- FindStat

Your data matches 36 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)

Matching statistic: St000455
(load all 2 compositions to match this statistic)

Mapping

Mp00156: Graphs —line graph⟶ Graphs
Mp00117: Graphs —Ore closure⟶ Graphs
Mp00111: Graphs —complement⟶ Graphs
St000455: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

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

Description

The second largest eigenvalue of a graph if it is integral. This statistic is undefined if the second largest eigenvalue of the graph is not integral. Chapter 4 of [1] provides lots of context.

Matching statistic: St000535
(load all 4 compositions to match this statistic)

Mapping

Mp00156: Graphs —line graph⟶ Graphs
Mp00117: Graphs —Ore closure⟶ Graphs
Mp00157: Graphs —connected complement⟶ Graphs
St000535: Graphs ⟶ ℤResult quality: 97% ●values known / values provided: 97%●distinct values known / distinct values provided: 100%

Values

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

Description

The rank-width of a graph.

Matching statistic: St001734
(load all 3 compositions to match this statistic)

Mapping

Mp00156: Graphs —line graph⟶ Graphs
Mp00117: Graphs —Ore closure⟶ Graphs
St001734: Graphs ⟶ ℤResult quality: 65% ●values known / values provided: 65%●distinct values known / distinct values provided: 100%

Values

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

Description

The lettericity of a graph. Let $D$ be a digraph on $k$ vertices, possibly with loops and let $w$ be a word of length $n$ whose letters are vertices of $D$. The letter graph corresponding to $D$ and $w$ is the graph with vertex set $\{1,\dots,n\}$ whose edges are the pairs $(i,j)$ with $i < j$ sucht that $(w_i, w_j)$ is a (directed) edge of $D$.

Matching statistic: St000260
(load all 3 compositions to match this statistic)

Mapping

Mp00156: Graphs —line graph⟶ Graphs
Mp00117: Graphs —Ore closure⟶ Graphs
Mp00157: Graphs —connected complement⟶ Graphs
St000260: Graphs ⟶ ℤResult quality: 52% ●values known / values provided: 52%●distinct values known / distinct values provided: 67%

Values

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

Description

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

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

Mapping

Mp00157: Graphs —connected complement⟶ Graphs
Mp00156: Graphs —line graph⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
St000259: Graphs ⟶ ℤResult quality: 50% ●values known / values provided: 50%●distinct values known / distinct values provided: 67%

Values

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

Description

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

Matching statistic: St000985

Mapping

Mp00157: Graphs —connected complement⟶ Graphs
Mp00156: Graphs —line graph⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
St000985: Graphs ⟶ ℤResult quality: 50% ●values known / values provided: 50%●distinct values known / distinct values provided: 67%

Values

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

Description

The number of positive eigenvalues of the adjacency matrix of the graph.

Matching statistic: St001271

Mapping

Mp00157: Graphs —connected complement⟶ Graphs
Mp00156: Graphs —line graph⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
St001271: Graphs ⟶ ℤResult quality: 50% ●values known / values provided: 50%●distinct values known / distinct values provided: 67%

Values

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

Description

The competition number of a graph. The competition graph of a digraph $D$ is a (simple undirected) graph which has the same vertex set as $D$ and has an edge between $x$ and $y$ if and only if there exists a vertex $v$ in $D$ such that $(x, v)$ and $(y, v)$ are arcs of $D$. For any graph, $G$ together with sufficiently many isolated vertices is the competition graph of some acyclic digraph. The competition number $k(G)$ is the smallest number of such isolated vertices.

Matching statistic: St001333

Mapping

Mp00157: Graphs —connected complement⟶ Graphs
Mp00156: Graphs —line graph⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
St001333: Graphs ⟶ ℤResult quality: 50% ●values known / values provided: 50%●distinct values known / distinct values provided: 67%

Values

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

Description

The cardinality of a minimal edge-isolating set of a graph. Let $\mathcal F$ be a set of graphs. A set of vertices $S$ is $\mathcal F$-isolating, if the subgraph induced by the vertices in the complement of the closed neighbourhood of $S$ does not contain any graph in $\mathcal F$. This statistic returns the cardinality of the smallest isolating set when $\mathcal F$ contains only the graph with one edge.

Matching statistic: St001340

Mapping

Mp00157: Graphs —connected complement⟶ Graphs
Mp00156: Graphs —line graph⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
St001340: Graphs ⟶ ℤResult quality: 50% ●values known / values provided: 50%●distinct values known / distinct values provided: 67%

Values

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

Description

The cardinality of a minimal non-edge isolating set of a graph. Let $\mathcal F$ be a set of graphs. A set of vertices $S$ is $\mathcal F$-isolating, if the subgraph induced by the vertices in the complement of the closed neighbourhood of $S$ does not contain any graph in $\mathcal F$. This statistic returns the cardinality of the smallest isolating set when $\mathcal F$ contains only the graph with two isolated vertices.

Matching statistic: St001349

Mapping

Mp00157: Graphs —connected complement⟶ Graphs
Mp00156: Graphs —line graph⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
St001349: Graphs ⟶ ℤResult quality: 50% ●values known / values provided: 50%●distinct values known / distinct values provided: 67%

Values

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

Description

The number of different graphs obtained from the given graph by removing an edge.

The following 26 statistics, ordered by result quality, also match your data. Click on any of them to see the details.

St001354The number of series nodes in the modular decomposition of a graph. St001393The induced matching number of a graph. St001512The minimum rank of a graph. St000258The burning number of a graph. St000299The number of nonisomorphic vertex-induced subtrees. St000452The number of distinct eigenvalues of a graph. St000453The number of distinct Laplacian eigenvalues of a graph. St000777The number of distinct eigenvalues of the distance Laplacian of a connected graph. St000918The 2-limited packing number of a graph. St001093The detour number of a graph. St001261The Castelnuovo-Mumford regularity of a graph. St001315The dissociation number of a graph. St001318The number of vertices of the largest induced subforest with the same number of connected components of a graph. St001321The number of vertices of the largest induced subforest of a graph. St001674The number of vertices of the largest induced star graph in the graph. St001195The global dimension of the algebra $A/AfA$ of the corresponding Nakayama algebra $A$ with minimal left faithful projective-injective module $Af$. St001704The size of the largest multi-subset-intersection of the deck of a graph with the deck of another graph. St001738The minimal order of a graph which is not an induced subgraph of the given graph. St000264The girth of a graph, which is not a tree. St000990The first ascent of a permutation. St001570The minimal number of edges to add to make a graph Hamiltonian. St001060The distinguishing index of a graph. St001581The achromatic number of a graph. St000771The largest multiplicity of a distance Laplacian eigenvalue in a connected graph. St000772The multiplicity of the largest distance Laplacian eigenvalue in a connected graph. St000456The monochromatic index of a connected graph.