Your data matches 54 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000181
(load all 2 compositions to match this statistic)
Mapping
St000181: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => 1
([],2)
 => 2
([(0,1)],2)
 => 1
([],3)
 => 3
([(1,2)],3)
 => 2
([(0,1),(0,2)],3)
 => 1
([(0,2),(2,1)],3)
 => 1
([(0,2),(1,2)],3)
 => 1
([],4)
 => 4
([(2,3)],4)
 => 3
([(1,2),(1,3)],4)
 => 2
([(0,1),(0,2),(0,3)],4)
 => 1
([(0,2),(0,3),(3,1)],4)
 => 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
([(1,2),(2,3)],4)
 => 2
([(0,3),(3,1),(3,2)],4)
 => 1
([(1,3),(2,3)],4)
 => 2
([(0,3),(1,3),(3,2)],4)
 => 1
([(0,3),(1,3),(2,3)],4)
 => 1
([(0,3),(1,2)],4)
 => 2
([(0,3),(1,2),(1,3)],4)
 => 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => 1
([(0,3),(2,1),(3,2)],4)
 => 1
([(0,3),(1,2),(2,3)],4)
 => 1
([],5)
 => 5
([(3,4)],5)
 => 4
([(2,3),(2,4)],5)
 => 3
([(1,2),(1,3),(1,4)],5)
 => 2
([(0,1),(0,2),(0,3),(0,4)],5)
 => 1
([(0,2),(0,3),(0,4),(4,1)],5)
 => 1
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 1
([(1,3),(1,4),(4,2)],5)
 => 2
([(0,3),(0,4),(4,1),(4,2)],5)
 => 1
([(1,2),(1,3),(2,4),(3,4)],5)
 => 2
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
([(0,3),(0,4),(3,2),(4,1)],5)
 => 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => 1
([(2,3),(3,4)],5)
 => 3
([(1,4),(4,2),(4,3)],5)
 => 2
([(0,4),(4,1),(4,2),(4,3)],5)
 => 1
([(2,4),(3,4)],5)
 => 3
([(1,4),(2,4),(4,3)],5)
 => 2
([(0,4),(1,4),(4,2),(4,3)],5)
 => 1
([(1,4),(2,4),(3,4)],5)
 => 2
([(0,4),(1,4),(2,4),(4,3)],5)
 => 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => 1
([(0,4),(1,4),(2,3)],5)
 => 2
([(0,4),(1,3),(2,3),(2,4)],5)
 => 1
Description
The number of connected components of the Hasse diagram for the poset.
Matching statistic: St000286
(load all 16 compositions to match this statistic)
Mapping
Mp00198: Posets —incomparability graph⟶ Graphs
St000286: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => ([],1)
 => 1
([],2)
 => ([(0,1)],2)
 => 2
([(0,1)],2)
 => ([],2)
 => 1
([],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 3
([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 2
([(0,1),(0,2)],3)
 => ([(1,2)],3)
 => 1
([(0,2),(2,1)],3)
 => ([],3)
 => 1
([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => 1
([],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4
([(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 3
([(1,2),(1,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,1),(0,2),(0,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => 1
([(0,2),(0,3),(3,1)],4)
 => ([(1,3),(2,3)],4)
 => 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 1
([(1,2),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => 2
([(0,3),(3,1),(3,2)],4)
 => ([(2,3)],4)
 => 1
([(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,3),(1,3),(3,2)],4)
 => ([(2,3)],4)
 => 1
([(0,3),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => 1
([(0,3),(1,2)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2
([(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2)],4)
 => 1
([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 1
([(0,3),(1,2),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => 1
([],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 5
([(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4
([(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
([(1,2),(1,3),(1,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,1),(0,2),(0,3),(0,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,2),(0,3),(0,4),(4,1)],5)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => 1
([(1,3),(1,4),(4,2)],5)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,3),(0,4),(4,1),(4,2)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(3,4)],5)
 => 1
([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,4),(2,3)],5)
 => 1
([(2,3),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
([(1,4),(4,2),(4,3)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(4,1),(4,2),(4,3)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => 1
([(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
([(1,4),(2,4),(4,3)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,4),(4,2),(4,3)],5)
 => ([(1,4),(2,3)],5)
 => 1
([(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,4),(2,4),(4,3)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,4),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => 2
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 1
Description
The number of connected components of the complement of a graph. The complement of a graph is the graph on the same vertex set with complementary edges.
