Processing math: 100%

Your data matches 226 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001060
(load all 18 compositions to match this statistic)
Mapping
Mp00250: Graphs —clique graph⟶ Graphs
Mp00111: Graphs —complement⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
St001060: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],3)
 => ([],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 3
([],4)
 => ([],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 3
([(2,3)],4)
 => ([],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(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)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
([(3,4)],5)
 => ([],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 3
([(2,4),(3,4)],5)
 => ([(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 3
([(1,4),(2,3)],5)
 => ([],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 3
([(1,4),(2,3),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 3
([(2,3),(2,4),(3,4)],5)
 => ([],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 3
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 3
([(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)
 => 3
([],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)
 => ([(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)
 => 2
([(4,5)],6)
 => ([],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
([(3,5),(4,5)],6)
 => ([(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 3
([(2,5),(3,5),(4,5)],6)
 => ([(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
([(2,5),(3,4)],6)
 => ([],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 3
([(2,5),(3,4),(4,5)],6)
 => ([(2,4),(3,4)],5)
 => ([(0,3),(0,4),(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)
 => 3
([(1,2),(3,5),(4,5)],6)
 => ([(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 3
([(3,4),(3,5),(4,5)],6)
 => ([],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 3
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(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
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 3
([(2,4),(2,5),(3,4),(3,5)],6)
 => ([(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(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)
 => 3
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(1,2),(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),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => 3
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 3
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 3
([(0,5),(1,4),(2,3)],6)
 => ([],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 3
([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(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),(2,5),(3,4),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 3
([(1,2),(3,4),(3,5),(4,5)],6)
 => ([],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 3
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 3
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 3
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => 2
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => 3
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 3
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(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),(0,2),(1,2)],3)
 => 3
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 3
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 3
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 3
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 3
([(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)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => 3
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 3
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 3
([(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)
 => ([(0,1),(0,2),(1,2)],3)
 => 3
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 3
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],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)
 => 3
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],6)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],6)
 => ([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => 3
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],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)
 => 3
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 3
([(5,6)],7)
 => ([],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)
 => ([(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)
 => 2
([(4,6),(5,6)],7)
 => ([(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),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
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: St000455
(load all 27 compositions to match this statistic)
Mapping
Mp00250: Graphs —clique graph⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
St000455: Graphs ⟶ ℤResult quality: 50% ●values known / values provided: 84%●distinct values known / distinct values provided: 50%
Values
([],3)
 => ([],3)
 => ([],1)
 => ? = 3 - 4
([],4)
 => ([],4)
 => ([],1)
 => ? = 3 - 4
([(2,3)],4)
 => ([],3)
 => ([],1)
 => ? = 3 - 4
([],5)
 => ([],5)
 => ([],1)
 => ? = 3 - 4
([(3,4)],5)
 => ([],4)
 => ([],1)
 => ? = 3 - 4
([(2,4),(3,4)],5)
 => ([(2,3)],4)
 => ([(0,1)],2)
 => -1 = 3 - 4
([(1,4),(2,3)],5)
 => ([],3)
 => ([],1)
 => ? = 3 - 4
([(1,4),(2,3),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => -1 = 3 - 4
([(2,3),(2,4),(3,4)],5)
 => ([],3)
 => ([],1)
 => ? = 3 - 4
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => -1 = 3 - 4
([(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)
 => ? = 3 - 4
([],6)
 => ([],6)
 => ([],1)
 => ? = 2 - 4
([(4,5)],6)
 => ([],5)
 => ([],1)
 => ? = 3 - 4
([(3,5),(4,5)],6)
 => ([(3,4)],5)
 => ([(0,1)],2)
 => -1 = 3 - 4
([(2,5),(3,5),(4,5)],6)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => -1 = 3 - 4
([(2,5),(3,4)],6)
 => ([],4)
 => ([],1)
 => ? = 3 - 4
([(2,5),(3,4),(4,5)],6)
 => ([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => -1 = 3 - 4
([(1,2),(3,5),(4,5)],6)
 => ([(2,3)],4)
 => ([(0,1)],2)
 => -1 = 3 - 4
([(3,4),(3,5),(4,5)],6)
 => ([],4)
 => ([],1)
 => ? = 3 - 4
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => -1 = 3 - 4
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,3)],4)
 => ([(0,1)],2)
 => -1 = 3 - 4
([(2,4),(2,5),(3,4),(3,5)],6)
 => ([(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1)],2)
 => -1 = 3 - 4
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => -1 = 3 - 4
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,3)],4)
 => ([(0,1)],2)
 => -1 = 3 - 4
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => -1 = 3 - 4
([(0,5),(1,4),(2,3)],6)
 => ([],3)
 => ([],1)
 => ? = 3 - 4
([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => -1 = 3 - 4
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => -1 = 3 - 4
([(1,2),(3,4),(3,5),(4,5)],6)
 => ([],3)
 => ([],1)
 => ? = 3 - 4
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => -1 = 3 - 4
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => -1 = 3 - 4
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ? = 2 - 4
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => -1 = 3 - 4
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => -1 = 3 - 4
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => -1 = 3 - 4
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => -1 = 3 - 4
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => -1 = 3 - 4
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => -1 = 3 - 4
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => -1 = 3 - 4
([(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)
 => ([(0,1),(0,2),(1,2)],3)
 => -1 = 3 - 4
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],3)
 => ([],1)
 => ? = 3 - 4
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => -1 = 3 - 4
([(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)
 => ([(0,1)],2)
 => -1 = 3 - 4
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => -1 = 3 - 4
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ? = 3 - 4
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],6)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => -1 = 3 - 4
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ? = 3 - 4
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => -1 = 3 - 4
([(5,6)],7)
 => ([],6)
 => ([],1)
 => ? = 2 - 4
([(4,6),(5,6)],7)
 => ([(4,5)],6)
 => ([(0,1)],2)
 => -1 = 3 - 4
([(3,6),(4,6),(5,6)],7)
 => ([(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => -1 = 3 - 4
([(2,6),(3,6),(4,6),(5,6)],7)
 => ([(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 = 3 - 4
([(3,6),(4,5)],7)
 => ([],5)
 => ([],1)
 => ? = 3 - 4
([(3,6),(4,5),(5,6)],7)
 => ([(3,5),(4,5)],6)
 => ([(0,1)],2)
 => -1 = 3 - 4
([(2,3),(4,6),(5,6)],7)
 => ([(3,4)],5)
 => ([(0,1)],2)
 => -1 = 3 - 4
([(4,5),(4,6),(5,6)],7)
 => ([],5)
 => ([],1)
 => ? = 3 - 4
([(2,6),(3,6),(4,5),(5,6)],7)
 => ([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => -1 = 3 - 4
([(1,2),(3,6),(4,6),(5,6)],7)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => -1 = 3 - 4
([(3,6),(4,5),(4,6),(5,6)],7)
 => ([(3,4)],5)
 => ([(0,1)],2)
 => -1 = 3 - 4
([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => ([(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 = 3 - 4
([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => -1 = 3 - 4
([(1,6),(2,6),(3,5),(4,5)],7)
 => ([(1,4),(2,3)],5)
 => ([(0,1)],2)
 => -1 = 3 - 4
([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => -1 = 3 - 4
([(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(3,4)],5)
 => ([(0,1)],2)
 => -1 = 3 - 4
([(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => -1 = 3 - 4
([(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => -1 = 3 - 4
([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => -1 = 3 - 4
([(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => -1 = 3 - 4
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => -1 = 3 - 4
([(1,6),(2,5),(3,5),(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 = 3 - 4
([(1,6),(2,5),(3,4)],7)
 => ([],4)
 => ([],1)
 => ? = 3 - 4
([(2,6),(3,5),(4,5),(4,6)],7)
 => ([(2,5),(3,4),(4,5)],6)
 => ([(0,1)],2)
 => -1 = 3 - 4
([(2,3),(4,5),(4,6),(5,6)],7)
 => ([],4)
 => ([],1)
 => ? = 3 - 4
([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([],4)
 => ([],1)
 => ? = 3 - 4
([(1,2),(1,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ? = 2 - 4
([(0,3),(1,2),(4,5),(4,6),(5,6)],7)
 => ([],3)
 => ([],1)
 => ? = 3 - 4
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5)],7)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ? = 2 - 4
([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7)
 => ([],3)
 => ([],1)
 => ? = 3 - 4
([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([],3)
 => ([],1)
 => ? = 3 - 4
([(0,6),(1,2),(1,3),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ? = 3 - 4
([(0,1),(0,5),(1,4),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ? = 3 - 4
([(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ? = 2 - 4
([(0,4),(0,6),(1,3),(1,5),(2,5),(2,6),(3,4),(3,5),(4,6)],7)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ? = 3 - 4
([(0,4),(0,5),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(5,6)],7)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ? = 3 - 4
