2,3)],4)
 => ([(0,1)],2)
 => 2
([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => 2
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([],5)
 => ([],1)
 => 1
([(3,4)],5)
 => ([(0,1)],2)
 => 2
([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(1,4),(2,3)],5)
 => ([(0,1)],2)
 => 2
([(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(0,1),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => 2
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => 2
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(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)
 => 3
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([],6)
 => ([],1)
 => 1
([(4,5)],6)
 => ([(0,1)],2)
 => 2
([(3,5),(4,5)],6)
 => ([(0,1)],2)
 => 2
([(2,5),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => 2

Description

The Castelnuovo-Mumford regularity of a graph.

Matching statistic: St001315
(load all 6 compositions to match this statistic)

Mapping

Mp00154: Graphs —core⟶ Graphs
St001315: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

([],1)
 => ([],1)
 => 1
([],2)
 => ([],1)
 => 1
([(0,1)],2)
 => ([(0,1)],2)
 => 2
([],3)
 => ([],1)
 => 1
([(1,2)],3)
 => ([(0,1)],2)
 => 2
([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 2
([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([],4)
 => ([],1)
 => 1
([(2,3)],4)
 => ([(0,1)],2)
 => 2
([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 2
([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 2
([(0,3),(1,2)],4)
 => ([(0,1)],2)
 => 2
([(0,3),(1,2),(2,3)],4)
 => ([(0,1)],2)
 => 2
([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => 2
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([],5)
 => ([],1)
 => 1
([(3,4)],5)
 => ([(0,1)],2)
 => 2
([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(1,4),(2,3)],5)
 => ([(0,1)],2)
 => 2
([(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(0,1),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => 2
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => 2
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(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)
 => 3
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([],6)
 => ([],1)
 => 1
([(4,5)],6)
 => ([(0,1)],2)
 => 2
([(3,5),(4,5)],6)
 => ([(0,1)],2)
 => 2
([(2,5),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => 2

Description

The dissociation number of a graph.

Matching statistic: St001674
(load all 4 compositions to match this statistic)

Mapping

Mp00154: Graphs —core⟶ Graphs
St001674: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

([],1)
 => ([],1)
 => 1
([],2)
 => ([],1)
 => 1
([(0,1)],2)
 => ([(0,1)],2)
 => 2
([],3)
 => ([],1)
 => 1
([(1,2)],3)
 => ([(0,1)],2)
 => 2
([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 2
([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([],4)
 => ([],1)
 => 1
([(2,3)],4)
 => ([(0,1)],2)
 => 2
([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 2
([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 2
([(0,3),(1,2)],4)
 => ([(0,1)],2)
 => 2
([(0,3),(1,2),(2,3)],4)
 => ([(0,1)],2)
 => 2
([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => 2
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([],5)
 => ([],1)
 => 1
([(3,4)],5)
 => ([(0,1)],2)
 => 2
([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(1,4),(2,3)],5)
 => ([(0,1)],2)
 => 2
([(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(0,1),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => 2
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => 2
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(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)
 => 3
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([],6)
 => ([],1)
 => 1
([(4,5)],6)
 => ([(0,1)],2)
 => 2
([(3,5),(4,5)],6)
 => ([(0,1)],2)
 => 2
([(2,5),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => 2

Description

The number of vertices of the largest induced star graph in the graph.

Matching statistic: St000259
(load all 4 compositions to match this statistic)

Mapping

Mp00154: Graphs —core⟶ Graphs
St000259: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

([],1)
 => ([],1)
 => 0 = 1 - 1
([],2)
 => ([],1)
 => 0 = 1 - 1
([(0,1)],2)
 => ([(0,1)],2)
 => 1 = 2 - 1
([],3)
 => ([],1)
 => 0 = 1 - 1
([(1,2)],3)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 1 = 2 - 1
([],4)
 => ([],1)
 => 0 = 1 - 1
([(2,3)],4)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,3),(1,2)],4)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,3),(1,2),(2,3)],4)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 1 = 2 - 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 1 = 2 - 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 1 = 2 - 1
([],5)
 => ([],1)
 => 0 = 1 - 1
([(3,4)],5)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(1,4),(2,3)],5)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,1),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 1 = 2 - 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 1 = 2 - 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)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(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),(3,4)],5)
 => ([(0,1),(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)
 => 1 = 2 - 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => 1 = 2 - 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)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 1 = 2 - 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 1 = 2 - 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 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)
 => ([(0,1),(0,2),(1,2)],3)
 => 1 = 2 - 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)
 => ([(0,1),(0,2),(1,2)],3)
 => 1 = 2 - 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 1 = 2 - 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 1 = 2 - 1
([],6)
 => ([],1)
 => 0 = 1 - 1
([(4,5)],6)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(3,5),(4,5)],6)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(2,5),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => 1 = 2 - 1

Description

The diameter of a connected graph. This is the greatest distance between any pair of vertices.

