Your data matches 142 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000387
(load all 7 compositions to match this statistic)
Mapping
St000387: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => 0 = 1 - 1
([],2)
 => 0 = 1 - 1
([(0,1)],2)
 => 1 = 2 - 1
([],3)
 => 0 = 1 - 1
([(1,2)],3)
 => 1 = 2 - 1
([(0,2),(1,2)],3)
 => 1 = 2 - 1
([(0,1),(0,2),(1,2)],3)
 => 1 = 2 - 1
([],4)
 => 0 = 1 - 1
([(2,3)],4)
 => 1 = 2 - 1
([(1,3),(2,3)],4)
 => 1 = 2 - 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)
 => 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)
 => 2 = 3 - 1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2 = 3 - 1
Description
The matching number of a graph. For a graph $G$, this is defined as the maximal size of a '''matching''' or '''independent edge set''' (a set of edges without common vertices) contained in $G$.
Matching statistic: St000093
(load all 2 compositions to match this statistic)
Mapping
Mp00156: Graphs —line graph⟶ Graphs
St000093: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => ([],0)
 => 0 = 1 - 1
([],2)
 => ([],0)
 => 0 = 1 - 1
([(0,1)],2)
 => ([],1)
 => 1 = 2 - 1
([],3)
 => ([],0)
 => 0 = 1 - 1
([(1,2)],3)
 => ([],1)
 => 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)
 => ([],0)
 => 0 = 1 - 1
([(2,3)],4)
 => ([],1)
 => 1 = 2 - 1
([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 1 = 2 - 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)
 => ([(0,1),(0,2),(1,2)],3)
 => 1 = 2 - 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2 = 3 - 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)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 2 = 3 - 1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 2 = 3 - 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: St000453
(load all 2 compositions to match this statistic)
Mapping
Mp00156: Graphs —line graph⟶ Graphs
Mp00203: Graphs —cone⟶ Graphs
St000453: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => ([],0)
 => ([],1)
 => 1
([],2)
 => ([],0)
 => ([],1)
 => 1
([(0,1)],2)
 => ([],1)
 => ([(0,1)],2)
 => 2
([],3)
 => ([],0)
 => ([],1)
 => 1
([(1,2)],3)
 => ([],1)
 => ([(0,1)],2)
 => 2
([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([],4)
 => ([],0)
 => ([],1)
 => 1
([(2,3)],4)
 => ([],1)
 => ([(0,1)],2)
 => 2
([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(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)
 => ([(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),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
([(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)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => 3
Description
The number of distinct Laplacian eigenvalues of a graph.
Matching statistic: St000777
(load all 20 compositions to match this statistic)
Mapping
Mp00156: Graphs —line graph⟶ Graphs
Mp00203: Graphs —cone⟶ Graphs
St000777: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => ([],0)
 => ([],1)
 => 1
([],2)
 => ([],0)
 => ([],1)
 => 1
([(0,1)],2)
 => ([],1)
 => ([(0,1)],2)
 => 2
([],3)
 => ([],0)
 => ([],1)
 => 1
([(1,2)],3)
 => ([],1)
 => ([(0,1)],2)
 => 2
([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([],4)
 => ([],0)
 => ([],1)
 => 1
([(2,3)],4)
 => ([],1)
 => ([(0,1)],2)
 => 2
([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(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)
 => ([(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),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
([(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)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => 3
Description
The number of distinct eigenvalues of the distance Laplacian of a connected graph.
Matching statistic: St001093
(load all 3 compositions to match this statistic)
Mapping
Mp00156: Graphs —line graph⟶ Graphs
Mp00203: Graphs —cone⟶ Graphs
St001093: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => ([],0)
 => ([],1)
 => 1
([],2)
 => ([],0)
 => ([],1)
 => 1
([(0,1)],2)
 => ([],1)
 => ([(0,1)],2)
 => 2
([],3)
 => ([],0)
 => ([],1)
 => 1
([(1,2)],3)
 => ([],1)
 => ([(0,1)],2)
 => 2
([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([],4)
 => ([],0)
 => ([],1)
 => 1
([(2,3)],4)
 => ([],1)
 => ([(0,1)],2)
 => 2
([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(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)
 => ([(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),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
([(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)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => 3
Description
The detour number of a graph. This is the number of vertices in a longest induced path in a graph. Note that [1] defines the detour number as the number of edges in a longest induced path, which is unsuitable for the empty graph.
