- FindStat

Your data matches 13 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)

Matching statistic: St000381

Mapping

Mp00156: Graphs —line graph⟶ Graphs
Mp00324: Graphs —chromatic difference sequence⟶ Integer compositions
St000381: Integer compositions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

([(0,1)],2)
 => ([],1)
 => [1] => 1
([(1,2)],3)
 => ([],1)
 => [1] => 1
([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => [1,1] => 1
([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => [1,1,1] => 1
([(2,3)],4)
 => ([],1)
 => [1] => 1
([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => [1,1] => 1
([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => [1,1,1] => 1
([(0,3),(1,2)],4)
 => ([],2)
 => [2] => 2
([(0,3),(1,2),(2,3)],4)
 => ([(0,2),(1,2)],3)
 => [2,1] => 2
([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => [1,1,1] => 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [2,1,1] => 2
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => [2,2] => 2
([(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)
 => [2,2,1] => 2
([(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)
 => [2,2,2] => 2
([(3,4)],5)
 => ([],1)
 => [1] => 1
([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => [1,1] => 1
([(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => [1,1,1] => 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [1,1,1,1] => 1
([(1,4),(2,3)],5)
 => ([],2)
 => [2] => 2
([(1,4),(2,3),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => [2,1] => 2
([(0,1),(2,4),(3,4)],5)
 => ([(1,2)],3)
 => [2,1] => 2
([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => [1,1,1] => 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => [2,1,1] => 2
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [2,1,1] => 2
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [2,1,1,1] => 2
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => [2,2] => 2
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [2,2,1] => 2
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => [2,2,1] => 2
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => [2,2,1] => 2
([(0,4),(1,3),(1,4),(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)
 => [2,2,1,1] => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => [2,2,2] => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => [2,2,2,1] => 2
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,3),(1,2),(2,3)],4)
 => [2,2] => 2
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => [2,1,1] => 2
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => [2,2,1] => 2
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [2,2,1,1] => 2
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => [2,2,1] => 2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => [2,2,2] => 2
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [2,2,2,1] => 2
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => [2,2,2] => 2
([(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),(2,4),(2,5),(3,4),(3,5)],6)
 => [2,2,2] => 2
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => [2,2,2,1] => 2
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(5,6)],7)
 => [2,2,2,1] => 2
([(4,5)],6)
 => ([],1)
 => [1] => 1
([(3,5),(4,5)],6)
 => ([(0,1)],2)
 => [1,1] => 1
([(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => [1,1,1] => 1
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [1,1,1,1] => 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [1,1,1,1,1] => 1
([(2,5),(3,4)],6)
 => ([],2)
 => [2] => 2
([(2,5),(3,4),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => [2,1] => 2

Description

The largest part of an integer composition.

Matching statistic: St000382

Mapping

Mp00156: Graphs —line graph⟶ Graphs
Mp00324: Graphs —chromatic difference sequence⟶ Integer compositions
St000382: Integer compositions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

([(0,1)],2)
 => ([],1)
 => [1] => 1
([(1,2)],3)
 => ([],1)
 => [1] => 1
([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => [1,1] => 1
([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => [1,1,1] => 1
([(2,3)],4)
 => ([],1)
 => [1] => 1
([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => [1,1] => 1
([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => [1,1,1] => 1
([(0,3),(1,2)],4)
 => ([],2)
 => [2] => 2
([(0,3),(1,2),(2,3)],4)
 => ([(0,2),(1,2)],3)
 => [2,1] => 2
([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => [1,1,1] => 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [2,1,1] => 2
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => [2,2] => 2
([(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)
 => [2,2,1] => 2
([(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)
 => [2,2,2] => 2
([(3,4)],5)
 => ([],1)
 => [1] => 1
([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => [1,1] => 1
([(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => [1,1,1] => 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [1,1,1,1] => 1
([(1,4),(2,3)],5)
 => ([],2)
 => [2] => 2
([(1,4),(2,3),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => [2,1] => 2
([(0,1),(2,4),(3,4)],5)
 => ([(1,2)],3)
 => [2,1] => 2
([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => [1,1,1] => 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => [2,1,1] => 2
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [2,1,1] => 2
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [2,1,1,1] => 2
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => [2,2] => 2
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [2,2,1] => 2
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => [2,2,1] => 2
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => [2,2,1] => 2
([(0,4),(1,3),(1,4),(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)
 => [2,2,1,1] => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => [2,2,2] => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => [2,2,2,1] => 2
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,3),(1,2),(2,3)],4)
 => [2,2] => 2
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => [2,1,1] => 2
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => [2,2,1] => 2
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [2,2,1,1] => 2
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => [2,2,1] => 2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => [2,2,2] => 2
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [2,2,2,1] => 2
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => [2,2,2] => 2
([(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),(2,4),(2,5),(3,4),(3,5)],6)
 => [2,2,2] => 2
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => [2,2,2,1] => 2
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(5,6)],7)
 => [2,2,2,1] => 2
([(4,5)],6)
 => ([],1)
 => [1] => 1
([(3,5),(4,5)],6)
 => ([(0,1)],2)
 => [1,1] => 1
([(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => [1,1,1] => 1
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [1,1,1,1] => 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [1,1,1,1,1] => 1
([(2,5),(3,4)],6)
 => ([],2)
 => [2] => 2
([(2,5),(3,4),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => [2,1] => 2

Description

The first part of an integer composition.