Matching statistic: St000260
(load all 4 compositions to match this statistic)

Mapping

Mp00154: Graphs —core⟶ Graphs
St000260: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

([],1)
 => ([],1)
 => 0 = 1 - 1
([],2)
 => ([],1)
 => 0 = 1 - 1
([(0,1)],2)
 => ([(0,1)],2)
 => 1 = 2 - 1
([],3)
 => ([],1)
 => 0 = 1 - 1
([(1,2)],3)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 1 = 2 - 1
([],4)
 => ([],1)
 => 0 = 1 - 1
([(2,3)],4)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,3),(1,2)],4)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,3),(1,2),(2,3)],4)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 1 = 2 - 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 1 = 2 - 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 1 = 2 - 1
([],5)
 => ([],1)
 => 0 = 1 - 1
([(3,4)],5)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(1,4),(2,3)],5)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,1),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 1 = 2 - 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 1 = 2 - 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)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(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),(3,4)],5)
 => ([(0,1),(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)
 => 1 = 2 - 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => 1 = 2 - 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)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 1 = 2 - 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 1 = 2 - 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 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)
 => ([(0,1),(0,2),(1,2)],3)
 => 1 = 2 - 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)
 => ([(0,1),(0,2),(1,2)],3)
 => 1 = 2 - 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 1 = 2 - 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 1 = 2 - 1
([],6)
 => ([],1)
 => 0 = 1 - 1
([(4,5)],6)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(3,5),(4,5)],6)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(2,5),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => 1 = 2 - 1

Description

The radius of a connected graph. This is the minimum eccentricity of any vertex.

The following 253 statistics, ordered by result quality, also match your data. Click on any of them to see the details.

St000387The matching number of a graph. St000535The rank-width of a graph. St001271The competition number of a graph. St001333The cardinality of a minimal edge-isolating set of a graph. St001340The cardinality of a minimal non-edge isolating set of a graph. St000378The diagonal inversion number of an integer partition. St000644The number of graphs with given frequency partition. St001642The Prague dimension of a graph. St001716The 1-improper chromatic number of a graph. St001738The minimal order of a graph which is not an induced subgraph of the given graph. St000093The cardinality of a maximal independent set of vertices of a graph. St000149The number of cells of the partition whose leg is zero and arm is odd. St001767The largest minimal number of arrows pointing to a cell in the Ferrers diagram in any assignment. St001777The number of weak descents in an integer composition. St000010The length of the partition. St000011The number of touch points (or returns) of a Dyck path. St000015The number of peaks of a Dyck path. St000097The order of the largest clique of the graph. St000098The chromatic number of a graph. St000172The Grundy number of a graph. St000288The number of ones in a binary word. St000321The number of integer partitions of n that are dominated by an integer partition. St000345The number of refinements of a partition. St000384The maximal part of the shifted composition of an integer partition. St000393The number of strictly increasing runs in a binary word. St000636The hull number of a graph. St000676The number of odd rises of a Dyck path. St000757The length of the longest weakly inreasing subsequence of parts of an integer composition. St000765The number of weak records in an integer composition. St000767The number of runs in an integer composition. St000784The maximum of the length and the largest part of the integer partition. St000822The Hadwiger number of the graph. St000935The number of ordered refinements of an integer partition. St001029The size of the core of a graph. St001068Number of torsionless simple modules in the corresponding Nakayama algebra. St001093The detour number of a graph. St001116The game chromatic number of a graph. St001165Number of simple modules with even projective dimension in the corresponding Nakayama algebra. St001202Call a CNakayama algebra (a Nakayama algebra with a cyclic quiver) with Kupisch series

$L=[c_0,c_1,...,c_{n−1}]$ such that

$n=c_0 < c_i$ for all

$i > 0$ a special CNakayama algebra. St001203We associate to a CNakayama algebra (a Nakayama algebra with a cyclic quiver) with Kupisch series

