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Your data matches 3 different statistics following compositions of up to 3 maps.
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Matching statistic: St001645
(load all 2 compositions to match this statistic)
Mapping
Mp00117: Graphs —Ore closure⟶ Graphs
Mp00111: Graphs —complement⟶ Graphs
Mp00250: Graphs —clique graph⟶ Graphs
St001645: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([],2)
 => ([],2)
 => ([(0,1)],2)
 => ([],1)
 => 1
([],3)
 => ([],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],1)
 => 1
([(1,2)],3)
 => ([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 2
([],4)
 => ([],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],1)
 => 1
([(2,3)],4)
 => ([(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 2
([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => 2
([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4
([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,2),(1,2)],3)
 => 4
([(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 3
([],5)
 => ([],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => 1
([(3,4)],5)
 => ([(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => 2
([(1,4),(2,3)],5)
 => ([(1,4),(2,3)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4
([(1,4),(2,3),(3,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 3
([(0,1),(2,4),(3,4)],5)
 => ([(0,1),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4
([(2,3),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 3
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => 4
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 3
([(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)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4
([(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)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => 4
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4
([(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)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => 6
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 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)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4
([],6)
 => ([],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],1)
 => 1
([(4,5)],6)
 => ([(4,5)],6)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => 2
([(3,5),(4,5)],6)
 => ([(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => 2
([(2,5),(3,5),(4,5)],6)
 => ([(2,5),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => 2
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(1,5),(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)
 => ([(0,1)],2)
 => 2
([(2,5),(3,4)],6)
 => ([(2,5),(3,4)],6)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4
([(2,5),(3,4),(4,5)],6)
 => ([(2,5),(3,4),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => 3
([(1,2),(3,5),(4,5)],6)
 => ([(1,2),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4
([(3,4),(3,5),(4,5)],6)
 => ([(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => 3
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => 3
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => 3
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ([(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)
 => ([(0,2),(1,2)],3)
 => 4
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => 3
([(2,4),(2,5),(3,4),(3,5)],6)
 => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4
([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => 3
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(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),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => 3
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(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)
 => ([(0,2),(1,2)],3)
 => 4
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => 3
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => 4
Description
The pebbling number of a connected graph.
Matching statistic: St001060
Mapping
Mp00247: Graphs —de-duplicate⟶ Graphs
Mp00259: Graphs —vertex addition⟶ Graphs
St001060: Graphs ⟶ ℤResult quality: 8% ●values known / values provided: 8%●distinct values known / distinct values provided: 29%
Values
([],1)
 => ([],1)
 => ([],2)
 => ? = 1 - 2
([],2)
 => ([],1)
 => ([],2)
 => ? = 1 - 2
([],3)
 => ([],1)
 => ([],2)
 => ? = 1 - 2
([(1,2)],3)
 => ([(1,2)],3)
 => ([(2,3)],4)
 => ? = 2 - 2
([],4)
 => ([],1)
 => ([],2)
 => ? = 1 - 2
([(2,3)],4)
 => ([(1,2)],3)
 => ([(2,3)],4)
 => ? = 2 - 2
([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => ([(2,3)],4)
 => ? = 2 - 2
([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => ([(1,4),(2,3)],5)
 => ? = 4 - 2
([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(1,4),(2,3),(3,4)],5)
 => 2 = 4 - 2
([(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(2,3),(2,4),(3,4)],5)
 => ? = 3 - 2
([],5)
 => ([],1)
 => ([],2)
 => ? = 1 - 2
([(3,4)],5)
 => ([(1,2)],3)
 => ([(2,3)],4)
 => ? = 2 - 2
([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ([(2,3)],4)
 => ? = 2 - 2
([(1,4),(2,4),(3,4)],5)
 => ([(1,2)],3)
 => ([(2,3)],4)
 => ? = 2 - 2
([(1,4),(2,3)],5)
 => ([(1,4),(2,3)],5)
 => ([(2,5),(3,4)],6)
 => ? = 4 - 2