Matching statistic: St000387
(load all 6 compositions to match this statistic)

Mapping

St000387: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

([(0,1)],2)
 => 1
([(1,2)],3)
 => 1
([(0,2),(1,2)],3)
 => 1
([(0,1),(0,2),(1,2)],3)
 => 1
([(2,3)],4)
 => 1
([(1,3),(2,3)],4)
 => 1
([(0,3),(1,3),(2,3)],4)
 => 1
([(0,3),(1,2)],4)
 => 2
([(0,3),(1,2),(2,3)],4)
 => 2
([(1,2),(1,3),(2,3)],4)
 => 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,2),(0,3),(1,2),(1,3)],4)
 => 2
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(3,4)],5)
 => 1
([(2,4),(3,4)],5)
 => 1
([(1,4),(2,4),(3,4)],5)
 => 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => 1
([(1,4),(2,3)],5)
 => 2
([(1,4),(2,3),(3,4)],5)
 => 2
([(0,1),(2,4),(3,4)],5)
 => 2
([(2,3),(2,4),(3,4)],5)
 => 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => 2
([(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(1,3),(1,4),(2,3),(2,4)],5)
 => 2
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 2
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,3),(2,3),(2,4)],5)
 => 2
([(0,1),(2,3),(2,4),(3,4)],5)
 => 2
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => 2
([(4,5)],6)
 => 1
([(3,5),(4,5)],6)
 => 1
([(2,5),(3,5),(4,5)],6)
 => 1
([(1,5),(2,5),(3,5),(4,5)],6)
 => 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 1
([(2,5),(3,4)],6)
 => 2
([(2,5),(3,4),(4,5)],6)
 => 2
([(0,5),(0,6),(1,2),(1,3),(2,3),(4,5),(4,6)],7)
 => ? = 3

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 3 compositions to match this statistic)

Mapping

Mp00156: Graphs —line graph⟶ Graphs
St000093: Graphs ⟶ ℤResult quality: 88% ●values known / values provided: 88%●distinct values known / distinct values provided: 100%

Values

([(0,1)],2)
 => ([],1)
 => 1
([(1,2)],3)
 => ([],1)
 => 1
([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 1
([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(2,3)],4)
 => ([],1)
 => 1
([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 1
([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(0,3),(1,2)],4)
 => ([],2)
 => 2
([(0,3),(1,2),(2,3)],4)
 => ([(0,2),(1,2)],3)
 => 2
([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2
([(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
([(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
([(3,4)],5)
 => ([],1)
 => 1
([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 1
([(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(1,4),(2,3)],5)
 => ([],2)
 => 2
([(1,4),(2,3),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => 2
([(0,1),(2,4),(3,4)],5)
 => ([(1,2)],3)
 => 2
([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,3),(1,4),(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)
 => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => 2
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,3),(1,2),(2,3)],4)
 => 2
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => 2
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 2
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => 2
([(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),(2,4),(2,5),(3,4),(3,5)],6)
 => 2
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => 2
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(5,6)],7)
 => 2
([(4,5)],6)
 => ([],1)
 => 1
([(3,5),(4,5)],6)
 => ([(0,1)],2)
 => 1
([(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(2,5),(3,4)],6)
 => ([],2)
 => 2
([(2,5),(3,4),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => 2
([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,1),(0,6),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,3),(0,4),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(5,6)],7)
 => ? = 2
([(0,6),(1,6),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,4),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3
([(0,6),(1,6),(2,5),(3,4),(3,6),(4,5),(5,6)],7)
 => ([(0,4),(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 3
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 3
([(0,6),(1,6),(2,3),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3
([(0,6),(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3
([(0,5),(1,6),(2,3),(2,4),(3,6),(4,6),(5,6)],7)
 => ([(0,6),(1,2),(1,5),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3
([(0,5),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6)],7)
 => ([(0,2),(1,5),(1,6),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3
([(0,6),(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3
([(0,6),(1,5),(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5),(5,6)],7)
 => ([(0,4),(0,5),(1,2),(1,3),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2
([(0,6),(1,5),(2,3),(2,5),(3,6),(4,5),(4,6)],7)
 => ([(0,4),(0,6),(1,3),(1,5),(2,5),(2,6),(3,4),(3,5),(4,6)],7)
 => ? = 3
([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7)
 => ([(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,4),(3,6),(4,5)],7)
 => ? = 3
([(0,6),(1,6),(2,3),(2,5),(3,5),(4,5),(4,6)],7)
 => ([(0,4),(0,5),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5)],7)
 => ? = 3
([(0,6),(1,2),(1,3),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(0,1),(0,3),(1,2),(2,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3
([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6),(5,6)],7)
 => ([(0,1),(0,5),(1,4),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 3
([(0,4),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
 => ? = 3
([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7)
 => ([(0,3),(1,2),(1,5),(2,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3
([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(5,6)],7)
 => ([(0,1),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 3
([(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(5,6)],7)
 => ([(0,2),(1,5),(1,6),(2,4),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 3
([(0,6),(1,6),(2,3),(2,4),(3,5),(4,5),(5,6)],7)
 => ([(0,1),(0,6),(1,6),(2,3),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => ? = 3
([(0,4),(1,4),(2,5),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,5),(1,5),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3
([(0,5),(1,4),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,6),(1,5),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3
([(0,6),(1,4),(2,3),(2,6),(3,5),(4,5),(5,6)],7)
 => ([(0,5),(1,3),(1,4),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 3
([(0,4),(1,3),(2,5),(2,6),(3,5),(4,6),(5,6)],7)
 => ([(0,5),(1,4),(2,3),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 3
([(0,5),(1,2),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,6),(1,2),(1,3),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => ? = 3
([(0,6),(1,4),(2,3),(2,5),(3,5),(4,6),(5,6)],7)
 => ([(0,5),(1,3),(1,4),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ? = 3
([(0,5),(1,4),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => ? = 3
([(0,6),(1,2),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3
([(0,5),(0,6),(1,2),(1,3),(2,3),(4,5),(4,6)],7)
 => ([(0,5),(0,6),(1,2),(1,3),(2,3),(4,5),(4,6)],7)
 => ? = 3

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: St000097
(load all 3 compositions to match this statistic)

Mapping

Mp00156: Graphs —line graph⟶ Graphs
Mp00111: Graphs —complement⟶ Graphs
St000097: Graphs ⟶ ℤResult quality: 88% ●values known / values provided: 88%●distinct values known / distinct values provided: 100%