$L=[c_0,c_1,...,c_{n-1}]$ such that

$n=c_0 < c_i$ for all

$i > 0$ a Dyck path as follows: St001235The global dimension of the corresponding Comp-Nakayama algebra. St001250The number of parts of a partition that are not congruent 0 modulo 3. St001267The length of the Lyndon factorization of the binary word. St001302The number of minimally dominating sets of vertices of a graph. St001304The number of maximally independent sets of vertices of a graph. St001345The Hamming dimension of a graph. St001389The number of partitions of the same length below the given integer partition. St001437The flex of a binary word. St001471The magnitude of a Dyck path. St001486The number of corners of the ribbon associated with an integer composition. St001494The Alon-Tarsi number of a graph. St001512The minimum rank of a graph. St001580The acyclic chromatic number of a graph. St001581The achromatic number of a graph. St001654The monophonic hull number of a graph. St001655The general position number of a graph. St001656The monophonic position number of a graph. St001670The connected partition number of a graph. St001785The number of ways to obtain a partition as the multiset of antidiagonal lengths of the Ferrers diagram of a partition. St001792The arboricity of a graph. St001884The number of borders of a binary word. St001963The tree-depth of a graph. St000053The number of valleys of the Dyck path. St000120The number of left tunnels of a Dyck path. St000142The number of even parts of a partition. St000143The largest repeated part of a partition. St000150The floored half-sum of the multiplicities of a partition. St000272The treewidth of a graph. St000306The bounce count of a Dyck path. St000329The number of evenly positioned ascents of the Dyck path, with the initial position equal to 1. St000362The size of a minimal vertex cover of a graph. St000380Half of the maximal perimeter of a rectangle fitting into the diagram of an integer partition. St000473The number of parts of a partition that are strictly bigger than the number of ones. St000506The number of standard desarrangement tableaux of shape equal to the given partition. St000513The number of invariant subsets of size 2 when acting with a permutation of given cycle type. St000536The pathwidth of a graph. St000547The number of even non-empty partial sums of an integer partition. St000766The number of inversions of an integer composition. St000778The metric dimension of a graph. St000985The number of positive eigenvalues of the adjacency matrix of the graph. St001011Number of simple modules of projective dimension 2 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. St001031The height of the bicoloured Motzkin path associated with the Dyck path. St001108The 2-dynamic chromatic number of a graph. St001125The number of simple modules that satisfy the 2-regular condition in the corresponding Nakayama algebra. St001142The projective dimension of the socle of the regular module as a bimodule in the Nakayama algebra corresponding to the Dyck path. St001169Number of simple modules with projective dimension at least two in the corresponding Nakayama algebra. St001188The number of simple modules

$S$ with grade

$\inf \{ i \geq 0 | Ext^i(S,A) \neq 0 \}$ at least two in the Nakayama algebra

$A$ corresponding to the Dyck path. St001197The global dimension of

$eAe$ for the corresponding Nakayama algebra

$A$ with minimal faithful projective-injective module

$eA$ . St001205The number of non-simple indecomposable projective-injective modules of the algebra

$eAe$ in the corresponding Nakayama algebra

$A$ with minimal faithful projective-injective module

$eA$ . St001212The number of simple modules in the corresponding Nakayama algebra that have non-zero second Ext-group with the regular module. St001215Let X be the direct sum of all simple modules of the corresponding Nakayama algebra. St001216The number of indecomposable injective modules in the corresponding Nakayama algebra that have non-vanishing second Ext-group with the regular module. St001222Number of simple modules in the corresponding LNakayama algebra that have a unique 2-extension with the regular module. St001225The vector space dimension of the first extension group between J and itself when J is the Jacobson radical of the corresponding Nakayama algebra. St001230The number of simple modules with injective dimension equal to the dominant dimension equal to one and the dual property. St001237The number of simple modules with injective dimension at most one or dominant dimension at least one. St001244The number of simple modules of projective dimension one that are not 1-regular for the Nakayama algebra associated to a Dyck path. St001251The number of parts of a partition that are not congruent 1 modulo 3. St001252Half the sum of the even parts of a partition. St001270The bandwidth of a graph. St001274The number of indecomposable injective modules with projective dimension equal to two. St001276The number of 2-regular indecomposable modules in the corresponding Nakayama algebra. St001277The degeneracy of a graph. St001278The number of indecomposable modules that are fixed by