([(0,1),(0,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ? = 3 - 4
([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([],3)
 => ([],1)
 => ? = 3 - 4
([(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(4,5)],7)
 => ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ? = 3 - 4
([(0,1),(0,6),(1,3),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ? = 3 - 4
([(0,5),(0,6),(1,2),(1,3),(1,4),(2,3),(2,4),(3,6),(4,5),(5,6)],7)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ? = 3 - 4
([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ? = 3 - 4
([(0,1),(0,2),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ? = 3 - 4
([(0,1),(0,6),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ? = 3 - 4
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: St000022
Mapping
Mp00037: Graphs —to partition of connected components⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
St000022: Permutations ⟶ ℤResult quality: 50% ●values known / values provided: 63%●distinct values known / distinct values provided: 50%
Values
([],3)
 => [1,1,1]
 => [1,0,1,1,1,0,0,0]
 => [3,1,4,5,2] => 0 = 3 - 3
([],4)
 => [1,1,1,1]
 => [1,0,1,1,1,1,0,0,0,0]
 => [3,1,4,5,6,2] => 0 = 3 - 3
([(2,3)],4)
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [5,1,4,2,3] => 0 = 3 - 3
([],5)
 => [1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [3,1,4,5,6,7,2] => ? = 3 - 3
([(3,4)],5)
 => [2,1,1,1]
 => [1,0,1,1,1,0,1,0,0,0]
 => [6,1,4,5,2,3] => 0 = 3 - 3
([(2,4),(3,4)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [3,1,5,2,4] => 0 = 3 - 3
([(1,4),(2,3)],5)
 => [2,2,1]
 => [1,0,1,0,1,1,0,0]
 => [4,1,2,5,3] => 0 = 3 - 3
([(1,4),(2,3),(3,4)],5)
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [6,3,4,1,2,5] => 0 = 3 - 3
([(2,3),(2,4),(3,4)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [3,1,5,2,4] => 0 = 3 - 3
([(1,3),(1,4),(2,3),(2,4)],5)
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [6,3,4,1,2,5] => 0 = 3 - 3
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => [5]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => [2,3,4,5,7,1,6] => 0 = 3 - 3
([],6)
 => [1,1,1,1,1,1]
 => [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => [3,1,4,5,6,7,8,2] => ? = 2 - 3
([(4,5)],6)
 => [2,1,1,1,1]
 => [1,0,1,1,1,1,0,1,0,0,0,0]
 => [7,1,4,5,6,2,3] => ? = 3 - 3
([(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [3,1,6,5,2,4] => 0 = 3 - 3
([(2,5),(3,5),(4,5)],6)
 => [4,1,1]
 => [1,1,0,1,1,0,0,0,1,0]
 => [4,3,1,6,2,5] => 0 = 3 - 3
([(2,5),(3,4)],6)
 => [2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => [5,1,4,2,6,3] => 0 = 3 - 3
([(2,5),(3,4),(4,5)],6)
 => [4,1,1]
 => [1,1,0,1,1,0,0,0,1,0]
 => [4,3,1,6,2,5] => 0 = 3 - 3
([(1,2),(3,5),(4,5)],6)
 => [3,2,1]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 0 = 3 - 3
([(3,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [3,1,6,5,2,4] => 0 = 3 - 3
([(1,5),(2,5),(3,4),(4,5)],6)
 => [5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => [7,3,4,5,1,2,6] => ? = 3 - 3
([(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1,1]
 => [1,1,0,1,1,0,0,0,1,0]
 => [4,3,1,6,2,5] => 0 = 3 - 3
([(2,4),(2,5),(3,4),(3,5)],6)
 => [4,1,1]
 => [1,1,0,1,1,0,0,0,1,0]
 => [4,3,1,6,2,5] => 0 = 3 - 3
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => [7,3,4,5,1,2,6] => ? = 3 - 3
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1,1]
 => [1,1,0,1,1,0,0,0,1,0]
 => [4,3,1,6,2,5] => 0 = 3 - 3
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => [7,3,4,5,1,2,6] => ? = 3 - 3
([(0,5),(1,4),(2,3)],6)
 => [2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => [2,4,1,5,6,3] => 0 = 3 - 3
([(1,5),(2,4),(3,4),(3,5)],6)
 => [5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => [7,3,4,5,1,2,6] => ? = 3 - 3
([(0,1),(2,5),(3,4),(4,5)],6)
 => [4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [2,6,4,1,3,5] => 0 = 3 - 3
([(1,2),(3,4),(3,5),(4,5)],6)
 => [3,2,1]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 0 = 3 - 3
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [2,3,4,5,6,8,1,7] => 0 = 3 - 3
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => [5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => [7,3,4,5,1,2,6] => ? = 3 - 3
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => [5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => [7,3,4,5,1,2,6] => ? = 2 - 3
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [2,3,4,5,6,8,1,7] => 0 = 3 - 3
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => [7,3,4,5,1,2,6] => ? = 3 - 3
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [2,3,4,5,6,8,1,7] => 0 = 3 - 3
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => [7,3,4,5,1,2,6] => ? = 3 - 3
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [2,3,4,5,6,8,1,7] => 0 = 3 - 3
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [2,3,4,5,6,8,1,7] => 0 = 3 - 3
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => [4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [2,6,4,1,3,5] => 0 = 3 - 3
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [2,3,4,5,6,8,1,7] => 0 = 3 - 3
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1,1]
 => [1,1,0,1,1,0,0,0,1,0]
 => [4,3,1,6,2,5] => 0 = 3 - 3
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => [5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => [7,3,4,5,1,2,6] => ? = 3 - 3
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [2,3,4,5,6,8,1,7] => 0 = 3 - 3
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [2,3,4,5,6,8,1,7] => 0 = 3 - 3
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [2,3,4,5,6,8,1,7] => 0 = 3 - 3
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [2,3,4,5,6,8,1,7] => 0 = 3 - 3
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [2,3,4,5,6,8,1,7] => 0 = 3 - 3
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [2,3,4,5,6,8,1,7] => 0 = 3 - 3
([(5,6)],7)
 => [2,1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
 => [8,1,4,5,6,7,2,3] => ? = 2 - 3
([(4,6),(5,6)],7)
 => [3,1,1,1,1]
 => [1,0,1,1,1,1,0,0,1,0,0,0]
 => [3,1,7,5,6,2,4] => ? = 3 - 3
([(3,6),(4,6),(5,6)],7)
 => [4,1,1,1]
 => [1,0,1,1,1,0,0,0,1,0]
 => [3,1,4,6,2,5] => 0 = 3 - 3
([(2,6),(3,6),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1,1,0,1,1,0,0,0,0,1,0]
 => [5,3,4,1,7,2,6] => ? = 3 - 3
([(3,6),(4,5)],7)
 => [2,2,1,1,1]
 => [1,0,1,1,1,0,1,1,0,0,0,0]
 => [6,1,4,5,2,7,3] => ? = 3 - 3
([(3,6),(4,5),(5,6)],7)
 => [4,1,1,1]
 => [1,0,1,1,1,0,0,0,1,0]
 => [3,1,4,6,2,5] => 0 = 3 - 3
([(2,3),(4,6),(5,6)],7)
 => [3,2,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [6,1,5,2,3,4] => 0 = 3 - 3
([(4,5),(4,6),(5,6)],7)
 => [3,1,1,1,1]
 => [1,0,1,1,1,1,0,0,1,0,0,0]
 => [3,1,7,5,6,2,4] => ? = 3 - 3
([(2,6),(3,6),(4,5),(5,6)],7)
 => [5,1,1]
 => [1,1,1,0,1,1,0,0,0,0,1,0]
 => [5,3,4,1,7,2,6] => ? = 3 - 3
([(1,2),(3,6),(4,6),(5,6)],7)
 => [4,2,1]
 => [1,1,0,1,0,1,0,0,1,0]
 => [6,4,1,2,3,5] => 0 = 3 - 3
([(3,6),(4,5),(4,6),(5,6)],7)
 => [4,1,1,1]
 => [1,0,1,1,1,0,0,0,1,0]
 => [3,1,4,6,2,5] => 0 = 3 - 3
([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [8,3,4,5,6,1,2,7] => ? = 3 - 3
([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1,1,0,1,1,0,0,0,0,1,0]
 => [5,3,4,1,7,2,6] => ? = 3 - 3
([(1,6),(2,6),(3,5),(4,5)],7)
 => [3,3,1]
 => [1,1,0,1,0,0,1,1,0,0]
 => [5,3,1,2,6,4] => 0 = 3 - 3
([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [8,3,4,5,6,1,2,7] => ? = 3 - 3
([(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [4,1,1,1]
 => [1,0,1,1,1,0,0,0,1,0]
 => [3,1,4,6,2,5] => 0 = 3 - 3
([(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1,1,0,1,1,0,0,0,0,1,0]
 => [5,3,4,1,7,2,6] => ? = 3 - 3
([(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [8,3,4,5,6,1,2,7] => ? = 3 - 3
([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1,1,0,1,1,0,0,0,0,1,0]
 => [5,3,4,1,7,2,6] => ? = 3 - 3
([(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [8,3,4,5,6,1,2,7] => ? = 3 - 3
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1,1,0,1,1,0,0,0,0,1,0]
 => [5,3,4,1,7,2,6] => ? = 3 - 3
([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [8,3,4,5,6,1,2,7] => ? = 3 - 3
([(1,6),(2,5),(3,4)],7)
 => [2,2,2,1]
 => [1,0,1,0,1,1,1,0,0,0]
 => [4,1,2,5,6,3] => 0 = 3 - 3
([(2,6),(3,5),(4,5),(4,6)],7)
 => [5,1,1]
 => [1,1,1,0,1,1,0,0,0,0,1,0]
 => [5,3,4,1,7,2,6] => ? = 3 - 3
([(1,2),(3,6),(4,5),(5,6)],7)
 => [4,2,1]
 => [1,1,0,1,0,1,0,0,1,0]
 => [6,4,1,2,3,5] => 0 = 3 - 3
([(0,3),(1,2),(4,6),(5,6)],7)
 => [3,2,2]
 => [1,1,0,0,1,1,0,1,0,0]
 => [2,6,1,5,3,4] => 0 = 3 - 3
([(2,3),(4,5),(4,6),(5,6)],7)
 => [3,2,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [6,1,5,2,3,4] => 0 = 3 - 3
([(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [8,3,4,5,6,1,2,7] => ? = 3 - 3
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
 => [5,2]
 => [1,1,1,1,0,0,1,0,0,0,1,0]
 => [2,7,4,5,1,3,6] => ? = 3 - 3
([(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1,1,0,1,1,0,0,0,0,1,0]
 => [5,3,4,1,7,2,6] => ? = 3 - 3
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
 => [4,2,1]
 => [1,1,0,1,0,1,0,0,1,0]
 => [6,4,1,2,3,5] => 0 = 3 - 3
([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => [7]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
 => [2,3,4,5,6,7,9,1,8] => 0 = 3 - 3
([(1,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [8,3,4,5,6,1,2,7] => ? = 3 - 3
([(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1,1,0,1,1,0,0,0,0,1,0]
 => [5,3,4,1,7,2,6] => ? = 3 - 3
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
 => [7]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
 => [2,3,4,5,6,7,9,1,8] => 0 = 3 - 3
([(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1,1,0,1,1,0,0,0,0,1,0]
 => [5,3,4,1,7,2,6] => ? = 3 - 3
([(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1,1,0,1,1,0,0,0,0,1,0]
 => [5,3,4,1,7,2,6] => ? = 3 - 3
([(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [8,3,4,5,6,1,2,7] => ? = 3 - 3
([(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [8,3,4,5,6,1,2,7] => ? = 3 - 3
([(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [8,3,4,5,6,1,2,7] => ? = 3 - 3
([(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1,1,0,1,1,0,0,0,0,1,0]
 => [5,3,4,1,7,2,6] => ? = 3 - 3
([(1,6),(2,5),(3,4),(3,5),(4,6)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [8,3,4,5,6,1,2,7] => ? = 3 - 3
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => [5,2]
 => [1,1,1,1,0,0,1,0,0,0,1,0]
 => [2,7,4,5,1,3,6] => ? = 3 - 3
([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [8,3,4,5,6,1,2,7] => ? = 3 - 3
([(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [8,3,4,5,6,1,2,7] => ? = 3 - 3
([(0,1),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [5,2]
 => [1,1,1,1,0,0,1,0,0,0,1,0]
 => [2,7,4,5,1,3,6] => ? = 3 - 3
([(1,5),(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [8,3,4,5,6,1,2,7] => ? = 3 - 3
([(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [8,3,4,5,6,1,2,7] => ? = 3 - 3
([(1,4),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [8,3,4,5,6,1,2,7] => ? = 3 - 3
([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [8,3,4,5,6,1,2,7] => ? = 3 - 3
([(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [8,3,4,5,6,1,2,7] => ? = 3 - 3
([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1,1,0,1,1,0,0,0,0,1,0]
 => [5,3,4,1,7,2,6] => ? = 3 - 3
Description
The number of fixed points of a permutation.