([(1,4),(2,3),(3,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(2,5),(3,4),(4,5)],6)
 => ? = 3 - 2
([(0,1),(2,4),(3,4)],5)
 => ([(0,3),(1,2)],4)
 => ([(1,4),(2,3)],5)
 => ? = 4 - 2
([(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(2,3),(2,4),(3,4)],5)
 => ? = 3 - 2
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(1,4),(2,3),(3,4)],5)
 => 2 = 4 - 2
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 - 2
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,2)],3)
 => ([(2,3)],4)
 => ? = 4 - 2
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(2,3),(2,4),(3,4)],5)
 => ? = 4 - 2
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => 2 = 4 - 2
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 2 = 4 - 2
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(3,4),(3,5),(4,5)],6)
 => ? = 6 - 2
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => 3 = 5 - 2
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 4 - 2
([],6)
 => ([],1)
 => ([],2)
 => ? = 1 - 2
([(4,5)],6)
 => ([(1,2)],3)
 => ([(2,3)],4)
 => ? = 2 - 2
([(3,5),(4,5)],6)
 => ([(1,2)],3)
 => ([(2,3)],4)
 => ? = 2 - 2
([(2,5),(3,5),(4,5)],6)
 => ([(1,2)],3)
 => ([(2,3)],4)
 => ? = 2 - 2
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(1,2)],3)
 => ([(2,3)],4)
 => ? = 2 - 2
([(2,5),(3,4)],6)
 => ([(1,4),(2,3)],5)
 => ([(2,5),(3,4)],6)
 => ? = 4 - 2
([(2,5),(3,4),(4,5)],6)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(2,5),(3,4),(4,5)],6)
 => ? = 3 - 2
([(1,2),(3,5),(4,5)],6)
 => ([(1,4),(2,3)],5)
 => ([(2,5),(3,4)],6)
 => ? = 4 - 2
([(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(2,3),(2,4),(3,4)],5)
 => ? = 3 - 2
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(2,5),(3,4),(4,5)],6)
 => ? = 3 - 2
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([(0,3),(1,2)],4)
 => ([(1,4),(2,3)],5)
 => ? = 4 - 2
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 - 2
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(1,4),(2,3),(3,4)],5)
 => 2 = 4 - 2
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 - 2
([(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,2)],3)
 => ([(2,3)],4)
 => ? = 4 - 2
([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(0,3),(1,2)],4)
 => ([(1,4),(2,3)],5)
 => ? = 4 - 2
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(2,5),(3,4),(4,5)],6)
 => ? = 3 - 2
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 2 = 4 - 2
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(2,3),(2,4),(3,4)],5)
 => ? = 4 - 2
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 2
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(1,4),(2,3),(3,4)],5)
 => 2 = 4 - 2
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 - 2
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => 2 = 4 - 2
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,2)],3)
 => ([(2,3)],4)
 => ? = 3 - 2
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 2 = 4 - 2
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(2,3),(2,4),(3,4)],5)
 => ? = 3 - 2
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => 2 = 4 - 2
([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(2,6),(3,5),(4,5),(4,6)],7)
 => ? = 4 - 2
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(1,2),(3,6),(4,5),(5,6)],7)
 => ? = 6 - 2
([(1,2),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(3,4),(3,5),(4,5)],6)
 => ([(2,3),(4,5),(4,6),(5,6)],7)
 => ? = 6 - 2
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => ? = 5 - 2
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => ? = 5 - 2
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 6 - 2
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ? = 5 - 2
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 2 = 4 - 2
([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(1,4),(2,3),(3,4)],5)
 => 2 = 4 - 2
([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 2 = 4 - 2
([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(1,4),(2,3),(3,4)],5)
 => 2 = 4 - 2
([(0,6),(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => 2 = 4 - 2
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 2 = 4 - 2
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 2 = 4 - 2
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => 2 = 4 - 2
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => 2 = 4 - 2
([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 2 = 4 - 2
([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => 2 = 4 - 2
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(1,4),(2,3),(3,4)],5)
 => 2 = 4 - 2
([(0,6),(1,6),(2,3),(2,4),(3,5),(4,5),(5,6)],7)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 2 = 4 - 2
([(0,4),(0,5),(1,2),(1,3),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 2 = 4 - 2
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 2 = 4 - 2
([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 2 = 4 - 2
([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(4,5)],7)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => 3 = 5 - 2
Description
The distinguishing index of a graph. This is the smallest number of colours such that there is a colouring of the edges which is not preserved by any automorphism. If the graph has a connected component which is a single edge, or at least two isolated vertices, this statistic is undefined.