$\tau \Omega^1$ composed with its inverse in the corresponding Nakayama algebra. St001280The number of parts of an integer partition that are at least two. St001290The first natural number n such that the tensor product of n copies of D(A) is zero for the corresponding Nakayama algebra A. St001354The number of series nodes in the modular decomposition of a graph. St001358The largest degree of a regular subgraph of a graph. St001424The number of distinct squares in a binary word. St001505The number of elements generated by the Dyck path as a map in the full transformation monoid. St001506Half the projective dimension of the unique simple module with even projective dimension in a magnitude 1 Nakayama algebra. St001507The sum of projective dimension of simple modules with even projective dimension divided by 2 in the LNakayama algebra corresponding to Dyck paths. St001508The degree of the standard monomial associated to a Dyck path relative to the diagonal boundary. St001524The degree of symmetry of a binary word. St001644The dimension of a graph. St001657The number of twos in an integer partition. St001812The biclique partition number of a graph. St001873For a Nakayama algebra corresponding to a Dyck path, we define the matrix C with entries the Hom-spaces between

$e_i J$ and

$e_j J$ (the radical of the indecomposable projective modules). St001962The proper pathwidth of a graph. St001616The number of neutral elements in a lattice. St001720The minimal length of a chain of small intervals in a lattice. St001754The number of tolerances of a finite lattice. St000741The Colin de Verdière graph invariant. St001613The binary logarithm of the size of the center of a lattice. St001617The dimension of the space of valuations of a lattice. St001330The hat guessing number of a graph. St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset. St001514The dimension of the top of the Auslander-Reiten translate of the regular modules as a bimodule. St001431Half of the Loewy length minus one of a modified stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001553The number of indecomposable summands of the square of the Jacobson radical as a bimodule in the Nakayama algebra corresponding to the Dyck path. St000455The second largest eigenvalue of a graph if it is integral. St000273The domination number of a graph. St000544The cop number of a graph. St000698The number of 2-rim hooks removed from an integer partition to obtain its associated 2-core. St000786The maximal number of occurrences of a colour in a proper colouring of a graph. St000917The open packing number of a graph. St001286The annihilation number of a graph. St001322The size of a minimal independent dominating set in a graph. St001337The upper domination number of a graph. St001338The upper irredundance number of a graph. St001339The irredundance number of a graph. St001774The degree of the minimal polynomial of the smallest eigenvalue of a graph. St001776The degree of the minimal polynomial of the largest Laplacian eigenvalue of a graph. St001829The common independence number of a graph. St000379The number of Hamiltonian cycles in a graph. St000671The maximin edge-connectivity for choosing a subgraph. St001056The Grundy value for the game of deleting vertices of a graph until it has no edges. St001324The minimal number of occurrences of the chordal-pattern in a linear ordering of the vertices of the graph. St001325The minimal number of occurrences of the comparability-pattern in a linear ordering of the vertices of the graph. St001793The difference between the clique number and the chromatic number of a graph. St001798The difference of the number of edges in a graph and the number of edges in the complement of the Turán graph. St000939The number of characters of the symmetric group whose value on the partition is positive. 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

$eA$ . St001704The size of the largest multi-subset-intersection of the deck of a graph with the deck of another graph. St000268The number of strongly connected orientations of a graph. St000566The number of ways to select a row of a Ferrers shape and two cells in this row. St000621The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is even. St000668The least common multiple of the parts of the partition. St000706The product of the factorials of the multiplicities of an integer partition. St000762The sum of the positions of the weak records of an integer composition. St000770The major index of an integer partition when read from bottom to top. St000806The semiperimeter of the associated bargraph. St000993The multiplicity of the largest part of an integer partition. St001073The number of nowhere zero 3-flows of a graph. St001128The exponens consonantiae of a partition. St001199The dominant dimension of

$eAe$ for the corresponding Nakayama algebra

$A$ with minimal faithful projective-injective module

$eA$ . St001281The normalized isoperimetric number of a graph. St001316The domatic number of a graph. St001499The number of indecomposable projective-injective modules of a magnitude 1 Nakayama algebra. St001957The number of Hasse diagrams with a given underlying undirected graph. St000303The determinant of the product of the incidence matrix and its transpose of a graph divided by