Matching statistic: St000153
Mapping
Mp00037: Graphs —to partition of connected components⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
St000153: Permutations ⟶ ℤResult quality: 50% ●values known / values provided: 63%●distinct values known / distinct values provided: 50%
Values
([],3)
 => [1,1,1]
 => [1,0,1,1,1,0,0,0]
 => [3,1,4,5,2] => 0 = 3 - 3
([],4)
 => [1,1,1,1]
 => [1,0,1,1,1,1,0,0,0,0]
 => [3,1,4,5,6,2] => 0 = 3 - 3
([(2,3)],4)
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [5,1,4,2,3] => 0 = 3 - 3
([],5)
 => [1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [3,1,4,5,6,7,2] => ? = 3 - 3
([(3,4)],5)
 => [2,1,1,1]
 => [1,0,1,1,1,0,1,0,0,0]
 => [6,1,4,5,2,3] => 0 = 3 - 3
([(2,4),(3,4)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [3,1,5,2,4] => 0 = 3 - 3
([(1,4),(2,3)],5)
 => [2,2,1]
 => [1,0,1,0,1,1,0,0]
 => [4,1,2,5,3] => 0 = 3 - 3
([(1,4),(2,3),(3,4)],5)
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [6,3,4,1,2,5] => 0 = 3 - 3
([(2,3),(2,4),(3,4)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [3,1,5,2,4] => 0 = 3 - 3
([(1,3),(1,4),(2,3),(2,4)],5)
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [6,3,4,1,2,5] => 0 = 3 - 3
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => [5]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => [2,3,4,5,7,1,6] => 0 = 3 - 3
([],6)
 => [1,1,1,1,1,1]
 => [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => [3,1,4,5,6,7,8,2] => ? = 2 - 3
([(4,5)],6)
 => [2,1,1,1,1]
 => [1,0,1,1,1,1,0,1,0,0,0,0]
 => [7,1,4,5,6,2,3] => ? = 3 - 3
([(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [3,1,6,5,2,4] => 0 = 3 - 3
([(2,5),(3,5),(4,5)],6)
 => [4,1,1]
 => [1,1,0,1,1,0,0,0,1,0]
 => [4,3,1,6,2,5] => 0 = 3 - 3
([(2,5),(3,4)],6)
 => [2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => [5,1,4,2,6,3] => 0 = 3 - 3
([(2,5),(3,4),(4,5)],6)
 => [4,1,1]
 => [1,1,0,1,1,0,0,0,1,0]
 => [4,3,1,6,2,5] => 0 = 3 - 3
([(1,2),(3,5),(4,5)],6)
 => [3,2,1]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 0 = 3 - 3
([(3,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [3,1,6,5,2,4] => 0 = 3 - 3
([(1,5),(2,5),(3,4),(4,5)],6)
 => [5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => [7,3,4,5,1,2,6] => ? = 3 - 3
([(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1,1]
 => [1,1,0,1,1,0,0,0,1,0]
 => [4,3,1,6,2,5] => 0 = 3 - 3
([(2,4),(2,5),(3,4),(3,5)],6)
 => [4,1,1]
 => [1,1,0,1,1,0,0,0,1,0]
 => [4,3,1,6,2,5] => 0 = 3 - 3
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => [7,3,4,5,1,2,6] => ? = 3 - 3
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1,1]
 => [1,1,0,1,1,0,0,0,1,0]
 => [4,3,1,6,2,5] => 0 = 3 - 3
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => [7,3,4,5,1,2,6] => ? = 3 - 3
([(0,5),(1,4),(2,3)],6)
 => [2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => [2,4,1,5,6,3] => 0 = 3 - 3
([(1,5),(2,4),(3,4),(3,5)],6)
 => [5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => [7,3,4,5,1,2,6] => ? = 3 - 3
([(0,1),(2,5),(3,4),(4,5)],6)
 => [4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [2,6,4,1,3,5] => 0 = 3 - 3
([(1,2),(3,4),(3,5),(4,5)],6)
 => [3,2,1]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 0 = 3 - 3
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [2,3,4,5,6,8,1,7] => 0 = 3 - 3
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => [5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => [7,3,4,5,1,2,6] => ? = 3 - 3
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => [5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => [7,3,4,5,1,2,6] => ? = 2 - 3
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [2,3,4,5,6,8,1,7] => 0 = 3 - 3
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => [7,3,4,5,1,2,6] => ? = 3 - 3
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [2,3,4,5,6,8,1,7] => 0 = 3 - 3
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => [7,3,4,5,1,2,6] => ? = 3 - 3
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [2,3,4,5,6,8,1,7] => 0 = 3 - 3
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [2,3,4,5,6,8,1,7] => 0 = 3 - 3
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => [4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [2,6,4,1,3,5] => 0 = 3 - 3
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [2,3,4,5,6,8,1,7] => 0 = 3 - 3
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1,1]
 => [1,1,0,1,1,0,0,0,1,0]
 => [4,3,1,6,2,5] => 0 = 3 - 3
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => [5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => [7,3,4,5,1,2,6] => ? = 3 - 3
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [2,3,4,5,6,8,1,7] => 0 = 3 - 3
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [2,3,4,5,6,8,1,7] => 0 = 3 - 3
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [2,3,4,5,6,8,1,7] => 0 = 3 - 3
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [2,3,4,5,6,8,1,7] => 0 = 3 - 3
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [2,3,4,5,6,8,1,7] => 0 = 3 - 3
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [2,3,4,5,6,8,1,7] => 0 = 3 - 3
([(5,6)],7)
 => [2,1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
 => [8,1,4,5,6,7,2,3] => ? = 2 - 3
([(4,6),(5,6)],7)
 => [3,1,1,1,1]
 => [1,0,1,1,1,1,0,0,1,0,0,0]
 => [3,1,7,5,6,2,4] => ? = 3 - 3
([(3,6),(4,6),(5,6)],7)
 => [4,1,1,1]
 => [1,0,1,1,1,0,0,0,1,0]
 => [3,1,4,6,2,5] => 0 = 3 - 3
([(2,6),(3,6),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1,1,0,1,1,0,0,0,0,1,0]
 => [5,3,4,1,7,2,6] => ? = 3 - 3
([(3,6),(4,5)],7)
 => [2,2,1,1,1]
 => [1,0,1,1,1,0,1,1,0,0,0,0]
 => [6,1,4,5,2,7,3] => ? = 3 - 3
([(3,6),(4,5),(5,6)],7)
 => [4,1,1,1]
 => [1,0,1,1,1,0,0,0,1,0]
 => [3,1,4,6,2,5] => 0 = 3 - 3
([(2,3),(4,6),(5,6)],7)
 => [3,2,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [6,1,5,2,3,4] => 0 = 3 - 3
([(4,5),(4,6),(5,6)],7)
 => [3,1,1,1,1]
 => [1,0,1,1,1,1,0,0,1,0,0,0]
 => [3,1,7,5,6,2,4] => ? = 3 - 3
([(2,6),(3,6),(4,5),(5,6)],7)
 => [5,1,1]
 => [1,1,1,0,1,1,0,0,0,0,1,0]
 => [5,3,4,1,7,2,6] => ? = 3 - 3
([(1,2),(3,6),(4,6),(5,6)],7)
 => [4,2,1]
 => [1,1,0,1,0,1,0,0,1,0]
 => [6,4,1,2,3,5] => 0 = 3 - 3
([(3,6),(4,5),(4,6),(5,6)],7)
 => [4,1,1,1]
 => [1,0,1,1,1,0,0,0,1,0]
 => [3,1,4,6,2,5] => 0 = 3 - 3
([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [8,3,4,5,6,1,2,7] => ? = 3 - 3
([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1,1,0,1,1,0,0,0,0,1,0]
 => [5,3,4,1,7,2,6] => ? = 3 - 3
([(1,6),(2,6),(3,5),(4,5)],7)
 => [3,3,1]
 => [1,1,0,1,0,0,1,1,0,0]
 => [5,3,1,2,6,4] => 0 = 3 - 3
([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [8,3,4,5,6,1,2,7] => ? = 3 - 3
([(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [4,1,1,1]
 => [1,0,1,1,1,0,0,0,1,0]
 => [3,1,4,6,2,5] => 0 = 3 - 3
([(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1,1,0,1,1,0,0,0,0,1,0]
 => [5,3,4,1,7,2,6] => ? = 3 - 3
([(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [8,3,4,5,6,1,2,7] => ? = 3 - 3
([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1,1,0,1,1,0,0,0,0,1,0]
 => [5,3,4,1,7,2,6] => ? = 3 - 3
([(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [8,3,4,5,6,1,2,7] => ? = 3 - 3