Matching statistic: St000454
Mapping
Mp00324: Graphs —chromatic difference sequence⟶ Integer compositions
Mp00172: Integer compositions —rotate back to front⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000454: Graphs ⟶ ℤResult quality: 6% ●values known / values provided: 6%●distinct values known / distinct values provided: 29%
Values
([],1)
 => [1] => [1] => ([],1)
 => 0 = 1 - 1
([],2)
 => [2] => [2] => ([],2)
 => 0 = 1 - 1
([],3)
 => [3] => [3] => ([],3)
 => 0 = 1 - 1
([(1,2)],3)
 => [2,1] => [1,2] => ([(1,2)],3)
 => 1 = 2 - 1
([],4)
 => [4] => [4] => ([],4)
 => 0 = 1 - 1
([(2,3)],4)
 => [3,1] => [1,3] => ([(2,3)],4)
 => 1 = 2 - 1
([(1,3),(2,3)],4)
 => [3,1] => [1,3] => ([(2,3)],4)
 => 1 = 2 - 1
([(0,3),(1,2)],4)
 => [2,2] => [2,2] => ([(1,3),(2,3)],4)
 => ? = 4 - 1
([(0,3),(1,2),(2,3)],4)
 => [2,2] => [2,2] => ([(1,3),(2,3)],4)
 => ? = 4 - 1
([(1,2),(1,3),(2,3)],4)
 => [2,1,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ? = 3 - 1
([],5)
 => [5] => [5] => ([],5)
 => 0 = 1 - 1
([(3,4)],5)
 => [4,1] => [1,4] => ([(3,4)],5)
 => 1 = 2 - 1
([(2,4),(3,4)],5)
 => [4,1] => [1,4] => ([(3,4)],5)
 => 1 = 2 - 1
([(1,4),(2,4),(3,4)],5)
 => [4,1] => [1,4] => ([(3,4)],5)
 => 1 = 2 - 1
([(1,4),(2,3)],5)
 => [3,2] => [2,3] => ([(2,4),(3,4)],5)
 => ? = 4 - 1
([(1,4),(2,3),(3,4)],5)
 => [3,2] => [2,3] => ([(2,4),(3,4)],5)
 => ? = 3 - 1
([(0,1),(2,4),(3,4)],5)
 => [3,2] => [2,3] => ([(2,4),(3,4)],5)
 => ? = 4 - 1
([(2,3),(2,4),(3,4)],5)
 => [3,1,1] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 3 - 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => [3,2] => [2,3] => ([(2,4),(3,4)],5)
 => ? = 4 - 1
([(1,4),(2,3),(2,4),(3,4)],5)
 => [3,1,1] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 3 - 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => [3,2] => [2,3] => ([(2,4),(3,4)],5)
 => ? = 4 - 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,1,1] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 4 - 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [3,1,1] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 4 - 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => [3,2] => [2,3] => ([(2,4),(3,4)],5)
 => ? = 4 - 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => [2,2,1] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 6 - 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => [2,2,1] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 5 - 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [2,1,1,1] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 4 - 1
([],6)
 => [6] => [6] => ([],6)
 => 0 = 1 - 1
([(4,5)],6)
 => [5,1] => [1,5] => ([(4,5)],6)
 => 1 = 2 - 1
([(3,5),(4,5)],6)
 => [5,1] => [1,5] => ([(4,5)],6)
 => 1 = 2 - 1
([(2,5),(3,5),(4,5)],6)
 => [5,1] => [1,5] => ([(4,5)],6)
 => 1 = 2 - 1
([(1,5),(2,5),(3,5),(4,5)],6)
 => [5,1] => [1,5] => ([(4,5)],6)
 => 1 = 2 - 1
([(2,5),(3,4)],6)
 => [4,2] => [2,4] => ([(3,5),(4,5)],6)
 => ? = 4 - 1
([(2,5),(3,4),(4,5)],6)
 => [4,2] => [2,4] => ([(3,5),(4,5)],6)
 => ? = 3 - 1
([(1,2),(3,5),(4,5)],6)
 => [4,2] => [2,4] => ([(3,5),(4,5)],6)
 => ? = 4 - 1
([(3,4),(3,5),(4,5)],6)
 => [4,1,1] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 - 1
([(1,5),(2,5),(3,4),(4,5)],6)
 => [4,2] => [2,4] => ([(3,5),(4,5)],6)
 => ? = 3 - 1
([(0,1),(2,5),(3,5),(4,5)],6)