Values

([(0,1)],2)
 => ([],1)
 => ([],1)
 => 1
([(1,2)],3)
 => ([],1)
 => ([],1)
 => 1
([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => 1
([(2,3)],4)
 => ([],1)
 => ([],1)
 => 1
([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => 1
([(0,3),(1,2)],4)
 => ([],2)
 => ([(0,1)],2)
 => 2
([(0,3),(1,2),(2,3)],4)
 => ([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => 2
([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => 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
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2)],4)
 => 2
([(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
([(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
([(3,4)],5)
 => ([],1)
 => ([],1)
 => 1
([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => 1
([(1,4),(2,3)],5)
 => ([],2)
 => ([(0,1)],2)
 => 2
([(1,4),(2,3),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => 2
([(0,1),(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 2
([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => 2
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 2
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => 2
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2)],4)
 => 2
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 2
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,3)],5)
 => 2
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => 2
([(0,4),(1,3),(1,4),(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)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],7)
 => 2
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 2
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => 2
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6),(5,6)],7)
 => 2
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => 2
([(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),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,5),(1,4),(2,3)],6)
 => 2
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(5,6)],7)
 => ([(0,3),(0,6),(1,2),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => 2
([(4,5)],6)
 => ([],1)
 => ([],1)
 => 1
([(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => 1
([(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => 1
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => 1
([(2,5),(3,4)],6)
 => ([],2)
 => ([(0,1)],2)
 => 2
([(2,5),(3,4),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => 2
([(0,6),(1,6),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,4),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3
([(0,6),(1,6),(2,5),(3,4),(3,6),(4,5),(5,6)],7)
 => ([(0,4),(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(5,6)],7)
 => ? = 3
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ? = 3
([(0,6),(1,6),(2,3),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5)],7)
 => ? = 3
([(0,6),(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3
([(0,5),(1,6),(2,3),(2,4),(3,6),(4,6),(5,6)],7)
 => ([(0,6),(1,2),(1,5),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 3
([(0,5),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6)],7)
 => ([(0,2),(1,5),(1,6),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(0,6),(1,4),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)
 => ? = 3
([(0,6),(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,5),(1,6),(2,3),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3
([(0,6),(1,5),(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 3
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5),(5,6)],7)
 => ([(0,4),(0,5),(1,2),(1,3),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
 => ? = 2
([(0,6),(1,5),(2,3),(2,5),(3,6),(4,5),(4,6)],7)
 => ([(0,4),(0,6),(1,3),(1,5),(2,5),(2,6),(3,4),(3,5),(4,6)],7)
 => ([(0,1),(0,3),(0,5),(1,2),(1,4),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3
([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7)
 => ([(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,4),(3,6),(4,5)],7)
 => ([(0,2),(0,4),(0,6),(1,2),(1,3),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3
([(0,6),(1,6),(2,3),(2,5),(3,5),(4,5),(4,6)],7)
 => ([(0,4),(0,5),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5)],7)
 => ([(0,1),(0,2),(0,6),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 3
([(0,6),(1,2),(1,3),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(0,1),(0,3),(1,2),(2,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(4,6)],7)
 => ? = 3
([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6),(5,6)],7)
 => ([(0,1),(0,5),(1,4),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
 => ? = 3
([(0,4),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(0,3),(0,6),(1,2),(1,5),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => ? = 3
([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7)
 => ([(0,3),(1,2),(1,5),(2,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ? = 3
([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(5,6)],7)
 => ([(0,1),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ? = 3
([(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(5,6)],7)
 => ([(0,2),(1,5),(1,6),(2,4),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
 => ? = 3
([(0,6),(1,6),(2,3),(2,4),(3,5),(4,5),(5,6)],7)
 => ([(0,1),(0,6),(1,6),(2,3),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => ? = 3
([(0,4),(1,4),(2,5),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,5),(1,5),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,3),(1,4),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ? = 3
([(0,5),(1,4),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,6),(1,5),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => ? = 3
([(0,6),(1,4),(2,3),(2,6),(3,5),(4,5),(5,6)],7)
 => ([(0,5),(1,3),(1,4),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,2),(1,3),(1,6),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3
([(0,4),(1,3),(2,5),(2,6),(3,5),(4,6),(5,6)],7)
 => ([(0,5),(1,4),(2,3),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3
([(0,5),(1,2),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,6),(1,2),(1,3),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => ([(0,3),(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3
([(0,6),(1,4),(2,3),(2,5),(3,5),(4,6),(5,6)],7)
 => ([(0,5),(1,3),(1,4),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,2),(1,3),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3
([(0,5),(1,4),(1,5),(2,3),(2,6),(3,6),(4,6)],7)
 => ([(0,3),(1,3),(1,4),(2,5),(2,6),(4,5),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(0,6),(1,3),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ? = 3
([(0,5),(1,4),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => ? = 3
([(0,6),(1,2),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
 => ? = 3
([(0,5),(0,6),(1,2),(1,4),(2,3),(3,5),(4,6)],7)
 => ([(0,5),(0,6),(1,2),(1,4),(2,3),(3,5),(4,6)],7)
 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(4,6)],7)
 => ? = 3
([(0,5),(0,6),(1,2),(1,3),(2,3),(4,5),(4,6)],7)
 => ([(0,5),(0,6),(1,2),(1,3),(2,3),(4,5),(4,6)],7)
 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
 => ? = 3

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: St001337
(load all 3 compositions to match this statistic)

Mapping

Mp00117: Graphs —Ore closure⟶ Graphs
Mp00156: Graphs —line graph⟶ Graphs
St001337: Graphs ⟶ ℤResult quality: 85% ●values known / values provided: 85%●distinct values known / distinct values provided: 100%