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1,1,0,1,1,0,0,0,0,1,0]
 => [5,3,4,1,7,2,6] => ? = 3 - 3
([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [8,3,4,5,6,1,2,7] => ? = 3 - 3
([(1,6),(2,5),(3,4)],7)
 => [2,2,2,1]
 => [1,0,1,0,1,1,1,0,0,0]
 => [4,1,2,5,6,3] => 0 = 3 - 3
([(2,6),(3,5),(4,5),(4,6)],7)
 => [5,1,1]
 => [1,1,1,0,1,1,0,0,0,0,1,0]
 => [5,3,4,1,7,2,6] => ? = 3 - 3
([(1,2),(3,6),(4,5),(5,6)],7)
 => [4,2,1]
 => [1,1,0,1,0,1,0,0,1,0]
 => [6,4,1,2,3,5] => 0 = 3 - 3
([(0,3),(1,2),(4,6),(5,6)],7)
 => [3,2,2]
 => [1,1,0,0,1,1,0,1,0,0]
 => [2,6,1,5,3,4] => 0 = 3 - 3
([(2,3),(4,5),(4,6),(5,6)],7)
 => [3,2,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [6,1,5,2,3,4] => 0 = 3 - 3
([(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [8,3,4,5,6,1,2,7] => ? = 3 - 3
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
 => [5,2]
 => [1,1,1,1,0,0,1,0,0,0,1,0]
 => [2,7,4,5,1,3,6] => ? = 3 - 3
([(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1,1,0,1,1,0,0,0,0,1,0]
 => [5,3,4,1,7,2,6] => ? = 3 - 3
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
 => [4,2,1]
 => [1,1,0,1,0,1,0,0,1,0]
 => [6,4,1,2,3,5] => 0 = 3 - 3
([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => [7]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
 => [2,3,4,5,6,7,9,1,8] => 0 = 3 - 3
([(1,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [8,3,4,5,6,1,2,7] => ? = 3 - 3
([(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1,1,0,1,1,0,0,0,0,1,0]
 => [5,3,4,1,7,2,6] => ? = 3 - 3
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
 => [7]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
 => [2,3,4,5,6,7,9,1,8] => 0 = 3 - 3
([(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1,1,0,1,1,0,0,0,0,1,0]
 => [5,3,4,1,7,2,6] => ? = 3 - 3
([(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1,1,0,1,1,0,0,0,0,1,0]
 => [5,3,4,1,7,2,6] => ? = 3 - 3
([(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [8,3,4,5,6,1,2,7] => ? = 3 - 3
([(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [8,3,4,5,6,1,2,7] => ? = 3 - 3
([(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [8,3,4,5,6,1,2,7] => ? = 3 - 3
([(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1,1,0,1,1,0,0,0,0,1,0]
 => [5,3,4,1,7,2,6] => ? = 3 - 3
([(1,6),(2,5),(3,4),(3,5),(4,6)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [8,3,4,5,6,1,2,7] => ? = 3 - 3
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => [5,2]
 => [1,1,1,1,0,0,1,0,0,0,1,0]
 => [2,7,4,5,1,3,6] => ? = 3 - 3
([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [8,3,4,5,6,1,2,7] => ? = 3 - 3
([(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [8,3,4,5,6,1,2,7] => ? = 3 - 3
([(0,1),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [5,2]
 => [1,1,1,1,0,0,1,0,0,0,1,0]
 => [2,7,4,5,1,3,6] => ? = 3 - 3
([(1,5),(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [8,3,4,5,6,1,2,7] => ? = 3 - 3
([(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [8,3,4,5,6,1,2,7] => ? = 3 - 3
([(1,4),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [8,3,4,5,6,1,2,7] => ? = 3 - 3
([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [8,3,4,5,6,1,2,7] => ? = 3 - 3
([(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [8,3,4,5,6,1,2,7] => ? = 3 - 3
([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1,1,0,1,1,0,0,0,0,1,0]
 => [5,3,4,1,7,2,6] => ? = 3 - 3
Description
The number of adjacent cycles of a permutation. This is the number of cycles of the permutation of the form (i,i+1,i+2,...i+k) which includes the fixed points (i).
Matching statistic: St001465
Mapping
Mp00037: Graphs —to partition of connected components⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
St001465: Permutations ⟶ ℤResult quality: 50% ●values known / values provided: 63%●distinct values known / distinct values provided: 50%
Values
([],3)
 => [1,1,1]
 => [1,0,1,1,1,0,0,0]
 => [3,1,4,5,2] => 0 = 3 - 3
([],4)
 => [1,1,1,1]
 => [1,0,1,1,1,1,0,0,0,0]
 => [3,1,4,5,6,2] => 0 = 3 - 3
([(2,3)],4)
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [5,1,4,2,3] => 0 = 3 - 3
([],5)
 => [1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [3,1,4,5,6,7,2] => ? = 3 - 3
([(3,4)],5)
 => [2,1,1,1]
 => [1,0,1,1,1,0,1,0,0,0]
 => [6,1,4,5,2,3] => 0 = 3 - 3
([(2,4),(3,4)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [3,1,5,2,4] => 0 = 3 - 3
([(1,4),(2,3)],5)
 => [2,2,1]
 => [1,0,1,0,1,1,0,0]
 => [4,1,2,5,3] => 0 = 3 - 3
([(1,4),(2,3),(3,4)],5)
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [6,3,4,1,2,5] => 0 = 3 - 3
([(2,3),(2,4),(3,4)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [3,1,5,2,4] => 0 = 3 - 3
([(1,3),(1,4),(2,3),(2,4)],5)
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [6,3,4,1,2,5] => 0 = 3 - 3
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => [5]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => [2,3,4,5,7,1,6] => 0 = 3 - 3
([],6)
 => [1,1,1,1,1,1]
 => [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => [3,1,4,5,6,7,8,2] => ? = 2 - 3
([(4,5)],6)
 => [2,1,1,1,1]
 => [1,0,1,1,1,1,0,1,0,0,0,0]
 => [7,1,4,5,6,2,3] => ? = 3 - 3
([(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [3,1,6,5,2,4] => 0 = 3 - 3
([(2,5),(3,5),(4,5)],6)
 => [4,1,1]
 => [1,1,0,1,1,0,0,0,1,0]
 => [4,3,1,6,2,5] => 0 = 3 - 3
([(2,5),(3,4)],6)
 => [2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => [5,1,4,2,6,3] => 0 = 3 - 3
([(2,5),(3,4),(4,5)],6)
 => [4,1,1]
 => [1,1,0,1,1,0,0,0,1,0]
 => [4,3,1,6,2,5] => 0 = 3 - 3
([(1,2),(3,5),(4,5)],6)
 => [3,2,1]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 0 = 3 - 3
([(3,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [3,1,6,5,2,4] => 0 = 3 - 3
([(1,5),(2,5),(3,4),(4,5)],6)
 => [5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => [7,3,4,5,1,2,6] => ? = 3 - 3
([(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1,1]
 => [1,1,0,1,1,0,0,0,1,0]
 => [4,3,1,6,2,5] => 0 = 3 - 3
([(2,4),(2,5),(3,4),(3,5)],6)
 => [4,1,1]
 => [1,1,0,1,1,0,0,0,1,0]
 => [4,3,1,6,2,5] => 0 = 3 - 3
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => [7,3,4,5,1,2,6] => ? = 3 - 3
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1,1]
 => [1,1,0,1,1,0,0,0,1,0]
 => [4,3,1,6,2,5] => 0 = 3 - 3
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => [7,3,4,5,1,2,6] => ? = 3 - 3
([(0,5),(1,4),(2,3)],6)
 => [2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => [2,4,1,5,6,3] => 0 = 3 - 3
([(1,5),(2,4),(3,4),(3,5)],6)
 => [5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => [7,3,4,5,1,2,6] => ? = 3 - 3
([(0,1),(2,5),(3,4),(4,5)],6)
 => [4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [2,6,4,1,3,5] => 0 = 3 - 3
([(1,2),(3,4),(3,5),(4,5)],6)
 => [3,2,1]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 0 = 3 - 3
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [2,3,4,5,6,8,1,7] => 0 = 3 - 3
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => [5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => [7,3,4,5,1,2,6] => ? = 3 - 3
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => [5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => [7,3,4,5,1,2,6] => ? = 2 - 3