Matching statistic: St000287
(load all 28 compositions to match this statistic)
Mapping
Mp00074: Posets —to graph⟶ Graphs
St000287: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => ([],1)
 => 1
([],2)
 => ([],2)
 => 2
([(0,1)],2)
 => ([(0,1)],2)
 => 1
([],3)
 => ([],3)
 => 3
([(1,2)],3)
 => ([(1,2)],3)
 => 2
([(0,1),(0,2)],3)
 => ([(0,2),(1,2)],3)
 => 1
([(0,2),(2,1)],3)
 => ([(0,2),(1,2)],3)
 => 1
([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 1
([],4)
 => ([],4)
 => 4
([(2,3)],4)
 => ([(2,3)],4)
 => 3
([(1,2),(1,3)],4)
 => ([(1,3),(2,3)],4)
 => 2
([(0,1),(0,2),(0,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => 1
([(0,2),(0,3),(3,1)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 1
([(1,2),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => 2
([(0,3),(3,1),(3,2)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => 1
([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => 2
([(0,3),(1,3),(3,2)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => 1
([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => 1
([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => 2
([(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 1
([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 1
([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 1
([],5)
 => ([],5)
 => 5
([(3,4)],5)
 => ([(3,4)],5)
 => 4
([(2,3),(2,4)],5)
 => ([(2,4),(3,4)],5)
 => 3
([(1,2),(1,3),(1,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => 2
([(0,1),(0,2),(0,3),(0,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 1
([(0,2),(0,3),(0,4),(4,1)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 1
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 1
([(1,3),(1,4),(4,2)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => 2
([(0,3),(0,4),(4,1),(4,2)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 1
([(1,2),(1,3),(2,4),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => 2
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 1
([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 1
([(2,3),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => 3
([(1,4),(4,2),(4,3)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => 2
([(0,4),(4,1),(4,2),(4,3)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 1
([(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => 3
([(1,4),(2,4),(4,3)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => 2
([(0,4),(1,4),(4,2),(4,3)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 1
([(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => 2
([(0,4),(1,4),(2,4),(4,3)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 1
([(0,4),(1,4),(2,3)],5)
 => ([(0,1),(2,4),(3,4)],5)
 => 2
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 1
Description
The number of connected components of a graph.
Matching statistic: St000010
(load all 2 compositions to match this statistic)
Mapping
Mp00074: Posets —to graph⟶ Graphs
Mp00037: Graphs —to partition of connected components⟶ Integer partitions
St000010: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => ([],1)
 => [1]
 => 1
([],2)
 => ([],2)
 => [1,1]
 => 2
([(0,1)],2)
 => ([(0,1)],2)
 => [2]
 => 1
([],3)
 => ([],3)
 => [1,1,1]
 => 3
([(1,2)],3)
 => ([(1,2)],3)
 => [2,1]
 => 2
([(0,1),(0,2)],3)
 => ([(0,2),(1,2)],3)
 => [3]
 => 1
([(0,2),(2,1)],3)
 => ([(0,2),(1,2)],3)
 => [3]
 => 1
([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => [3]
 => 1
([],4)
 => ([],4)
 => [1,1,1,1]
 => 4
([(2,3)],4)
 => ([(2,3)],4)
 => [2,1,1]
 => 3
([(1,2),(1,3)],4)
 => ([(1,3),(2,3)],4)
 => [3,1]
 => 2
([(0,1),(0,2),(0,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => [4]
 => 1
([(0,2),(0,3),(3,1)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => [4]
 => 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => [4]
 => 1
([(1,2),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => [3,1]
 => 2
([(0,3),(3,1),(3,2)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => [4]
 => 1
([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => [3,1]
 => 2
([(0,3),(1,3),(3,2)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => [4]
 => 1
([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => [4]
 => 1
([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => [2,2]
 => 2
([(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => [4]
 => 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => [4]
 => 1
([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => [4]
 => 1
([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => [4]
 => 1
([],5)
 => ([],5)
 => [1,1,1,1,1]
 => 5
([(3,4)],5)
 => ([(3,4)],5)
 => [2,1,1,1]
 => 4
([(2,3),(2,4)],5)
 => ([(2,4),(3,4)],5)
 => [3,1,1]
 => 3
([(1,2),(1,3),(1,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => [4,1]
 => 2
([(0,1),(0,2),(0,3),(0,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => [5]
 => 1
([(0,2),(0,3),(0,4),(4,1)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => [5]
 => 1
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [5]