Values

([(0,1)],2)
 => ([(0,1)],2)
 => ([],1)
 => 1
([(1,2)],3)
 => ([(1,2)],3)
 => ([],1)
 => 1
([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 1
([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(2,3)],4)
 => ([(2,3)],4)
 => ([],1)
 => 1
([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 1
([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => ([],2)
 => 2
([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,2),(1,2)],3)
 => 2
([(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(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
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 2
([(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)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 2
([(3,4)],5)
 => ([(3,4)],5)
 => ([],1)
 => 1
([(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 1
([(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 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),(1,2),(1,3),(2,3)],4)
 => 1
([(1,4),(2,3)],5)
 => ([(1,4),(2,3)],5)
 => ([],2)
 => 2
([(1,4),(2,3),(3,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => 2
([(0,1),(2,4),(3,4)],5)
 => ([(0,1),(2,4),(3,4)],5)
 => ([(1,2)],3)
 => 2
([(2,3),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(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),(2,4),(2,5),(3,4),(3,5)],6)
 => 2
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(1,4),(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)
 => 2
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(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),(2,4),(2,5),(3,4),(3,5)],6)
 => 2
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(1,4),(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)
 => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ? = 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ? = 2
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,3),(1,2),(2,3)],4)
 => 2
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => 2
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 2
([(0,1),(0,4),(1,3),(2,3),(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)
 => ([(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(1,3),(1,6),(1,7),(1,8),(1,9),(2,3),(2,4),(2,5),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(4,9),(5,6),(5,8),(6,7),(6,8),(7,9),(8,9)],10)
 => ? = 2
([(0,3),(0,4),(1,2),(1,4),(2,3),(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)
 => ([(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(1,3),(1,6),(1,7),(1,8),(1,9),(2,3),(2,4),(2,5),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(4,9),(5,6),(5,8),(6,7),(6,8),(7,9),(8,9)],10)
 => ? = 2
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => 2
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(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),(2,4),(2,5),(3,4),(3,5)],6)
 => 2
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => 2
([(0,3),(0,4),(1,2),(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)
 => ([(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(1,3),(1,6),(1,7),(1,8),(1,9),(2,3),(2,4),(2,5),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(4,9),(5,6),(5,8),(6,7),(6,8),(7,9),(8,9)],10)
 => ? = 2
([(4,5)],6)
 => ([(4,5)],6)
 => ([],1)
 => 1
([(3,5),(4,5)],6)
 => ([(3,5),(4,5)],6)
 => ([(0,1)],2)
 => 1
([(2,5),(3,5),(4,5)],6)
 => ([(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(2,5),(3,4)],6)
 => ([(2,5),(3,4)],6)
 => ([],2)
 => 2
([(2,5),(3,4),(4,5)],6)
 => ([(2,5),(3,4),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => 2
([(1,2),(3,5),(4,5)],6)
 => ([(1,2),(3,5),(4,5)],6)
 => ([(1,2)],3)
 => 2
([(3,4),(3,5),(4,5)],6)
 => ([(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(2,5),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => 2
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ? = 2
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,6),(0,7),(1,2),(1,5),(1,7),(2,4),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ? = 2
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(1,3),(1,6),(1,7),(1,8),(1,9),(2,3),(2,4),(2,5),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(4,9),(5,6),(5,8),(6,7),(6,8),(7,9),(8,9)],10)
 => ? = 2
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(0,5),(0,7),(1,2),(1,4),(1,6),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 3
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(1,3),(1,6),(1,7),(1,8),(1,9),(2,3),(2,4),(2,5),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(4,9),(5,6),(5,8),(6,7),(6,8),(7,9),(8,9)],10)
 => ? = 2
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(0,6),(1,2),(1,4),(1,7),(2,3),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 3
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,6),(0,7),(1,2),(1,5),(1,7),(2,5),(2,6),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(0,6),(0,7),(0,8),(1,3),(1,4),(1,7),(1,8),(1,9),(2,3),(2,4),(2,5),(2,6),(2,9),(3,5),(3,6),(3,9),(4,7),(4,8),(4,9),(5,6),(5,8),(5,9),(6,7),(6,9),(7,8),(7,9),(8,9)],10)
 => ? = 3
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(0,6),(1,2),(1,4),(1,6),(1,7),(2,3),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 3
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(1,3),(1,6),(1,7),(1,8),(1,9),(2,3),(2,4),(2,5),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(4,9),(5,6),(5,8),(6,7),(6,8),(7,9),(8,9)],10)
 => ? = 2
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,7),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 3
([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,6),(0,7),(0,8),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,8),(3,6),(3,7),(3,8),(4,5),(4,7),(4,8),(5,6),(5,8),(6,7),(6,8),(7,8)],9)
 => ? = 3
([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2
([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,6),(0,7),(1,5),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ? = 2
([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,6),(0,7),(1,2),(1,5),(1,7),(2,4),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(0,7),(1,2),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ? = 2
([(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(1,3),(1,6),(1,7),(1,8),(1,9),(2,3),(2,4),(2,5),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(4,9),(5,6),(5,8),(6,7),(6,8),(7,9),(8,9)],10)
 => ? = 2
([(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,2),(0,5),(0,7),(1,2),(1,4),(1,6),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 3
([(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(1,3),(1,6),(1,7),(1,8),(1,9),(2,3),(2,4),(2,5),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(4,9),(5,6),(5,8),(6,7),(6,8),(7,9),(8,9)],10)
 => ? = 2
([(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,2),(1,4),(1,7),(2,3),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 3
([(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,6),(0,7),(1,2),(1,5),(1,7),(2,5),(2,6),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2
([(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(0,7),(0,8),(1,3),(1,4),(1,7),(1,8),(1,9),(2,3),(2,4),(2,5),(2,6),(2,9),(3,5),(3,6),(3,9),(4,7),(4,8),(4,9),(5,6),(5,8),(5,9),(6,7),(6,9),(7,8),(7,9),(8,9)],10)
 => ? = 3
([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,4),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
 => ? = 3
([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,2),(1,4),(1,6),(1,7),(2,3),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 3
([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(1,3),(1,6),(1,7),(1,8),(1,9),(2,3),(2,4),(2,5),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(4,9),(5,6),(5,8),(6,7),(6,8),(7,9),(8,9)],10)
 => ? = 2
([(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,7),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 3
([(1,6),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,3),(0,6),(0,7),(0,8),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,8),(3,6),(3,7),(3,8),(4,5),(4,7),(4,8),(5,6),(5,8),(6,7),(6,8),(7,8)],9)
 => ? = 3
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7)
 => ([(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
 => ? = 3
([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(5,6)],7)
 => ([(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
 => ? = 3
([(0,1),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 3
([(0,1),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(5,6),(5,7),(6,7)],8)
 => ? = 3
([(0,5),(0,6),(1,2),(1,3),(2,3),(4,5),(4,6)],7)
 => ([(0,1),(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,2),(3,5),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8)],9)
 => ? = 3

Description

The upper domination number of a graph. This is the maximum cardinality of a minimal dominating set of

$G$ . The smallest graph with different upper irredundance number and upper domination number has eight vertices. It is obtained from the disjoint union of two copies of

$K_4$ by joining three of the four vertices of the first with three of the four vertices of the second. For bipartite graphs the two parameters always coincide [1].