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [2,3,4,5,6,8,1,7] => 0 = 3 - 3
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => [7,3,4,5,1,2,6] => ? = 3 - 3
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [2,3,4,5,6,8,1,7] => 0 = 3 - 3
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => [7,3,4,5,1,2,6] => ? = 3 - 3
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [2,3,4,5,6,8,1,7] => 0 = 3 - 3
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [2,3,4,5,6,8,1,7] => 0 = 3 - 3
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => [4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [2,6,4,1,3,5] => 0 = 3 - 3
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [2,3,4,5,6,8,1,7] => 0 = 3 - 3
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1,1]
 => [1,1,0,1,1,0,0,0,1,0]
 => [4,3,1,6,2,5] => 0 = 3 - 3
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => [5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => [7,3,4,5,1,2,6] => ? = 3 - 3
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [2,3,4,5,6,8,1,7] => 0 = 3 - 3
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [2,3,4,5,6,8,1,7] => 0 = 3 - 3
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [2,3,4,5,6,8,1,7] => 0 = 3 - 3
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [2,3,4,5,6,8,1,7] => 0 = 3 - 3
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [2,3,4,5,6,8,1,7] => 0 = 3 - 3
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [2,3,4,5,6,8,1,7] => 0 = 3 - 3
([(5,6)],7)
 => [2,1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
 => [8,1,4,5,6,7,2,3] => ? = 2 - 3
([(4,6),(5,6)],7)
 => [3,1,1,1,1]
 => [1,0,1,1,1,1,0,0,1,0,0,0]
 => [3,1,7,5,6,2,4] => ? = 3 - 3
([(3,6),(4,6),(5,6)],7)
 => [4,1,1,1]
 => [1,0,1,1,1,0,0,0,1,0]
 => [3,1,4,6,2,5] => 0 = 3 - 3
([(2,6),(3,6),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1,1,0,1,1,0,0,0,0,1,0]
 => [5,3,4,1,7,2,6] => ? = 3 - 3
([(3,6),(4,5)],7)
 => [2,2,1,1,1]
 => [1,0,1,1,1,0,1,1,0,0,0,0]
 => [6,1,4,5,2,7,3] => ? = 3 - 3
([(3,6),(4,5),(5,6)],7)
 => [4,1,1,1]
 => [1,0,1,1,1,0,0,0,1,0]
 => [3,1,4,6,2,5] => 0 = 3 - 3
([(2,3),(4,6),(5,6)],7)
 => [3,2,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [6,1,5,2,3,4] => 0 = 3 - 3
([(4,5),(4,6),(5,6)],7)
 => [3,1,1,1,1]
 => [1,0,1,1,1,1,0,0,1,0,0,0]
 => [3,1,7,5,6,2,4] => ? = 3 - 3
([(2,6),(3,6),(4,5),(5,6)],7)
 => [5,1,1]
 => [1,1,1,0,1,1,0,0,0,0,1,0]
 => [5,3,4,1,7,2,6] => ? = 3 - 3
([(1,2),(3,6),(4,6),(5,6)],7)
 => [4,2,1]
 => [1,1,0,1,0,1,0,0,1,0]
 => [6,4,1,2,3,5] => 0 = 3 - 3
([(3,6),(4,5),(4,6),(5,6)],7)
 => [4,1,1,1]
 => [1,0,1,1,1,0,0,0,1,0]
 => [3,1,4,6,2,5] => 0 = 3 - 3
([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [8,3,4,5,6,1,2,7] => ? = 3 - 3
([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1,1,0,1,1,0,0,0,0,1,0]
 => [5,3,4,1,7,2,6] => ? = 3 - 3
([(1,6),(2,6),(3,5),(4,5)],7)
 => [3,3,1]
 => [1,1,0,1,0,0,1,1,0,0]
 => [5,3,1,2,6,4] => 0 = 3 - 3
([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [8,3,4,5,6,1,2,7] => ? = 3 - 3
([(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [4,1,1,1]
 => [1,0,1,1,1,0,0,0,1,0]
 => [3,1,4,6,2,5] => 0 = 3 - 3
([(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1,1,0,1,1,0,0,0,0,1,0]
 => [5,3,4,1,7,2,6] => ? = 3 - 3
([(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [8,3,4,5,6,1,2,7] => ? = 3 - 3
([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1,1,0,1,1,0,0,0,0,1,0]
 => [5,3,4,1,7,2,6] => ? = 3 - 3
([(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [8,3,4,5,6,1,2,7] => ? = 3 - 3
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1,1,0,1,1,0,0,0,0,1,0]
 => [5,3,4,1,7,2,6] => ? = 3 - 3
([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [8,3,4,5,6,1,2,7] => ? = 3 - 3
([(1,6),(2,5),(3,4)],7)
 => [2,2,2,1]
 => [1,0,1,0,1,1,1,0,0,0]
 => [4,1,2,5,6,3] => 0 = 3 - 3
([(2,6),(3,5),(4,5),(4,6)],7)
 => [5,1,1]
 => [1,1,1,0,1,1,0,0,0,0,1,0]
 => [5,3,4,1,7,2,6] => ? = 3 - 3
([(1,2),(3,6),(4,5),(5,6)],7)
 => [4,2,1]
 => [1,1,0,1,0,1,0,0,1,0]
 => [6,4,1,2,3,5] => 0 = 3 - 3
([(0,3),(1,2),(4,6),(5,6)],7)
 => [3,2,2]
 => [1,1,0,0,1,1,0,1,0,0]
 => [2,6,1,5,3,4] => 0 = 3 - 3
([(2,3),(4,5),(4,6),(5,6)],7)
 => [3,2,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [6,1,5,2,3,4] => 0 = 3 - 3
([(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [8,3,4,5,6,1,2,7] => ? = 3 - 3
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
 => [5,2]
 => [1,1,1,1,0,0,1,0,0,0,1,0]
 => [2,7,4,5,1,3,6] => ? = 3 - 3
([(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1,1,0,1,1,0,0,0,0,1,0]
 => [5,3,4,1,7,2,6] => ? = 3 - 3
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
 => [4,2,1]
 => [1,1,0,1,0,1,0,0,1,0]
 => [6,4,1,2,3,5] => 0 = 3 - 3
([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => [7]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
 => [2,3,4,5,6,7,9,1,8] => 0 = 3 - 3
([(1,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [8,3,4,5,6,1,2,7] => ? = 3 - 3
([(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1,1,0,1,1,0,0,0,0,1,0]
 => [5,3,4,1,7,2,6] => ? = 3 - 3
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
 => [7]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
 => [2,3,4,5,6,7,9,1,8] => 0 = 3 - 3
([(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1,1,0,1,1,0,0,0,0,1,0]
 => [5,3,4,1,7,2,6] => ? = 3 - 3
([(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1,1,0,1,1,0,0,0,0,1,0]
 => [5,3,4,1,7,2,6] => ? = 3 - 3
([(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [8,3,4,5,6,1,2,7] => ? = 3 - 3
([(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [8,3,4,5,6,1,2,7] => ? = 3 - 3
([(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [8,3,4,5,6,1,2,7] => ? = 3 - 3
([(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1,1,0,1,1,0,0,0,0,1,0]
 => [5,3,4,1,7,2,6] => ? = 3 - 3
([(1,6),(2,5),(3,4),(3,5),(4,6)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [8,3,4,5,6,1,2,7] => ? = 3 - 3
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => [5,2]
 => [1,1,1,1,0,0,1,0,0,0,1,0]
 => [2,7,4,5,1,3,6] => ? = 3 - 3
([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [8,3,4,5,6,1,2,7] => ? = 3 - 3
([(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [8,3,4,5,6,1,2,7] => ? = 3 - 3
([(0,1),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => [5,2]
 => [1,1,1,1,0,0,1,0,0,0,1,0]
 => [2,7,4,5,1,3,6] => ? = 3 - 3
([(1,5),(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [8,3,4,5,6,1,2,7] => ? = 3 - 3
([(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [8,3,4,5,6,1,2,7] => ? = 3 - 3
([(1,4),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [8,3,4,5,6,1,2,7] => ? = 3 - 3
([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [8,3,4,5,6,1,2,7] => ? = 3 - 3
([(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => [6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [8,3,4,5,6,1,2,7] => ? = 3 - 3
([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => [5,1,1]
 => [1,1,1,0,1,1,0,0,0,0,1,0]
 => [5,3,4,1,7,2,6] => ? = 3 - 3
Description
The number of adjacent transpositions in the cycle decomposition of a permutation.