 => 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [5]
 => 1
([(1,3),(1,4),(4,2)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => [4,1]
 => 2
([(0,3),(0,4),(4,1),(4,2)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => [5]
 => 1
([(1,2),(1,3),(2,4),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => [4,1]
 => 2
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [5]
 => 1
([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => [5]
 => 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [5]
 => 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [5]
 => 1
([(2,3),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => [3,1,1]
 => 3
([(1,4),(4,2),(4,3)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => [4,1]
 => 2
([(0,4),(4,1),(4,2),(4,3)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => [5]
 => 1
([(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => [3,1,1]
 => 3
([(1,4),(2,4),(4,3)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => [4,1]
 => 2
([(0,4),(1,4),(4,2),(4,3)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => [5]
 => 1
([(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => [4,1]
 => 2
([(0,4),(1,4),(2,4),(4,3)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => [5]
 => 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => [5]
 => 1
([(0,4),(1,4),(2,3)],5)
 => ([(0,1),(2,4),(3,4)],5)
 => [3,2]
 => 2
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => [5]
 => 1
Description
The length of the partition.
Matching statistic: St000273
(load all 4 compositions to match this statistic)
Mapping
Mp00074: Posets —to graph⟶ Graphs
Mp00147: Graphs —square⟶ Graphs
St000273: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => ([],1)
 => ([],1)
 => 1
([],2)
 => ([],2)
 => ([],2)
 => 2
([(0,1)],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 1
([],3)
 => ([],3)
 => ([],3)
 => 3
([(1,2)],3)
 => ([(1,2)],3)
 => ([(1,2)],3)
 => 2
([(0,1),(0,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(0,2),(2,1)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([],4)
 => ([],4)
 => ([],4)
 => 4
([(2,3)],4)
 => ([(2,3)],4)
 => ([(2,3)],4)
 => 3
([(1,2),(1,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => 2
([(0,1),(0,2),(0,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,2),(0,3),(3,1)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(1,2),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => 2
([(0,3),(3,1),(3,2)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => 2
([(0,3),(1,3),(3,2)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => 2
([(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([],5)
 => ([],5)
 => ([],5)
 => 5
([(3,4)],5)
 => ([(3,4)],5)
 => ([(3,4)],5)
 => 4
([(2,3),(2,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => 3
([(1,2),(1,3),(1,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,1),(0,2),(0,3),(0,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,2),(0,3),(0,4),(4,1)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(1,3),(1,4),(4,2)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,3),(0,4),(4,1),(4,2)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(1,2),(1,3),(2,4),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(2,3),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => 3
([(1,4),(4,2),(4,3)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(4,1),(4,2),(4,3)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => 3
([(1,4),(2,4),(4,3)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,4),(4,2),(4,3)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,4),(2,4),(4,3)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,4),(1,4),(2,3)],5)
 => ([(0,1),(2,4),(3,4)],5)
 => ([(0,1),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => 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: St000383
(load all 4 compositions to match this statistic)
Mapping
Mp00074: Posets —to graph⟶ Graphs
Mp00152: Graphs —Laplacian multiplicities⟶ Integer compositions
St000383: Integer compositions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => ([],1)
 => [1] => 1
([],2)
 => ([],2)
 => [2] => 2
([(0,1)],2)
 => ([(0,1)],2)
 => [1,1] => 1
([],3)
 => ([],3)
 => [3] => 3
([(1,2)],3)
 => ([(1,2)],3)
 => [1,2] => 2
([(0,1),(0,2)],3)
 => ([(0,2),(1,2)],3)
 => [1,1,1] => 1
([(0,2),(2,1)],3)
 => ([(0,2),(1,2)],3)
 => [1,1,1] => 1
([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => [1,1,1] => 1
([],4)
 => ([],4)
 => [4] => 4
([(2,3)],4)
 => ([(2,3)],4)
 => [1,3] => 3
([(1,2),(1,3)],4)
 => ([(1,3),(2,3)],4)
 => [1,1,2] => 2
([(0,1),(0,2),(0,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => [1,2,1] => 1
([(0,2),(0,3),(3,1)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => [1,1,1,1] => 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => [1,2,1] => 1
([(1,2),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => [1,1,2] => 2
([(0,3),(3,1),(3,2)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => [1,2,1] => 1