Matching statistic: St001338
(load all 3 compositions to match this statistic)

Mapping

Mp00117: Graphs —Ore closure⟶ Graphs
Mp00156: Graphs —line graph⟶ Graphs
St001338: Graphs ⟶ ℤResult quality: 85% ●values known / values provided: 85%●distinct values known / distinct values provided: 100%

Values

([(0,1)],2)
 => ([(0,1)],2)
 => ([],1)
 => 1
([(1,2)],3)
 => ([(1,2)],3)
 => ([],1)
 => 1
([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 1
([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(2,3)],4)
 => ([(2,3)],4)
 => ([],1)
 => 1
([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 1
([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => ([],2)
 => 2
([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,2),(1,2)],3)
 => 2
([(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(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
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 2
([(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)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 2
([(3,4)],5)
 => ([(3,4)],5)
 => ([],1)
 => 1
([(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 1
([(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 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),(1,2),(1,3),(2,3)],4)
 => 1
([(1,4),(2,3)],5)
 => ([(1,4),(2,3)],5)
 => ([],2)
 => 2
([(1,4),(2,3),(3,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => 2
([(0,1),(2,4),(3,4)],5)
 => ([(0,1),(2,4),(3,4)],5)
 => ([(1,2)],3)
 => 2
([(2,3),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(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),(2,4),(2,5),(3,4),(3,5)],6)
 => 2
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(1,4),(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)
 => 2
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(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),(2,4),(2,5),(3,4),(3,5)],6)
 => 2
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(1,4),(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)
 => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ? = 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ? = 2
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,3),(1,2),(2,3)],4)
 => 2
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => 2
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 2
([(0,1),(0,4),(1,3),(2,3),(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)
 => ([(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(1,3),(1,6),(1,7),(1,8),(1,9),(2,3),(2,4),(2,5),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(4,9),(5,6),(5,8),(6,7),(6,8),(7,9),(8,9)],10)
 => ? = 2
([(0,3),(0,4),(1,2),(1,4),(2,3),(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)
 => ([(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(1,3),(1,6),(1,7),(1,8),(1,9),(2,3),(2,4),(2,5),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(4,9),(5,6),(5,8),(6,7),(6,8),(7,9),(8,9)],10)
 => ? = 2
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => 2
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(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),(2,4),(2,5),(3,4),(3,5)],6)
 => 2
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => 2
([(0,3),(0,4),(1,2),(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)
 => ([(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(1,3),(1,6),(1,7),(1,8),(1,9),(2,3),(2,4),(2,5),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(4,9),(5,6),(5,8),(6,7),(6,8),(7,9),(8,9)],10)
 => ? = 2
([(4,5)],6)
 => ([(4,5)],6)
 => ([],1)
 => 1
([(3,5),(4,5)],6)
 => ([(3,5),(4,5)],6)
 => ([(0,1)],2)
 => 1
([(2,5),(3,5),(4,5)],6)
 => ([(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(2,5),(3,4)],6)
 => ([(2,5),(3,4)],6)
 => ([],2)
 => 2
([(2,5),(3,4),(4,5)],6)
 => ([(2,5),(3,4),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => 2
([(1,2),(3,5),(4,5)],6)
 => ([(1,2),(3,5),(4,5)],6)
 => ([(1,2)],3)
 => 2
([(3,4),(3,5),(4,5)],6)
 => ([(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(2,5),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => 2
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ? = 2
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,6),(0,7),(1,2),(1,5),(1,7),(2,4),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ? = 2
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(1,3),(1,6),(1,7),(1,8),(1,9),(2,3),(2,4),(2,5),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(4,9),(5,6),(5,8),(6,7),(6,8),(7,9),(8,9)],10)
 => ? = 2
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(0,5),(0,7),(1,2),(1,4),(1,6),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 3
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(1,3),(1,6),(1,7),(1,8),(1,9),(2,3),(2,4),(2,5),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(4,9),(5,6),(5,8),(6,7),(6,8),(7,9),(8,9)],10)
 => ? = 2
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(0,6),(1,2),(1,4),(1,7),(2,3),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 3
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,6),(0,7),(1,2),(1,5),(1,7),(2,5),(2,6),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(0,6),(0,7),(0,8),(1,3),(1,4),(1,7),(1,8),(1,9),(2,3),(2,4),(2,5),(2,6),(2,9),(3,5),(3,6),(3,9),(4,7),(4,8),(4,9),(5,6),(5,8),(5,9),(6,7),(6,9),(7,8),(7,9),(8,9)],10)
 => ? = 3
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(0,6),(1,2),(1,4),(1,6),(1,7),(2,3),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 3
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(1,3),(1,6),(1,7),(1,8),(1,9),(2,3),(2,4),(2,5),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(4,9),(5,6),(5,8),(6,7),(6,8),(7,9),(8,9)],10)
 => ? = 2
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,7),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 3
([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,6),(0,7),(0,8),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,8),(3,6),(3,7),(3,8),(4,5),(4,7),(4,8),(5,6),(5,8),(6,7),(6,8),(7,8)],9)
 => ? = 3
([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2
([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,6),(0,7),(1,5),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ? = 2
([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,6),(0,7),(1,2),(1,5),(1,7),(2,4),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(0,7),(1,2),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ? = 2
([(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(1,3),(1,6),(1,7),(1,8),(1,9),(2,3),(2,4),(2,5),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(4,9),(5,6),(5,8),(6,7),(6,8),(7,9),(8,9)],10)
 => ? = 2
([(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,2),(0,5),(0,7),(1,2),(1,4),(1,6),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 3
([(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(1,3),(1,6),(1,7),(1,8),(1,9),(2,3),(2,4),(2,5),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(4,9),(5,6),(5,8),(6,7),(6,8),(7,9),(8,9)],10)
 => ? = 2
([(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,2),(1,4),(1,7),(2,3),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 3
([(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,6),(0,7),(1,2),(1,5),(1,7),(2,5),(2,6),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2
([(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(0,7),(0,8),(1,3),(1,4),(1,7),(1,8),(1,9),(2,3),(2,4),(2,5),(2,6),(2,9),(3,5),(3,6),(3,9),(4,7),(4,8),(4,9),(5,6),(5,8),(5,9),(6,7),(6,9),(7,8),(7,9),(8,9)],10)
 => ? = 3
([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,4),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
 => ? = 3
([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,2),(1,4),(1,6),(1,7),(2,3),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 3
([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(1,3),(1,6),(1,7),(1,8),(1,9),(2,3),(2,4),(2,5),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(4,9),(5,6),(5,8),(6,7),(6,8),(7,9),(8,9)],10)
 => ? = 2
([(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,7),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 3
([(1,6),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,3),(0,6),(0,7),(0,8),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,8),(3,6),(3,7),(3,8),(4,5),(4,7),(4,8),(5,6),(5,8),(6,7),(6,8),(7,8)],9)
 => ? = 3
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7)
 => ([(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
 => ? = 3
([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(5,6)],7)
 => ([(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
 => ? = 3
([(0,1),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 3
([(0,1),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(5,6),(5,7),(6,7)],8)
 => ? = 3
([(0,5),(0,6),(1,2),(1,3),(2,3),(4,5),(4,6)],7)
 => ([(0,1),(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,2),(3,5),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8)],9)
 => ? = 3

Description

The upper irredundance number of a graph. A set

$S$ of vertices is irredundant, if there is no vertex in

$S$ , whose closed neighbourhood is contained in the union of the closed neighbourhoods of the other vertices of

$S$ . The upper irredundance number is the largest size of a maximal irredundant set. The smallest graph with different upper irredundance number and upper domination number [[St001337]] has eight vertices. It is obtained from the disjoint union of two copies of

$K_4$ by joining three of the four vertices of the first with three of the four vertices of the second. For bipartite graphs the two parameters always coincide [2].