Matching statistic: St001674
(load all 3 compositions to match this statistic)
Mapping
Mp00156: Graphs —line 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)
 => ([],0)
 => ([],1)
 => 1
([],2)
 => ([],0)
 => ([],1)
 => 1
([(0,1)],2)
 => ([],1)
 => ([(0,1)],2)
 => 2
([],3)
 => ([],0)
 => ([],1)
 => 1
([(1,2)],3)
 => ([],1)
 => ([(0,1)],2)
 => 2
([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([],4)
 => ([],0)
 => ([],1)
 => 1
([(2,3)],4)
 => ([],1)
 => ([(0,1)],2)
 => 2
([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(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)
 => ([(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),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
([(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)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => 3
Description
The number of vertices of the largest induced star graph in the graph.
Matching statistic: St001792
Mapping
Mp00147: Graphs —square⟶ Graphs
Mp00203: Graphs —cone⟶ Graphs
St001792: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => ([],1)
 => ([(0,1)],2)
 => 1
([],2)
 => ([],2)
 => ([(0,2),(1,2)],3)
 => 1
([(0,1)],2)
 => ([(0,1)],2)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([],3)
 => ([],3)
 => ([(0,3),(1,3),(2,3)],4)
 => 1
([(1,2)],3)
 => ([(1,2)],3)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([],4)
 => ([],4)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 1
([(2,3)],4)
 => ([(2,3)],4)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,3),(1,3),(2,3)],4)
 => ([(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)
 => 3
([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => 2
([(0,3),(1,2),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
([(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(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)
 => 3
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(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)
 => 3
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(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)
 => 3
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(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)
 => 3
Description
The arboricity of a graph. This is the minimum number of forests that covers all edges of the graph.
Matching statistic: St000097
(load all 3 compositions to match this statistic)
Mapping
Mp00156: Graphs —line graph⟶ Graphs
Mp00111: Graphs —complement⟶ Graphs
St000097: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => ([],0)
 => ([],0)
 => 0 = 1 - 1
([],2)
 => ([],0)
 => ([],0)
 => 0 = 1 - 1
([(0,1)],2)
 => ([],1)
 => ([],1)
 => 1 = 2 - 1
([],3)
 => ([],0)
 => ([],0)
 => 0 = 1 - 1
([(1,2)],3)
 => ([],1)
 => ([],1)
 => 1 = 2 - 1
([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => 1 = 2 - 1
([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => 1 = 2 - 1
([],4)
 => ([],0)
 => ([],0)
 => 0 = 1 - 1
([(2,3)],4)
 => ([],1)
 => ([],1)
 => 1 = 2 - 1
([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => 1 = 2 - 1
([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => 1 = 2 - 1
([(0,3),(1,2)],4)
 => ([],2)
 => ([(0,1)],2)
 => 2 = 3 - 1
([(0,3),(1,2),(2,3)],4)
 => ([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => 2 = 3 - 1
([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => 1 = 2 - 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 2 = 3 - 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2)],4)
 => 2 = 3 - 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,3)],5)
 => 2 = 3 - 1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,5),(1,4),(2,3)],6)
 => 2 = 3 - 1
Description
The order of the largest clique of the graph. A clique in a graph $G$ is a subset $U \subseteq V(G)$ such that any pair of vertices in $U$ are adjacent. I.e. the subgraph induced by $U$ is a complete graph.
Matching statistic: St000098
(load all 3 compositions to match this statistic)
Mapping
Mp00156: Graphs —line graph⟶ Graphs
Mp00111: Graphs —complement⟶ Graphs
St000098: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => ([],0)
 => ([],0)
 => 0 = 1 - 1
([],2)
 => ([],0)
 => ([],0)
 => 0 = 1 - 1
([(0,1)],2)
 => ([],1)
 => ([],1)
 => 1 = 2 - 1
([],3)
 => ([],0)
 => ([],0)
 => 0 = 1 - 1
([(1,2)],3)
 => ([],1)
 => ([],1)
 => 1 = 2 - 1
([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => 1 = 2 - 1
([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => 1 = 2 - 1
([],4)
 => ([],0)
 => ([],0)
 => 0 = 1 - 1
([(2,3)],4)
 => ([],1)
 => ([],1)
 => 1 = 2 - 1
([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => 1 = 2 - 1
([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => 1 = 2 - 1
([(0,3),(1,2)],4)
 => ([],2)
 => ([(0,1)],2)
 => 2 = 3 - 1
([(0,3),(1,2),(2,3)],4)
 => ([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => 2 = 3 - 1
([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => 1 = 2 - 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 2 = 3 - 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2)],4)
 => 2 = 3 - 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,3)],5)
 => 2 = 3 - 1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,5),(1,4),(2,3)],6)
 => 2 = 3 - 1
Description
The chromatic number of a graph. The minimal number of colors needed to color the vertices of the graph such that no two vertices which share an edge have the same color.