Matching statistic: St000287
(load all 5 compositions to match this statistic)
Mapping
Mp00250: Graphs —clique graph⟶ Graphs
Mp00203: Graphs —cone⟶ Graphs
St000287: Graphs ⟶ ℤResult quality: 50% ●values known / values provided: 56%●distinct values known / distinct values provided: 50%
Values
([],3)
 => ([],3)
 => ([(0,3),(1,3),(2,3)],4)
 => 1 = 3 - 2
([],4)
 => ([],4)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 1 = 3 - 2
([(2,3)],4)
 => ([],3)
 => ([(0,3),(1,3),(2,3)],4)
 => 1 = 3 - 2
([],5)
 => ([],5)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 1 = 3 - 2
([(3,4)],5)
 => ([],4)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 1 = 3 - 2
([(2,4),(3,4)],5)
 => ([(2,3)],4)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 3 - 2
([(1,4),(2,3)],5)
 => ([],3)
 => ([(0,3),(1,3),(2,3)],4)
 => 1 = 3 - 2
([(1,4),(2,3),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 3 - 2
([(2,3),(2,4),(3,4)],5)
 => ([],3)
 => ([(0,3),(1,3),(2,3)],4)
 => 1 = 3 - 2
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 1 = 3 - 2
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => 1 = 3 - 2
([],6)
 => ([],6)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ? = 2 - 2
([(4,5)],6)
 => ([],5)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 1 = 3 - 2
([(3,5),(4,5)],6)
 => ([(3,4)],5)
 => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 3 - 2
([(2,5),(3,5),(4,5)],6)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 3 - 2
([(2,5),(3,4)],6)
 => ([],4)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 1 = 3 - 2
([(2,5),(3,4),(4,5)],6)
 => ([(2,4),(3,4)],5)
 => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 3 - 2
([(1,2),(3,5),(4,5)],6)
 => ([(2,3)],4)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 3 - 2
([(3,4),(3,5),(4,5)],6)
 => ([],4)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 1 = 3 - 2
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 3 - 2
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,3)],4)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 3 - 2
([(2,4),(2,5),(3,4),(3,5)],6)
 => ([(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 3 - 2
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,6),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 2
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,3)],4)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 3 - 2
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 3 - 2
([(0,5),(1,4),(2,3)],6)
 => ([],3)
 => ([(0,3),(1,3),(2,3)],4)
 => 1 = 3 - 2
([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 3 - 2
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 3 - 2
([(1,2),(3,4),(3,5),(4,5)],6)
 => ([],3)
 => ([(0,3),(1,3),(2,3)],4)
 => 1 = 3 - 2
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 3 - 2
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 3 - 2
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ? = 2 - 2
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 2
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 1 = 3 - 2
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 2
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 3 - 2
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 3 - 2
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 1 = 3 - 2
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 1 = 3 - 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),(0,6),(1,2),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 2
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],3)
 => ([(0,3),(1,3),(2,3)],4)
 => 1 = 3 - 2
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 1 = 3 - 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),(0,6),(1,2),(1,3),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ? = 3 - 2
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 3 - 2
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => 1 = 3 - 2
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],6)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],6)
 => ([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ? = 3 - 2
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => 1 = 3 - 2
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 1 = 3 - 2
([(5,6)],7)
 => ([],6)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ? = 2 - 2
([(4,6),(5,6)],7)
 => ([(4,5)],6)
 => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 2
([(3,6),(4,6),(5,6)],7)
 => ([(3,4),(3,5),(4,5)],6)
 => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 2
([(2,6),(3,6),(4,6),(5,6)],7)
 => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 2
([(3,6),(4,5)],7)
 => ([],5)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 1 = 3 - 2
([(3,6),(4,5),(5,6)],7)
 => ([(3,5),(4,5)],6)
 => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 2
([(2,3),(4,6),(5,6)],7)
 => ([(3,4)],5)
 => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 3 - 2
([(4,5),(4,6),(5,6)],7)
 => ([],5)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 1 = 3 - 2
([(2,6),(3,6),(4,5),(5,6)],7)
 => ([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 2
([(1,2),(3,6),(4,6),(5,6)],7)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 3 - 2
([(3,6),(4,5),(4,6),(5,6)],7)
 => ([(3,4)],5)
 => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 3 - 2
([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 2
([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 3 - 2
([(1,6),(2,6),(3,5),(4,5)],7)
 => ([(1,4),(2,3)],5)
 => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => 1 = 3 - 2
([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,6),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 2
([(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(3,4)],5)
 => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 3 - 2
([(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(2,4),(3,4)],5)
 => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 3 - 2
([(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 2
([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 3 - 2
([(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 3 - 2
([(2,6),(3,5),(4,5),(4,6)],7)
 => ([(2,5),(3,4),(4,5)],6)
 => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 2
([(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 2
([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 2
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
 => ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
 => ([(0,4),(0,6),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 3 - 2
([(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 3 - 2
([(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,6),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 2
([(1,6),(2,5),(3,4),(3,5),(4,6)],7)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 3 - 2
([(1,2),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 3 - 2
([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
 => ([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,6),(1,2),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 2
([(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)
 => ([(0,6),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 2
([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,6),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 2
([(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,6),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 2
([(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 3 - 2
([(0,6),(1,5),(2,3),(2,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 2
([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,6),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 2
([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 3 - 2
([(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,6),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 2
([(0,6),(1,6),(2,3),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,6),(1,2),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 2
([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 2
([(1,6),(2,3),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 2
([(1,2),(1,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ? = 2 - 2
([(1,6),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,6),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 2
([(1,2),(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,6),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 2
([(0,6),(1,4),(2,3),(2,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(0,6),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 2
([(0,6),(1,2),(1,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 2
([(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 2
([(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),(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 3 - 2
([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 2
([(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,6),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 2
([(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,6),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 2
([(0,6),(1,5),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 2
([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5)],7)
 => ([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 2
Description
The number of connected components of a graph.
Matching statistic: St000315
(load all 4 compositions to match this statistic)
Mapping
Mp00250: Graphs —clique graph⟶ Graphs
Mp00203: Graphs —cone⟶ Graphs
St000315: Graphs ⟶ ℤResult quality: 50% ●values known / values provided: 56%●distinct values known / distinct values provided: 50%
Values
([],3)
 => ([],3)
 => ([(0,3),(1,3),(2,3)],4)
 => 0 = 3 - 3
([],4)
 => ([],4)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 0 = 3 - 3
([(2,3)],4)
 => ([],3)
 => ([(0,3),(1,3),(2,3)],4)
 => 0 = 3 - 3
([],5)
 => ([],5)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 0 = 3 - 3
([(3,4)],5)
 => ([],4)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 0 = 3 - 3
([(2,4),(3,4)],5)
 => ([(2,3)],4)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 0 = 3 - 3
([(1,4),(2,3)],5)
 => ([],3)
 => ([(0,3),(1,3),(2,3)],4)
 => 0 = 3 - 3
([(1,4),(2,3),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 0 = 3 - 3
([(2,3),(2,4),(3,4)],5)
 => ([],3)
 => ([(0,3),(1,3),(2,3)],4)
 => 0 = 3 - 3
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 0 = 3 - 3
([(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),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => 0 = 3 - 3
([],6)
 => ([],6)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ? = 2 - 3
([(4,5)],6)
 => ([],5)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 0 = 3 - 3
([(3,5),(4,5)],6)
 => ([(3,4)],5)
 => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 0 = 3 - 3
([(2,5),(3,5),(4,5)],6)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 0 = 3 - 3
([(2,5),(3,4)],6)
 => ([],4)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 0 = 3 - 3
([(2,5),(3,4),(4,5)],6)
 => ([(2,4),(3,4)],5)
 => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 0 = 3 - 3
([(1,2),(3,5),(4,5)],6)
 => ([(2,3)],4)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 0 = 3 - 3
([(3,4),(3,5),(4,5)],6)
 => ([],4)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 0 = 3 - 3
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 0 = 3 - 3
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,3)],4)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 0 = 3 - 3
([(2,4),(2,5),(3,4),(3,5)],6)
 => ([(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 3 - 3
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,6),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 3
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,3)],4)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 0 = 3 - 3
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 0 = 3 - 3
([(0,5),(1,4),(2,3)],6)
 => ([],3)
 => ([(0,3),(1,3),(2,3)],4)
 => 0 = 3 - 3
([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => 0 = 3 - 3
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 0 = 3 - 3
([(1,2),(3,4),(3,5),(4,5)],6)
 => ([],3)
 => ([(0,3),(1,3),(2,3)],4)
 => 0 = 3 - 3
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 0 = 3 - 3
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 0 = 3 - 3
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ? = 2 - 3
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 3
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 0 = 3 - 3
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 3
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 0 = 3 - 3
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 0 = 3 - 3
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 0 = 3 - 3
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 0 = 3 - 3
([(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),(0,6),(1,2),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 3
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],3)
 => ([(0,3),(1,3),(2,3)],4)
 => 0 = 3 - 3
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 0 = 3 - 3
([(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),(0,6),(1,2),(1,3),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ? = 3 - 3
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 0 = 3 - 3
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => 0 = 3 - 3
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],6)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],6)
 => ([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ? = 3 - 3
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => 0 = 3 - 3
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 0 = 3 - 3
([(5,6)],7)
 => ([],6)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ? = 2 - 3
([(4,6),(5,6)],7)
 => ([(4,5)],6)
 => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 3
([(3,6),(4,6),(5,6)],7)
 => ([(3,4),(3,5),(4,5)],6)
 => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 3
([(2,6),(3,6),(4,6),(5,6)],7)
 => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 3
([(3,6),(4,5)],7)
 => ([],5)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 0 = 3 - 3
([(3,6),(4,5),(5,6)],7)
 => ([(3,5),(4,5)],6)
 => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 3
([(2,3),(4,6),(5,6)],7)
 => ([(3,4)],5)
 => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 0 = 3 - 3
([(4,5),(4,6),(5,6)],7)
 => ([],5)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 0 = 3 - 3
([(2,6),(3,6),(4,5),(5,6)],7)
 => ([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 3
([(1,2),(3,6),(4,6),(5,6)],7)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 0 = 3 - 3
([(3,6),(4,5),(4,6),(5,6)],7)
 => ([(3,4)],5)
 => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 0 = 3 - 3
([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 3
([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 0 = 3 - 3
([(1,6),(2,6),(3,5),(4,5)],7)
 => ([(1,4),(2,3)],5)
 => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => 0 = 3 - 3
([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,6),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 3
([(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(3,4)],5)
 => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 0 = 3 - 3
([(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(2,4),(3,4)],5)
 => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 0 = 3 - 3
([(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 3
([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 0 = 3 - 3
([(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 0 = 3 - 3
([(2,6),(3,5),(4,5),(4,6)],7)
 => ([(2,5),(3,4),(4,5)],6)
 => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 3
([(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 3
([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 3
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
 => ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
 => ([(0,4),(0,6),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 3 - 3
([(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 3 - 3
([(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,6),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 3
([(1,6),(2,5),(3,4),(3,5),(4,6)],7)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 3 - 3
([(1,2),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 3 - 3
([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
 => ([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,6),(1,2),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 3
([(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)
 => ([(0,6),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 3
([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,6),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 3
([(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,6),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 3
([(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 3 - 3
([(0,6),(1,5),(2,3),(2,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 3
([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,6),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 3
([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 3 - 3
([(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,6),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 3
([(0,6),(1,6),(2,3),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,6),(1,2),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 3
([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 3
([(1,6),(2,3),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 3
([(1,2),(1,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ? = 2 - 3
([(1,6),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,6),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 3
([(1,2),(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,6),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 3
([(0,6),(1,4),(2,3),(2,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(0,6),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 3
([(0,6),(1,2),(1,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 3
([(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 3
([(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),(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 3 - 3
([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 3
([(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,6),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 3
([(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,6),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 3
([(0,6),(1,5),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 3
([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5)],7)
 => ([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 3
Description
The number of isolated vertices of a graph.