Matching statistic: St001316

Mapping

Mp00156: Graphs —line graph⟶ Graphs
Mp00111: Graphs —complement⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
St001316: Graphs ⟶ ℤResult quality: 65% ●values known / values provided: 65%●distinct values known / distinct values provided: 100%

Values

([(0,1)],2)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,2)],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ([],1)
 => 1
([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ([],1)
 => 1
([(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ([],1)
 => 1
([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ([],1)
 => 1
([(0,3),(1,2)],4)
 => ([],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 2
([(0,3),(1,2),(2,3)],4)
 => ([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => ([(0,1)],2)
 => 2
([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ([],1)
 => 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ([(0,1)],2)
 => 2
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2)],4)
 => ([(0,1)],2)
 => 2
([(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)
 => ([(0,1)],2)
 => 2
([(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)
 => ([(0,1)],2)
 => 2
([(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ([],1)
 => 1
([(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ([],1)
 => 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ([],1)
 => 1
([(1,4),(2,3)],5)
 => ([],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 2
([(1,4),(2,3),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => ([(0,1)],2)
 => 2
([(0,1),(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 2
([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ([],1)
 => 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 2
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ([(0,1)],2)
 => 2
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2)],4)
 => ([(0,1)],2)
 => 2
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => 2
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,3)],5)
 => ([(0,1)],2)
 => 2
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(0,4),(1,3),(1,4),(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)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,1)],2)
 => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => ([(0,1)],2)
 => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],7)
 => ?
 => ? = 2
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,1)],2)
 => 2
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 2
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,1)],2)
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6),(5,6)],7)
 => ?
 => ? = 2
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => 2
([(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),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,5),(1,4),(2,3)],6)
 => ([(0,1)],2)
 => 2
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ?
 => ? = 2
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(5,6)],7)
 => ([(0,3),(0,6),(1,2),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => ?
 => ? = 2
([(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ([],1)
 => 1
([(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ([],1)
 => 1
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ([],1)
 => 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ([],1)
 => 1
([(2,5),(3,4)],6)
 => ([],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 2
([(2,5),(3,4),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => ([(0,1)],2)
 => 2
([(1,2),(3,5),(4,5)],6)
 => ([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 2
([(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ([],1)
 => 1
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 2
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 2
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => ?
 => ? = 2
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(0,6),(1,2),(1,5),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6)],7)
 => ?
 => ? = 2
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],7)
 => ?
 => ? = 2
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,4),(1,6),(2,3),(2,6),(3,5),(4,5),(5,6)],7)
 => ?
 => ? = 2
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 3
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,5),(1,4),(1,5),(1,6),(2,3),(2,4),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,4),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6)],7)
 => ?
 => ? = 3
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,4),(2,3),(2,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 3
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6),(5,6)],7)
 => ?
 => ? = 2
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(1,4),(1,5),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ?
 => ? = 3
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
 => ?
 => ? = 3
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,5),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
 => ?
 => ? = 3
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)
 => ?
 => ? = 2
([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ?
 => ? = 2
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(4,5)],7)
 => ([(0,1),(0,4),(0,5),(1,2),(1,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ?
 => ? = 3
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(4,5),(5,6)],7)
 => ([(0,4),(0,5),(1,2),(1,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ?
 => ? = 3
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(5,6)],7)
 => ([(0,3),(0,6),(1,2),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => ?
 => ? = 2
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(4,5),(5,6)],7)
 => ?
 => ? = 3
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(0,6),(1,2),(1,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,4),(1,5),(2,3),(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => ?
 => ? = 3
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => ?
 => ? = 3
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(5,6)],7)
 => ([(0,3),(0,6),(1,2),(1,6),(2,5),(3,5),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 3
([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,4),(0,6),(1,2),(1,3),(1,5),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(1,3),(1,6),(2,3),(2,5),(2,6),(3,4),(4,6),(5,6)],7)
 => ?
 => ? = 3
([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(1,2),(1,4),(1,6),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(0,6),(1,3),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ?
 => ? = 3
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(4,5),(5,6)],7)
 => ?
 => ? = 3
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
 => ?
 => ? = 3
([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(2,6),(3,6),(4,6),(5,6)],7)
 => ?
 => ? = 2
([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,1),(0,6),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ?
 => ? = 2
([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => ?
 => ? = 2
([(0,6),(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ?
 => ? = 2
([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,1),(0,2),(0,6),(1,2),(1,5),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6)],7)
 => ?
 => ? = 2
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,3),(0,4),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(5,6)],7)
 => ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
 => ?
 => ? = 2
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],7)
 => ?
 => ? = 2
([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,4),(1,6),(2,3),(2,6),(3,5),(4,5),(5,6)],7)
 => ?
 => ? = 2
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)
 => ?
 => ? = 2
([(0,6),(1,6),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,4),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 3
([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 3
([(0,6),(1,6),(2,5),(3,4),(3,6),(4,5),(5,6)],7)
 => ([(0,4),(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(5,6)],7)
 => ?
 => ? = 3
([(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,3),(0,5),(1,4),(1,5),(1,6),(2,3),(2,4),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,4),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6)],7)
 => ?
 => ? = 3
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ?
 => ? = 3
([(0,6),(1,6),(2,3),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5)],7)
 => ?
 => ? = 3
([(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,4),(2,3),(2,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 3
([(0,6),(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 3
([(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6),(5,6)],7)
 => ?
 => ? = 2
([(0,5),(1,6),(2,3),(2,4),(3,6),(4,6),(5,6)],7)
 => ([(0,6),(1,2),(1,5),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ?
 => ? = 3
([(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(1,4),(1,5),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ?
 => ? = 3
([(0,5),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6)],7)
 => ([(0,2),(1,5),(1,6),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(0,6),(1,4),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)
 => ?
 => ? = 3
([(1,4),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(1,2),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
 => ?
 => ? = 3

Description

The domatic number of a graph. This is the maximal size of a partition of the vertices into dominating sets.