([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => [1,1,2] => 2
([(0,3),(1,3),(3,2)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => [1,2,1] => 1
([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => [1,2,1] => 1
([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => [2,2] => 2
([(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => [1,1,1,1] => 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => [1,2,1] => 1
([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => [1,1,1,1] => 1
([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => [1,1,1,1] => 1
([],5)
 => ([],5)
 => [5] => 5
([(3,4)],5)
 => ([(3,4)],5)
 => [1,4] => 4
([(2,3),(2,4)],5)
 => ([(2,4),(3,4)],5)
 => [1,1,3] => 3
([(1,2),(1,3),(1,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => [1,2,2] => 2
([(0,1),(0,2),(0,3),(0,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => [1,3,1] => 1
([(0,2),(0,3),(0,4),(4,1)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => [1,1,1,1,1] => 1
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [1,1,1,1,1] => 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [1,1,2,1] => 1
([(1,3),(1,4),(4,2)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => [1,1,1,2] => 2
([(0,3),(0,4),(4,1),(4,2)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => [1,1,1,1,1] => 1
([(1,2),(1,3),(2,4),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => [1,2,2] => 2
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [1,1,1,1,1] => 1
([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => [1,1,1,1,1] => 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [1,1,1,1,1] => 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [1,1,2,1] => 1
([(2,3),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => [1,1,3] => 3
([(1,4),(4,2),(4,3)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => [1,2,2] => 2
([(0,4),(4,1),(4,2),(4,3)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => [1,3,1] => 1
([(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => [1,1,3] => 3
([(1,4),(2,4),(4,3)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => [1,2,2] => 2
([(0,4),(1,4),(4,2),(4,3)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => [1,3,1] => 1
([(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => [1,2,2] => 2
([(0,4),(1,4),(2,4),(4,3)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => [1,3,1] => 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => [1,3,1] => 1
([(0,4),(1,4),(2,3)],5)
 => ([(0,1),(2,4),(3,4)],5)
 => [1,1,1,2] => 2
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => [1,1,1,1,1] => 1
Description
The last part of an integer composition.
Matching statistic: St000544
(load all 8 compositions to match this statistic)
Mapping
Mp00074: Posets —to graph⟶ Graphs
Mp00147: Graphs —square⟶ Graphs
St000544: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => ([],1)
 => ([],1)
 => 1
([],2)
 => ([],2)
 => ([],2)
 => 2
([(0,1)],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 1
([],3)
 => ([],3)
 => ([],3)
 => 3
([(1,2)],3)
 => ([(1,2)],3)
 => ([(1,2)],3)
 => 2
([(0,1),(0,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(0,2),(2,1)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([],4)
 => ([],4)
 => ([],4)
 => 4
([(2,3)],4)
 => ([(2,3)],4)
 => ([(2,3)],4)
 => 3
([(1,2),(1,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => 2
([(0,1),(0,2),(0,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,2),(0,3),(3,1)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(1,2),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => 2
([(0,3),(3,1),(3,2)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => 2
([(0,3),(1,3),(3,2)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => 2
([(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([],5)
 => ([],5)
 => ([],5)
 => 5
([(3,4)],5)
 => ([(3,4)],5)
 => ([(3,4)],5)
 => 4
([(2,3),(2,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => 3
([(1,2),(1,3),(1,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,1),(0,2),(0,3),(0,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,2),(0,3),(0,4),(4,1)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(1,3),(1,4),(4,2)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,3),(0,4),(4,1),(4,2)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(1,2),(1,3),(2,4),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(2,3),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => 3
([(1,4),(4,2),(4,3)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(4,1),(4,2),(4,3)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => 3
([(1,4),(2,4),(4,3)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,4),(4,2),(4,3)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,4),(2,4),(4,3)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,4),(1,4),(2,3)],5)
 => ([(0,1),(2,4),(3,4)],5)
 => ([(0,1),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
Description
The cop number of a graph. This is the minimal number of cops needed to catch the robber. The algorithm is from [2].