$4$ . St000369The dinv deficit of a Dyck path. St000478Another weight of a partition according to Alladi. St000934The 2-degree of an integer partition. St000936The number of even values of the symmetric group character corresponding to the partition. St000938The number of zeros of the symmetric group character corresponding to the partition. St001071The beta invariant of the graph. St001124The multiplicity of the standard representation in the Kronecker square corresponding to a partition. St001311The cyclomatic number of a graph. St001317The minimal number of occurrences of the forest-pattern in a linear ordering of the vertices of the graph. St001328The minimal number of occurrences of the bipartite-pattern in a linear ordering of the vertices of the graph. St001331The size of the minimal feedback vertex set. St001349The number of different graphs obtained from the given graph by removing an edge. St001393The induced matching number of a graph. St001572The minimal number of edges to remove to make a graph bipartite. St001638The book thickness of a graph. St001723The differential of a graph. St001724The 2-packing differential of a graph. St001736The total number of cycles in a graph. St001797The number of overfull subgraphs of a graph. St000422The energy of a graph, if it is integral. St000699The toughness times the least common multiple of 1,. St000718The largest Laplacian eigenvalue of a graph if it is integral. St001592The maximal number of simple paths between any two different vertices of a graph. St001570The minimal number of edges to add to make a graph Hamiltonian. St001604The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on polygons. 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. St001875The number of simple modules with projective dimension at most 1. St001877Number of indecomposable injective modules with projective dimension 2. St000618The number of self-evacuating tableaux of given shape. St000755The number of real roots of the characteristic polynomial of a linear recurrence associated with an integer partition. St000781The number of proper colouring schemes of a Ferrers diagram. St001901The largest multiplicity of an irreducible representation contained in the higher Lie character for an integer partition. St000205Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and partition weight. St000206Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and integer composition weight. St000749The smallest integer d such that the restriction of the representation corresponding to a partition of n to the symmetric group on n-d letters has a constituent of odd degree. St001175The size of a partition minus the hook length of the base cell. St001248Sum of the even parts of a partition. St001586The number of odd parts smaller than the largest even part in an integer partition. St001587Half of the largest even part of an integer partition. St001603The number of colourings of a polygon such that the multiplicities of a colour are given by a partition. St000464The Schultz index of a connected graph. St001545The second Elser number of a connected graph. St000456The monochromatic index of a connected graph. St001118The acyclic chromatic index of a graph. St000689The maximal n such that the minimal generator-cogenerator module in the LNakayama algebra of a Dyck path is n-rigid. St001001The number of indecomposable modules with projective and injective dimension equal to the global dimension of the Nakayama algebra corresponding to the Dyck path. St001195The global dimension of the algebra

$A/AfA$ of the corresponding Nakayama algebra

$A$ with minimal left faithful projective-injective module

$Af$ . St000454The largest eigenvalue of a graph if it is integral. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St000771The largest multiplicity of a distance Laplacian eigenvalue in a connected graph. St000772The multiplicity of the largest distance Laplacian eigenvalue in a connected graph. St001651The Frankl number of a lattice. St000264The girth of a graph, which is not a tree. St001621The number of atoms of a lattice. St001624The breadth of a lattice. St001060The distinguishing index of a graph. St000907The number of maximal antichains of minimal length in a poset. St001942The number of loops of the quiver corresponding to the reduced incidence algebra of a poset. St001804The minimal height of the rectangular inner shape in a cylindrical tableau associated to a tableau. St000914The sum of the values of the Möbius function of a poset. St001432The order dimension of the partition. St001609The number of coloured trees such that the multiplicities of colours are given by a partition. St001780The order of promotion on the set of standard tableaux of given shape. St001899The total number of irreducible representations contained in the higher Lie character for an integer partition. St001900The number of distinct irreducible representations contained in the higher Lie character for an integer partition. St001908The number of semistandard tableaux of distinct weight whose maximal entry is the length of the partition. St001913The number of preimages of an integer partition in Bulgarian solitaire. St001924The number of cells in an integer partition whose arm and leg length coincide. St001936The number of transitive factorisations of a permutation of given cycle type into star transpositions. St000175Degree of the polynomial counting the number of semistandard Young tableaux when stretching the shape. St000225Difference between largest and smallest parts in a partition. St001095The number of non-isomorphic posets with precisely one further covering relation. St001178Twelve times the variance of the major index among all standard Young tableaux of a partition. 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

$eA$ . St001568The smallest positive integer that does not appear twice in the partition. St001599The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on rooted trees. St001934The number of monotone factorisations of genus zero of a permutation of given cycle type. St000929The constant term of the character polynomial of an integer partition. St000944The 3-degree of an integer partition.