Matching statistic: St001656

Mapping

Mp00156: Graphs —line graph⟶ Graphs
Mp00111: Graphs —complement⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
St001656: Graphs ⟶ ℤResult quality: 65% ●values known / values provided: 65%●distinct values known / distinct values provided: 100%

Values

([(0,1)],2)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,2)],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ([],1)
 => 1
([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ([],1)
 => 1
([(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ([],1)
 => 1
([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ([],1)
 => 1
([(0,3),(1,2)],4)
 => ([],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 2
([(0,3),(1,2),(2,3)],4)
 => ([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => ([(0,1)],2)
 => 2
([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ([],1)
 => 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ([(0,1)],2)
 => 2
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2)],4)
 => ([(0,1)],2)
 => 2
([(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)
 => ([(0,1)],2)
 => 2
([(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)
 => ([(0,1)],2)
 => 2
([(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ([],1)
 => 1
([(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ([],1)
 => 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ([],1)
 => 1
([(1,4),(2,3)],5)
 => ([],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 2
([(1,4),(2,3),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => ([(0,1)],2)
 => 2
([(0,1),(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 2
([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ([],1)
 => 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 2
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ([(0,1)],2)
 => 2
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2)],4)
 => ([(0,1)],2)
 => 2
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => 2
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,3)],5)
 => ([(0,1)],2)
 => 2
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(0,4),(1,3),(1,4),(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)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,1)],2)
 => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => ([(0,1)],2)
 => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],7)
 => ?
 => ? = 2
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,1)],2)
 => 2
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 2
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,1)],2)
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6),(5,6)],7)
 => ?
 => ? = 2
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => 2
([(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),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,5),(1,4),(2,3)],6)
 => ([(0,1)],2)
 => 2
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ?
 => ? = 2
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(5,6)],7)
 => ([(0,3),(0,6),(1,2),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => ?
 => ? = 2
([(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ([],1)
 => 1
([(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ([],1)
 => 1
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ([],1)
 => 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ([],1)
 => 1
([(2,5),(3,4)],6)
 => ([],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 2
([(2,5),(3,4),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => ([(0,1)],2)
 => 2
([(1,2),(3,5),(4,5)],6)
 => ([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 2
([(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ([],1)
 => 1
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 2
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 2
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => ?
 => ? = 2
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(0,6),(1,2),(1,5),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6)],7)
 => ?
 => ? = 2
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],7)
 => ?
 => ? = 2
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,4),(1,6),(2,3),(2,6),(3,5),(4,5),(5,6)],7)
 => ?
 => ? = 2
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 3
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,5),(1,4),(1,5),(1,6),(2,3),(2,4),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,4),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6)],7)
 => ?
 => ? = 3
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,4),(2,3),(2,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 3
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6),(5,6)],7)
 => ?
 => ? = 2
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(1,4),(1,5),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ?
 => ? = 3
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
 => ?
 => ? = 3
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,5),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
 => ?
 => ? = 3
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)
 => ?
 => ? = 2
([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ?
 => ? = 2
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(4,5)],7)
 => ([(0,1),(0,4),(0,5),(1,2),(1,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ?
 => ? = 3
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(4,5),(5,6)],7)
 => ([(0,4),(0,5),(1,2),(1,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ?
 => ? = 3
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(5,6)],7)
 => ([(0,3),(0,6),(1,2),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => ?
 => ? = 2
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(4,5),(5,6)],7)
 => ?
 => ? = 3
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(0,6),(1,2),(1,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,4),(1,5),(2,3),(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => ?
 => ? = 3
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => ?
 => ? = 3
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(5,6)],7)
 => ([(0,3),(0,6),(1,2),(1,6),(2,5),(3,5),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 3
([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,4),(0,6),(1,2),(1,3),(1,5),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(1,3),(1,6),(2,3),(2,5),(2,6),(3,4),(4,6),(5,6)],7)
 => ?
 => ? = 3
([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(1,2),(1,4),(1,6),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(0,6),(1,3),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ?
 => ? = 3
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(4,5),(5,6)],7)
 => ?
 => ? = 3
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
 => ?
 => ? = 3
([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(2,6),(3,6),(4,6),(5,6)],7)
 => ?
 => ? = 2
([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,1),(0,6),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ?
 => ? = 2
([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => ?
 => ? = 2
([(0,6),(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ?
 => ? = 2
([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,1),(0,2),(0,6),(1,2),(1,5),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6)],7)
 => ?
 => ? = 2
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,3),(0,4),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(5,6)],7)
 => ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
 => ?
 => ? = 2
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],7)
 => ?
 => ? = 2
([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,4),(1,6),(2,3),(2,6),(3,5),(4,5),(5,6)],7)
 => ?
 => ? = 2
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)
 => ?
 => ? = 2
([(0,6),(1,6),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,4),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 3
([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 3
([(0,6),(1,6),(2,5),(3,4),(3,6),(4,5),(5,6)],7)
 => ([(0,4),(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(5,6)],7)
 => ?
 => ? = 3
([(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,3),(0,5),(1,4),(1,5),(1,6),(2,3),(2,4),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,4),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6)],7)
 => ?
 => ? = 3
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ?
 => ? = 3
([(0,6),(1,6),(2,3),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5)],7)
 => ?
 => ? = 3
([(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,4),(2,3),(2,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 3
([(0,6),(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 3
([(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6),(5,6)],7)
 => ?
 => ? = 2
([(0,5),(1,6),(2,3),(2,4),(3,6),(4,6),(5,6)],7)
 => ([(0,6),(1,2),(1,5),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ?
 => ? = 3
([(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(1,4),(1,5),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ?
 => ? = 3
([(0,5),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6)],7)
 => ([(0,2),(1,5),(1,6),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(0,6),(1,4),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)
 => ?
 => ? = 3
([(1,4),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(1,2),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
 => ?
 => ? = 3

Description

The monophonic position number of a graph. A subset

$M$ of the vertex set of a graph is a monophonic position set if no three vertices of

$M$ lie on a common induced path. The monophonic position number is the size of a largest monophonic position set.