Matching statistic: St001592
(load all 6 compositions to match this statistic)
Mapping
Mp00274: Graphs —block-cut tree⟶ Graphs
Mp00247: Graphs —de-duplicate⟶ Graphs
St001592: Graphs ⟶ ℤResult quality: 48% ●values known / values provided: 48%●distinct values known / distinct values provided: 50%
Values
([],3)
 => ([],3)
 => ([],1)
 => ? = 3 - 2
([],4)
 => ([],4)
 => ([],1)
 => ? = 3 - 2
([(2,3)],4)
 => ([],3)
 => ([],1)
 => ? = 3 - 2
([],5)
 => ([],5)
 => ([],1)
 => ? = 3 - 2
([(3,4)],5)
 => ([],4)
 => ([],1)
 => ? = 3 - 2
([(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => 1 = 3 - 2
([(1,4),(2,3)],5)
 => ([],3)
 => ([],1)
 => ? = 3 - 2
([(1,4),(2,3),(3,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 1 = 3 - 2
([(2,3),(2,4),(3,4)],5)
 => ([],3)
 => ([],1)
 => ? = 3 - 2
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([],2)
 => ([],1)
 => ? = 3 - 2
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([],1)
 => ([],1)
 => ? = 3 - 2
([],6)
 => ([],6)
 => ([],1)
 => ? = 2 - 2
([(4,5)],6)
 => ([],5)
 => ([],1)
 => ? = 3 - 2
([(3,5),(4,5)],6)
 => ([(3,5),(4,5)],6)
 => ([(1,2)],3)
 => 1 = 3 - 2
([(2,5),(3,5),(4,5)],6)
 => ([(2,5),(3,5),(4,5)],6)
 => ([(1,2)],3)
 => 1 = 3 - 2
([(2,5),(3,4)],6)
 => ([],4)
 => ([],1)
 => ? = 3 - 2
([(2,5),(3,4),(4,5)],6)
 => ([(2,6),(3,5),(4,5),(4,6)],7)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 1 = 3 - 2
([(1,2),(3,5),(4,5)],6)
 => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => 1 = 3 - 2
([(3,4),(3,5),(4,5)],6)
 => ([],4)
 => ([],1)
 => ? = 3 - 2
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 1 = 3 - 2
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => 1 = 3 - 2
([(2,4),(2,5),(3,4),(3,5)],6)
 => ([],3)
 => ([],1)
 => ? = 3 - 2
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => 1 = 3 - 2
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],3)
 => ([],1)
 => ? = 3 - 2
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 1 = 3 - 2
([(0,5),(1,4),(2,3)],6)
 => ([],3)
 => ([],1)
 => ? = 3 - 2
([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ? = 3 - 2
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 1 = 3 - 2
([(1,2),(3,4),(3,5),(4,5)],6)
 => ([],3)
 => ([],1)
 => ? = 3 - 2
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
 => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
 => ? = 3 - 2
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 1 = 3 - 2
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([],2)
 => ([],1)
 => ? = 2 - 2
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 1 = 3 - 2
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ? = 3 - 2
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 1 = 3 - 2
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => 1 = 3 - 2
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 1 = 3 - 2
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
 => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
 => ? = 3 - 2
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],2)
 => ([],1)
 => ? = 3 - 2
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 1 = 3 - 2
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],3)
 => ([],1)
 => ? = 3 - 2
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],2)
 => ([],1)
 => ? = 3 - 2
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => ([],1)
 => ([],1)
 => ? = 3 - 2
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 1 = 3 - 2
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ? = 3 - 2
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],6)
 => ([],1)
 => ([],1)
 => ? = 3 - 2
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],1)
 => ([],1)
 => ? = 3 - 2
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([],1)
 => ([],1)
 => ? = 3 - 2
([(5,6)],7)
 => ([],6)
 => ([],1)
 => ? = 2 - 2
([(4,6),(5,6)],7)
 => ([(4,6),(5,6)],7)
 => ([(1,2)],3)
 => 1 = 3 - 2
([(3,6),(4,6),(5,6)],7)
 => ([(3,6),(4,6),(5,6)],7)
 => ([(1,2)],3)
 => 1 = 3 - 2
([(2,6),(3,6),(4,6),(5,6)],7)
 => ([(2,6),(3,6),(4,6),(5,6)],7)
 => ([(1,2)],3)
 => 1 = 3 - 2
([(3,6),(4,5)],7)
 => ([],5)
 => ([],1)
 => ? = 3 - 2
([(3,6),(4,5),(5,6)],7)
 => ([(3,7),(4,6),(5,6),(5,7)],8)
 => ?
 => ? = 3 - 2
([(2,3),(4,6),(5,6)],7)
 => ([(3,5),(4,5)],6)
 => ([(1,2)],3)
 => 1 = 3 - 2
([(4,5),(4,6),(5,6)],7)
 => ([],5)
 => ([],1)
 => ? = 3 - 2
([(2,6),(3,6),(4,5),(5,6)],7)
 => ([(2,7),(3,7),(4,5),(5,6),(6,7)],8)
 => ?
 => ? = 3 - 2
([(1,2),(3,6),(4,6),(5,6)],7)
 => ([(2,5),(3,5),(4,5)],6)
 => ([(1,2)],3)
 => 1 = 3 - 2
([(3,6),(4,5),(4,6),(5,6)],7)
 => ([(3,5),(4,5)],6)
 => ([(1,2)],3)
 => 1 = 3 - 2
([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => ([(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
 => ?
 => ? = 3 - 2
([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(2,5),(3,5),(4,5)],6)
 => ([(1,2)],3)
 => 1 = 3 - 2
([(1,6),(2,6),(3,5),(4,5)],7)
 => ([(1,6),(2,6),(3,5),(4,5)],7)
 => ([(1,4),(2,3)],5)
 => 1 = 3 - 2
([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(1,7),(2,8),(3,8),(4,5),(4,6),(5,7),(6,8)],9)
 => ?
 => ? = 3 - 2
([(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([],4)
 => ([],1)
 => ? = 3 - 2
([(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(2,6),(3,5),(4,5),(4,6)],7)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 1 = 3 - 2
([(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => ([(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8)
 => ?
 => ? = 3 - 2
([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => 1 = 3 - 2
([(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 1 = 3 - 2
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([],3)
 => ([],1)
 => ? = 3 - 2
([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 1 = 3 - 2
([(1,6),(2,5),(3,4)],7)
 => ([],4)
 => ([],1)
 => ? = 3 - 2
([(2,6),(3,5),(4,5),(4,6)],7)
 => ([(2,8),(3,7),(4,5),(4,6),(5,7),(6,8)],9)
 => ?
 => ? = 3 - 2
([(1,2),(3,6),(4,5),(5,6)],7)
 => ([(2,6),(3,5),(4,5),(4,6)],7)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 1 = 3 - 2
([(0,3),(1,2),(4,6),(5,6)],7)
 => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => 1 = 3 - 2
([(2,3),(4,5),(4,6),(5,6)],7)
 => ([],4)
 => ([],1)
 => ? = 3 - 2
([(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(1,7),(2,6),(3,8),(4,6),(4,8),(5,7),(5,8)],9)
 => ?
 => ? = 3 - 2
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
 => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 1 = 3 - 2
([(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(2,6),(3,5),(4,5),(4,6)],7)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 1 = 3 - 2
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => 1 = 3 - 2
([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9)
 => ?
 => ? = 3 - 2
([(1,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 1 = 3 - 2
([(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => 1 = 3 - 2
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
 => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
 => ?
 => ? = 3 - 2
([(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([],3)
 => ([],1)
 => ? = 3 - 2
([(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => 1 = 3 - 2
([(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => ([(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
 => ?
 => ? = 3 - 2
([(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => 1 = 3 - 2
([(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 1 = 3 - 2
([(0,6),(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
 => ?