 => [4,2] => [2,4] => ([(3,5),(4,5)],6)
 => ? = 4 - 1
([(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1,1] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 - 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => [4,2] => [2,4] => ([(3,5),(4,5)],6)
 => ? = 4 - 1
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1,1] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 - 1
([(2,4),(2,5),(3,4),(3,5)],6)
 => [4,2] => [2,4] => ([(3,5),(4,5)],6)
 => ? = 4 - 1
([(0,5),(1,5),(2,4),(3,4)],6)
 => [4,2] => [2,4] => ([(3,5),(4,5)],6)
 => ? = 4 - 1
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [4,2] => [2,4] => ([(3,5),(4,5)],6)
 => ? = 3 - 1
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => [4,2] => [2,4] => ([(3,5),(4,5)],6)
 => ? = 4 - 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1,1] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 4 - 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [4,1,1] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 - 1
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => [4,2] => [2,4] => ([(3,5),(4,5)],6)
 => ? = 4 - 1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1,1] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 - 1
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [4,1,1] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 4 - 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [4,2] => [2,4] => ([(3,5),(4,5)],6)
 => ? = 3 - 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => [4,2] => [2,4] => ([(3,5),(4,5)],6)
 => ? = 4 - 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1,1] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 - 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1,1] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 4 - 1
([(1,5),(2,4),(3,4),(3,5)],6)
 => [4,2] => [2,4] => ([(3,5),(4,5)],6)
 => ? = 4 - 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6)
 => ? = 6 - 1
([(1,2),(3,4),(3,5),(4,5)],6)
 => [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 6 - 1
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6)
 => ? = 5 - 1
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 5 - 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 6 - 1
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 5 - 1
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 5 - 1
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 5 - 1
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 4 - 1
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 4 - 1
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 5 - 1
([],7)
 => [7] => [7] => ([],7)
 => 0 = 1 - 1
([(5,6)],7)
 => [6,1] => [1,6] => ([(5,6)],7)
 => 1 = 2 - 1
([(4,6),(5,6)],7)
 => [6,1] => [1,6] => ([(5,6)],7)
 => 1 = 2 - 1
([(3,6),(4,6),(5,6)],7)
 => [6,1] => [1,6] => ([(5,6)],7)
 => 1 = 2 - 1
([(2,6),(3,6),(4,6),(5,6)],7)
 => [6,1] => [1,6] => ([(5,6)],7)
 => 1 = 2 - 1
([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => [6,1] => [1,6] => ([(5,6)],7)
 => 1 = 2 - 1
Description
The largest eigenvalue of a graph if it is integral. If a graph is d-regular, then its largest eigenvalue equals d. One can show that the largest eigenvalue always lies between the average degree and the maximal degree. This statistic is undefined if the largest eigenvalue of the graph is not integral.