Matching statistic: St001330

Mapping

Mp00156: Graphs —line graph⟶ Graphs
Mp00111: Graphs —complement⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
St001330: Graphs ⟶ ℤResult quality: 65% ●values known / values provided: 65%●distinct values known / distinct values provided: 100%

Values

([(0,1)],2)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,2)],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ([],1)
 => 1
([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ([],1)
 => 1
([(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ([],1)
 => 1
([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ([],1)
 => 1
([(0,3),(1,2)],4)
 => ([],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 2
([(0,3),(1,2),(2,3)],4)
 => ([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => ([(0,1)],2)
 => 2
([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ([],1)
 => 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ([(0,1)],2)
 => 2
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2)],4)
 => ([(0,1)],2)
 => 2
([(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)
 => ([(0,1)],2)
 => 2
([(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)
 => ([(0,1)],2)
 => 2
([(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ([],1)
 => 1
([(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ([],1)
 => 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ([],1)
 => 1
([(1,4),(2,3)],5)
 => ([],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 2
([(1,4),(2,3),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => ([(0,1)],2)
 => 2
([(0,1),(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 2
([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ([],1)
 => 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 2
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ([(0,1)],2)
 => 2
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2)],4)
 => ([(0,1)],2)
 => 2
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => 2
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,3)],5)
 => ([(0,1)],2)
 => 2
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(0,4),(1,3),(1,4),(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)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,1)],2)
 => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => ([(0,1)],2)
 => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],7)
 => ?
 => ? = 2
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,1)],2)
 => 2
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 2
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,1)],2)
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6),(5,6)],7)
 => ?
 => ? = 2
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => 2
([(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),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,5),(1,4),(2,3)],6)
 => ([(0,1)],2)
 => 2
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ?
 => ? = 2
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(5,6)],7)
 => ([(0,3),(0,6),(1,2),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => ?
 => ? = 2
([(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ([],1)
 => 1
([(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ([],1)
 => 1
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ([],1)
 => 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ([],1)
 => 1
([(2,5),(3,4)],6)
 => ([],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 2
([(2,5),(3,4),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => ([(0,1)],2)
 => 2
([(1,2),(3,5),(4,5)],6)
 => ([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 2
([(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ([],1)
 => 1
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 2
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 2
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => ?
 => ? = 2
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(0,6),(1,2),(1,5),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6)],7)
 => ?
 => ? = 2
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],7)
 => ?
 => ? = 2
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,4),(1,6),(2,3),(2,6),(3,5),(4,5),(5,6)],7)
 => ?
 => ? = 2
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 3
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,5),(1,4),(1,5),(1,6),(2,3),(2,4),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,4),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6)],7)
 => ?
 => ? = 3
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,4),(2,3),(2,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 3
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6),(5,6)],7)
 => ?
 => ? = 2
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(1,4),(1,5),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ?
 => ? = 3
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
 => ?
 => ? = 3
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,5),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
 => ?
 => ? = 3
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)
 => ?
 => ? = 2
([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ?
 => ? = 2
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(4,5)],7)
 => ([(0,1),(0,4),(0,5),(1,2),(1,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ?
 => ? = 3
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(4,5),(5,6)],7)
 => ([(0,4),(0,5),(1,2),(1,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ?
 => ? = 3
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(5,6)],7)
 => ([(0,3),(0,6),(1,2),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => ?
 => ? = 2
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(4,5),(5,6)],7)
 => ?
 => ? = 3
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(0,6),(1,2),(1,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,4),(1,5),(2,3),(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => ?
 => ? = 3
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => ?
 => ? = 3
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(5,6)],7)
 => ([(0,3),(0,6),(1,2),(1,6),(2,5),(3,5),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 3
([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,4),(0,6),(1,2),(1,3),(1,5),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(1,3),(1,6),(2,3),(2,5),(2,6),(3,4),(4,6),(5,6)],7)
 => ?
 => ? = 3
([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(1,2),(1,4),(1,6),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(0,6),(1,3),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ?
 => ? = 3
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(4,5),(5,6)],7)
 => ?
 => ? = 3
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
 => ?
 => ? = 3
([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(2,6),(3,6),(4,6),(5,6)],7)
 => ?
 => ? = 2
([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,1),(0,6),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ?
 => ? = 2
([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => ?
 => ? = 2
([(0,6),(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ?
 => ? = 2
([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,1),(0,2),(0,6),(1,2),(1,5),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6)],7)
 => ?
 => ? = 2
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,3),(0,4),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(5,6)],7)
 => ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
 => ?
 => ? = 2
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],7)
 => ?
 => ? = 2
([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,4),(1,6),(2,3),(2,6),(3,5),(4,5),(5,6)],7)
 => ?
 => ? = 2
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)
 => ?
 => ? = 2
([(0,6),(1,6),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,4),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 3
([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 3
([(0,6),(1,6),(2,5),(3,4),(3,6),(4,5),(5,6)],7)
 => ([(0,4),(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(5,6)],7)
 => ?
 => ? = 3
([(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,3),(0,5),(1,4),(1,5),(1,6),(2,3),(2,4),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,4),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6)],7)
 => ?
 => ? = 3
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ?
 => ? = 3
([(0,6),(1,6),(2,3),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5)],7)
 => ?
 => ? = 3
([(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,4),(2,3),(2,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 3
([(0,6),(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ?
 => ? = 3
([(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6),(5,6)],7)
 => ?
 => ? = 2
([(0,5),(1,6),(2,3),(2,4),(3,6),(4,6),(5,6)],7)
 => ([(0,6),(1,2),(1,5),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ?
 => ? = 3
([(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(1,4),(1,5),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ?
 => ? = 3
([(0,5),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6)],7)
 => ([(0,2),(1,5),(1,6),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(0,6),(1,4),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)
 => ?
 => ? = 3
([(1,4),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(1,2),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
 => ?
 => ? = 3

Description

The hat guessing number of a graph. Suppose that each vertex of a graph corresponds to a player, wearing a hat whose color is arbitrarily chosen from a set of

$q$ possible colors. Each player can see the hat colors of his neighbors, but not his own hat color. All of the players are asked to guess their own hat colors simultaneously, according to a predetermined guessing strategy and the hat colors they see, where no communication between them is allowed. The hat guessing number

$HG(G)$ of a graph

$G$ is the largest integer

$q$ such that there exists a guessing strategy guaranteeing at least one correct guess for any hat assignment of

$q$ possible colors. Because it suffices that a single player guesses correctly, the hat guessing number of a graph is the maximum of the hat guessing numbers of its connected components.

The following 3 statistics, ordered by result quality, also match your data. Click on any of them to see the details.

St001674The number of vertices of the largest induced star graph in the graph. St000741The Colin de Verdière graph invariant. St001323The independence gap of a graph.