Matching statistic: St000259
(load all 16 compositions to match this statistic)
Mapping
Mp00156: Graphs —line graph⟶ Graphs
Mp00203: Graphs —cone⟶ Graphs
St000259: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => ([],0)
 => ([],1)
 => 0 = 1 - 1
([],2)
 => ([],0)
 => ([],1)
 => 0 = 1 - 1
([(0,1)],2)
 => ([],1)
 => ([(0,1)],2)
 => 1 = 2 - 1
([],3)
 => ([],0)
 => ([],1)
 => 0 = 1 - 1
([(1,2)],3)
 => ([],1)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([(0,1),(0,2),(1,2)],3)
 => 1 = 2 - 1
([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1 = 2 - 1
([],4)
 => ([],0)
 => ([],1)
 => 0 = 1 - 1
([(2,3)],4)
 => ([],1)
 => ([(0,1)],2)
 => 1 = 2 - 1
([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1),(0,2),(1,2)],3)
 => 1 = 2 - 1
([(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)
 => 1 = 2 - 1
([(0,3),(1,2)],4)
 => ([],2)
 => ([(0,2),(1,2)],3)
 => 2 = 3 - 1
([(0,3),(1,2),(2,3)],4)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2 = 3 - 1
([(1,2),(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)
 => 1 = 2 - 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2 = 3 - 1
([(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)
 => 2 = 3 - 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2 = 3 - 1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => 2 = 3 - 1
Description
The diameter of a connected graph. This is the greatest distance between any pair of vertices.
The following 132 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St001280The number of parts of an integer partition that are at least two. St001355Number of non-empty prefixes of a binary word that contain equally many 0's and 1's. St001512The minimum rank of a graph. St000013The height of a Dyck path. St000299The number of nonisomorphic vertex-induced subtrees. St000300The number of independent sets of vertices of a graph. St000390The number of runs of ones in a binary word. St000443The number of long tunnels of a Dyck path. St001007Number of simple modules with projective dimension 1 in the Nakayama algebra corresponding to the Dyck path. St001184Number of indecomposable injective modules with grade at least 1 in the corresponding Nakayama algebra. 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. St001267The length of the Lyndon factorization of the binary word. St001642The Prague dimension of a graph. St001814The number of partitions interlacing the given partition. St001884The number of borders of a binary word. St000024The number of double up and double down steps of a Dyck path. St000147The largest part of an integer partition. St000183The side length of the Durfee square of an integer partition. St000291The number of descents of a binary word. St000352The Elizalde-Pak rank of a permutation. St000378The diagonal inversion number of an integer partition. St000479The Ramsey number of a graph. St000875The semilength of the longest Dyck word in the Catalan factorisation of a binary word. St000994The number of cycle peaks and the number of cycle valleys of a permutation. St001089Number of indecomposable projective non-injective modules minus the number of indecomposable projective non-injective modules with dominant dimension equal to the injective dimension 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. St001229The vector space dimension of the first extension group between the Jacobson radical J and J^2. St001244The number of simple modules of projective dimension one that are not 1-regular for the Nakayama algebra associated to a Dyck path. St001269The sum of the minimum of the number of exceedances and deficiencies in each cycle of a permutation. St001413Half the length of the longest even length palindromic prefix of a binary word. St001420Half the length of a longest factor which is its own reverse-complement of a binary word. St001421Half the length of a longest factor which is its own reverse-complement and begins with a one of a binary word. 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). St001874Lusztig's a-function for the symmetric group. St001318The number of vertices of the largest induced subforest with the same number of connected components of a graph. St001321The number of vertices of the largest induced subforest of a graph. St000444The length of the maximal rise of a Dyck path. St000442The maximal area to the right of an up step of a Dyck path. St000829The Ulam distance of a permutation to the identity permutation. St001031The height of the bicoloured Motzkin path associated with the Dyck path. St000010The length of the partition. St000784The maximum of the length and the largest part of the integer partition. St001250The number of parts of a partition that are not congruent 0 modulo 3. St000301The number of facets of the stable set polytope of a graph. St000460The hook length of the last cell along the main diagonal of an integer partition. St000870The product of the hook lengths of the diagonal cells in an integer 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 $eA$. St001201The grade of the simple module $S_0$ in the special CNakayama algebra corresponding to the Dyck path. 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: 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 $eA$. St001360The number of covering relations in Young's lattice below a partition. St001380The number of monomer-dimer tilings of a Ferrers diagram. St001914The size of the orbit of an integer partition in Bulgarian solitaire. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St001291The number of indecomposable summands of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path. St000455The second largest eigenvalue of a graph if it is integral. 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. St001000Number of indecomposable modules with projective dimension equal to the global dimension in the Nakayama algebra corresponding to the Dyck path. St001514The dimension of the top of the Auslander-Reiten translate of the regular modules as a bimodule. St000939The number of characters of the symmetric group whose value on the partition is positive. St001621The number of atoms of a lattice. St001624The breadth of a lattice. St000993The multiplicity of the largest part of an integer partition. St001039The maximal height of a column in the parallelogram polyomino associated with a Dyck path. St001520The number of strict 3-descents. St000260The radius of a connected graph. St000771The largest multiplicity of a distance Laplacian eigenvalue in a connected graph. St000772The multiplicity of the largest distance Laplacian eigenvalue in a connected graph. St001704The size of the largest multi-subset-intersection of the deck of a graph with the deck of another graph. St000454The largest eigenvalue of a graph if it is integral. St000741The Colin de Verdière graph invariant. 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 $eA$. St001645The pebbling number of a connected graph. St000466The Gutman (or modified Schultz) index of a connected graph. St001668The number of points of the poset minus the width of the poset. St000318The number of addable cells of the Ferrers diagram of an integer partition. St000439The position of the first down step of a Dyck path. St000759The smallest missing part in an integer partition. 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 $c_{n-1}$. St001024Maximum of dominant dimensions of the simple modules 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. St001290The first natural number n such that the tensor product of n copies of D(A) is zero for the corresponding Nakayama algebra A. St001505The number of elements generated by the Dyck path as a map in the full transformation monoid. St001526The Loewy length of the Auslander-Reiten translate of the regular module as a bimodule of the Nakayama algebra corresponding to the Dyck path. St001733The number of weak left to right maxima of a Dyck path. St001060The distinguishing index of a graph. St001118The acyclic chromatic index of a 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. St001738The minimal order of a graph which is not an induced subgraph of the given graph. St000464The Schultz index of a connected graph. St000478Another weight of a partition according to Alladi. St000510The number of invariant oriented cycles when acting with a permutation of given cycle type. St001545The second Elser number of a connected graph. St001651The Frankl number of a lattice. St001568The smallest positive integer that does not appear twice in the partition. 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. St000422The energy of a graph, if it is integral. St000937The number of positive values of the symmetric group character corresponding to the partition. St000302The determinant of the distance matrix of a connected graph. St000467The hyper-Wiener index of a connected graph. St001330The hat guessing number of a graph. St001845The number of join irreducibles minus the rank of a lattice. St000420The number of Dyck paths that are weakly above a Dyck path. St000514The number of invariant simple graphs when acting with a permutation of given cycle type. St000515The number of invariant set partitions when acting with a permutation of given cycle type. St000668The least common multiple of the parts of the partition. St000675The number of centered multitunnels of a Dyck path. St000678The number of up steps after the last double rise of a Dyck path. St000707The product of the factorials of the parts. St000708The product of the parts of an integer partition. St000770The major index of an integer partition when read from bottom to top. St000815The number of semistandard Young tableaux of partition weight of given shape. St000933The number of multipartitions of sizes given by an integer partition. St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset. St001500The global dimension of magnitude 1 Nakayama algebras. St001501The dominant dimension of magnitude 1 Nakayama algebras. St001808The box weight or horizontal decoration of a Dyck path. St001816Eigenvalues of the top-to-random operator acting on a simple module. St001626The number of maximal proper sublattices of a lattice. St001247The number of parts of a partition that are not congruent 2 modulo 3. St001249Sum of the odd parts of a partition. St001262The dimension of the maximal parabolic seaweed algebra corresponding to the partition. St001378The product of the cohook lengths of the integer partition. St001564The value of the forgotten symmetric functions when all variables set to 1. St001607The number of coloured graphs such that the multiplicities of colours are given by a partition. St001608The number of coloured rooted trees such that the multiplicities of colours are given by a partition. St001611The number of multiset partitions such that the multiplicities of elements are given by a partition. St001785The number of ways to obtain a partition as the multiset of antidiagonal lengths of the Ferrers diagram of a partition. St001933The largest multiplicity of a part in an integer partition.