Matching statistic: St000553
(load all 10 compositions to match this statistic)
Mapping
Mp00074: Posets —to graph⟶ Graphs
Mp00147: Graphs —square⟶ Graphs
St000553: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => ([],1)
 => ([],1)
 => 1
([],2)
 => ([],2)
 => ([],2)
 => 2
([(0,1)],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 1
([],3)
 => ([],3)
 => ([],3)
 => 3
([(1,2)],3)
 => ([(1,2)],3)
 => ([(1,2)],3)
 => 2
([(0,1),(0,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(0,2),(2,1)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([],4)
 => ([],4)
 => ([],4)
 => 4
([(2,3)],4)
 => ([(2,3)],4)
 => ([(2,3)],4)
 => 3
([(1,2),(1,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => 2
([(0,1),(0,2),(0,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,2),(0,3),(3,1)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(1,2),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => 2
([(0,3),(3,1),(3,2)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => 2
([(0,3),(1,3),(3,2)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => 2
([(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([],5)
 => ([],5)
 => ([],5)
 => 5
([(3,4)],5)
 => ([(3,4)],5)
 => ([(3,4)],5)
 => 4
([(2,3),(2,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => 3
([(1,2),(1,3),(1,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,1),(0,2),(0,3),(0,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,2),(0,3),(0,4),(4,1)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(1,3),(1,4),(4,2)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,3),(0,4),(4,1),(4,2)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(1,2),(1,3),(2,4),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(2,3),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => 3
([(1,4),(4,2),(4,3)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(4,1),(4,2),(4,3)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => 3
([(1,4),(2,4),(4,3)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,4),(4,2),(4,3)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,4),(2,4),(4,3)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,4),(1,4),(2,3)],5)
 => ([(0,1),(2,4),(3,4)],5)
 => ([(0,1),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
Description
The number of blocks of a graph. A cut vertex is a vertex whose deletion increases the number of connected components. A block is a maximal connected subgraph which itself has no cut vertices. Two distinct blocks cannot overlap in more than a single cut vertex.
Matching statistic: St000773
(load all 3 compositions to match this statistic)
Mapping
Mp00198: Posets —incomparability graph⟶ Graphs
Mp00203: Graphs —cone⟶ Graphs
St000773: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => ([],1)
 => ([(0,1)],2)
 => 1
([],2)
 => ([(0,1)],2)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
([(0,1)],2)
 => ([],2)
 => ([(0,2),(1,2)],3)
 => 1
([],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 3
([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,1),(0,2)],3)
 => ([(1,2)],3)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,2),(2,1)],3)
 => ([],3)
 => ([(0,3),(1,3),(2,3)],4)
 => 1
([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([],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)
 => 4
([(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)],4)
 => ([(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)
 => 2
([(0,1),(0,2),(0,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,2),(0,3),(3,1)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(1,2),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,3),(3,1),(3,2)],4)
 => ([(2,3)],4)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(1,3),(2,3)],4)
 => ([(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)
 => 2
([(0,3),(1,3),(3,2)],4)
 => ([(2,3)],4)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,3),(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)
 => 1
([(0,3),(1,2)],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
([(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2)],4)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => 1
([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 1
([(0,3),(1,2),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 5
([(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 4
([(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
([(1,2),(1,3),(1,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
([(0,1),(0,2),(0,3),(0,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
([(0,2),(0,3),(0,4),(4,1)],5)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
([(1,3),(1,4),(4,2)],5)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
([(0,3),(0,4),(4,1),(4,2)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
([(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(3,4)],5)
 => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
([(0,3),(0,4),(3,2),(4,1)],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)
 => 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,4),(2,3)],5)
 => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => 1
([(2,3),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
([(1,4),(4,2),(4,3)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
([(0,4),(4,1),(4,2),(4,3)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
([(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
([(1,4),(2,4),(4,3)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
([(0,4),(1,4),(4,2),(4,3)],5)
 => ([(1,4),(2,3)],5)
 => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => 1
([(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
([(0,4),(1,4),(2,4),(4,3)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
([(0,4),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 2
([(0,4),(1,3),(2,3),(2,4)],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)
 => 1
Description
The multiplicity of the largest Laplacian eigenvalue in a graph.
Matching statistic: St000916
(load all 9 compositions to match this statistic)
Mapping
Mp00074: Posets —to graph⟶ Graphs
Mp00147: Graphs —square⟶ Graphs
St000916: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => ([],1)
 => ([],1)
 => 1
([],2)
 => ([],2)
 => ([],2)
 => 2
([(0,1)],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 1
([],3)
 => ([],3)
 => ([],3)
 => 3
([(1,2)],3)
 => ([(1,2)],3)
 => ([(1,2)],3)
 => 2
([(0,1),(0,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(0,2),(2,1)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([],4)
 => ([],4)
 => ([],4)
 => 4
([(2,3)],4)
 => ([(2,3)],4)
 => ([(2,3)],4)
 => 3
([(1,2),(1,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => 2
([(0,1),(0,2),(0,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,2),(0,3),(3,1)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(1,2),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => 2
([(0,3),(3,1),(3,2)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => 2
([(0,3),(1,3),(3,2)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => 2
([(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([],5)
 => ([],5)
 => ([],5)
 => 5
([(3,4)],5)
 => ([(3,4)],5)
 => ([(3,4)],5)
 => 4
([(2,3),(2,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => 3
([(1,2),(1,3),(1,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,1),(0,2),(0,3),(0,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,2),(0,3),(0,4),(4,1)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(1,3),(1,4),(4,2)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,3),(0,4),(4,1),(4,2)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(1,2),(1,3),(2,4),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(2,3),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => 3
([(1,4),(4,2),(4,3)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(4,1),(4,2),(4,3)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => 3
([(1,4),(2,4),(4,3)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,4),(4,2),(4,3)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,4),(2,4),(4,3)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,4),(1,4),(2,3)],5)
 => ([(0,1),(2,4),(3,4)],5)
 => ([(0,1),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
Description
The packing number of a graph. This is the size of a largest subset of vertices of a graph, such that any two distinct vertices in the subset have disjoint closed neighbourhoods, or, equivalently, have distance greater than two.
The following 44 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St001322The size of a minimal independent dominating set in a graph. St001339The irredundance number of a graph. St001363The Euler characteristic of a graph according to Knill. St001829The common independence number of a graph. St000147The largest part of an integer partition. St000288The number of ones in a binary word. St000378The diagonal inversion number of an integer partition. St000382The first part of an integer composition. St000733The row containing the largest entry of a standard tableau. St001184Number of indecomposable injective modules with grade at least 1 in the corresponding Nakayama algebra. St001227The vector space dimension of the first extension group between the socle of the regular module and the Jacobson radical of the corresponding Nakayama algebra. St001316The domatic number of a graph. St001828The Euler characteristic of a graph. St000157The number of descents of a standard tableau. St000319The spin of an integer partition. St000320The dinv adjustment of an integer partition. St000329The number of evenly positioned ascents of the Dyck path, with the initial position equal to 1. St000519The largest length of a factor maximising the subword complexity. St001508The degree of the standard monomial associated to a Dyck path relative to the diagonal boundary. St001553The number of indecomposable summands of the square of the Jacobson radical as a bimodule in the Nakayama algebra corresponding to the Dyck path. St001418Half of the global dimension of the stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001431Half of the Loewy length minus one of a modified stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St000456The monochromatic index of a connected graph. 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. St001934The number of monotone factorisations of genus zero of a permutation of given cycle type. 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. St001175The size of a partition minus the hook length of the base cell. 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. St001570The minimal number of edges to add to make a graph Hamiltonian. St001060The distinguishing index of a graph. St001250The number of parts of a partition that are not congruent 0 modulo 3. St001176The size of a partition minus its first part. St000379The number of Hamiltonian cycles in a graph. St000689The maximal n such that the minimal generator-cogenerator module in the LNakayama algebra of a Dyck path is n-rigid. St000261The edge connectivity of a graph. St000262The vertex connectivity of a graph. St000310The minimal degree of a vertex of a graph. St001330The hat guessing number of a graph. St001604The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on polygons. St000264The girth of a graph, which is not a tree.