 => ? = 3 - 2
([(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ([],3)
 => ([],1)
 => ? = 3 - 2
([(1,6),(2,6),(3,4),(3,5),(4,5)],7)
 => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => 1 = 3 - 2
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => 1 = 3 - 2
([(0,1),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 1 = 3 - 2
([(1,5),(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 1 = 3 - 2
([(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => 1 = 3 - 2
([(1,4),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 1 = 3 - 2
([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 1 = 3 - 2
([(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(1,2)],3)
 => 1 = 3 - 2
([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => 1 = 3 - 2
([(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => 1 = 3 - 2
Description
The maximal number of simple paths between any two different vertices of a graph.
Matching statistic: St000379
(load all 6 compositions to match this statistic)
Mapping
Mp00274: Graphs —block-cut tree⟶ Graphs
Mp00247: Graphs —de-duplicate⟶ Graphs
St000379: Graphs ⟶ ℤResult quality: 48% ●values known / values provided: 48%●distinct values known / distinct values provided: 50%
Values
([],3)
 => ([],3)
 => ([],1)
 => ? = 3 - 3
([],4)
 => ([],4)
 => ([],1)
 => ? = 3 - 3
([(2,3)],4)
 => ([],3)
 => ([],1)
 => ? = 3 - 3
([],5)
 => ([],5)
 => ([],1)
 => ? = 3 - 3
([(3,4)],5)
 => ([],4)
 => ([],1)
 => ? = 3 - 3
([(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => 0 = 3 - 3
([(1,4),(2,3)],5)
 => ([],3)
 => ([],1)
 => ? = 3 - 3
([(1,4),(2,3),(3,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 0 = 3 - 3
([(2,3),(2,4),(3,4)],5)
 => ([],3)
 => ([],1)
 => ? = 3 - 3
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([],2)
 => ([],1)
 => ? = 3 - 3
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([],1)
 => ([],1)
 => ? = 3 - 3
([],6)
 => ([],6)
 => ([],1)
 => ? = 2 - 3
([(4,5)],6)
 => ([],5)
 => ([],1)
 => ? = 3 - 3
([(3,5),(4,5)],6)
 => ([(3,5),(4,5)],6)
 => ([(1,2)],3)
 => 0 = 3 - 3
([(2,5),(3,5),(4,5)],6)
 => ([(2,5),(3,5),(4,5)],6)
 => ([(1,2)],3)
 => 0 = 3 - 3
([(2,5),(3,4)],6)
 => ([],4)
 => ([],1)
 => ? = 3 - 3
([(2,5),(3,4),(4,5)],6)
 => ([(2,6),(3,5),(4,5),(4,6)],7)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 0 = 3 - 3
([(1,2),(3,5),(4,5)],6)
 => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => 0 = 3 - 3
([(3,4),(3,5),(4,5)],6)
 => ([],4)
 => ([],1)
 => ? = 3 - 3
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 0 = 3 - 3
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => 0 = 3 - 3
([(2,4),(2,5),(3,4),(3,5)],6)
 => ([],3)
 => ([],1)
 => ? = 3 - 3
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => 0 = 3 - 3
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],3)
 => ([],1)
 => ? = 3 - 3
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 0 = 3 - 3
([(0,5),(1,4),(2,3)],6)
 => ([],3)
 => ([],1)
 => ? = 3 - 3
([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ? = 3 - 3
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 0 = 3 - 3
([(1,2),(3,4),(3,5),(4,5)],6)
 => ([],3)
 => ([],1)
 => ? = 3 - 3
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
 => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
 => ? = 3 - 3
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 0 = 3 - 3
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([],2)
 => ([],1)
 => ? = 2 - 3
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 0 = 3 - 3
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ? = 3 - 3
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 0 = 3 - 3
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => 0 = 3 - 3
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 0 = 3 - 3
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
 => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
 => ? = 3 - 3
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],2)
 => ([],1)
 => ? = 3 - 3
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 0 = 3 - 3
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],3)
 => ([],1)
 => ? = 3 - 3
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],2)
 => ([],1)
 => ? = 3 - 3
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => ([],1)
 => ([],1)
 => ? = 3 - 3
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => 0 = 3 - 3
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ? = 3 - 3
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],6)
 => ([],1)
 => ([],1)
 => ? = 3 - 3
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],1)
 => ([],1)
 => ? = 3 - 3
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([],1)
 => ([],1)
 => ? = 3 - 3
([(5,6)],7)
 => ([],6)
 => ([],1)
 => ? = 2 - 3
([(4,6),(5,6)],7)
 => ([(4,6),(5,6)],7)
 => ([(1,2)],3)
 => 0 = 3 - 3
([(3,6),(4,6),(5,6)],7)
 => ([(3,6),(4,6),(5,6)],7)
 => ([(1,2)],3)
 => 0 = 3 - 3
([(2,6),(3,6),(4,6),(5,6)],7)
 => ([(2,6),(3,6),(4,6),(5,6)],7)
 => ([(1,2)],3)
 => 0 = 3 - 3
([(3,6),(4,5)],7)
 => ([],5)
 => ([],1)
 => ? = 3 - 3
([(3,6),(4,5),(5,6)],7)
 => ([(3,7),(4,6),(5,6),(5,7)],8)
 => ?
 => ? = 3 - 3
([(2,3),(4,6),(5,6)],7)
 => ([(3,5),(4,5)],6)
 => ([(1,2)],3)
 => 0 = 3 - 3
([(4,5),(4,6),(5,6)],7)
 => ([],5)
 => ([],1)
 => ? = 3 - 3
([(2,6),(3,6),(4,5),(5,6)],7)
 => ([(2,7),(3,7),(4,5),(5,6),(6,7)],8)
 => ?
 => ? = 3 - 3
([(1,2),(3,6),(4,6),(5,6)],7)
 => ([(2,5),(3,5),(4,5)],6)
 => ([(1,2)],3)
 => 0 = 3 - 3
([(3,6),(4,5),(4,6),(5,6)],7)
 => ([(3,5),(4,5)],6)
 => ([(1,2)],3)
 => 0 = 3 - 3
([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => ([(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
 => ?
 => ? = 3 - 3
([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(2,5),(3,5),(4,5)],6)
 => ([(1,2)],3)
 => 0 = 3 - 3
([(1,6),(2,6),(3,5),(4,5)],7)
 => ([(1,6),(2,6),(3,5),(4,5)],7)
 => ([(1,4),(2,3)],5)
 => 0 = 3 - 3
([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(1,7),(2,8),(3,8),(4,5),(4,6),(5,7),(6,8)],9)
 => ?
 => ? = 3 - 3
([(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([],4)
 => ([],1)
 => ? = 3 - 3
([(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(2,6),(3,5),(4,5),(4,6)],7)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 0 = 3 - 3
([(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => ([(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8)
 => ?
 => ? = 3 - 3
([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => 0 = 3 - 3
([(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 0 = 3 - 3
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([],3)
 => ([],1)
 => ? = 3 - 3
([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 0 = 3 - 3
([(1,6),(2,5),(3,4)],7)
 => ([],4)
 => ([],1)
 => ? = 3 - 3
([(2,6),(3,5),(4,5),(4,6)],7)
 => ([(2,8),(3,7),(4,5),(4,6),(5,7),(6,8)],9)
 => ?
 => ? = 3 - 3
([(1,2),(3,6),(4,5),(5,6)],7)
 => ([(2,6),(3,5),(4,5),(4,6)],7)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 0 = 3 - 3
([(0,3),(1,2),(4,6),(5,6)],7)
 => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => 0 = 3 - 3
([(2,3),(4,5),(4,6),(5,6)],7)
 => ([],4)
 => ([],1)
 => ? = 3 - 3
([(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(1,7),(2,6),(3,8),(4,6),(4,8),(5,7),(5,8)],9)
 => ?
 => ? = 3 - 3
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
 => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 0 = 3 - 3
([(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(2,6),(3,5),(4,5),(4,6)],7)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 0 = 3 - 3
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => 0 = 3 - 3
([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9)
 => ?
 => ? = 3 - 3
([(1,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 0 = 3 - 3
([(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => 0 = 3 - 3
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
 => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
 => ?
 => ? = 3 - 3
([(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([],3)
 => ([],1)
 => ? = 3 - 3
([(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => 0 = 3 - 3
([(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => ([(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
 => ?
 => ? = 3 - 3
([(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => 0 = 3 - 3
([(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 0 = 3 - 3
([(0,6),(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
 => ?
 => ? = 3 - 3
([(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ([],3)
 => ([],1)
 => ? = 3 - 3
([(1,6),(2,6),(3,4),(3,5),(4,5)],7)
 => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => 0 = 3 - 3
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => 0 = 3 - 3
([(0,1),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 0 = 3 - 3
([(1,5),(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 0 = 3 - 3
([(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => 0 = 3 - 3
([(1,4),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 0 = 3 - 3
([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 0 = 3 - 3
([(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(1,2)],3)
 => 0 = 3 - 3
([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(2,4),(3,4)],5)
 => ([(1,2)],3)
 => 0 = 3 - 3
([(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,3),(2,3)],4)
 => ([(1,2)],3)
 => 0 = 3 - 3
Description
The number of Hamiltonian cycles in a graph. A Hamiltonian cycle in a graph G is a subgraph (this is, a subset of the edges) that is a cycle which contains every vertex of G. Since it is unclear whether the graph on one vertex is Hamiltonian, the statistic is undefined for this graph.
Matching statistic: St000260
(load all 14 compositions to match this statistic)
Mapping
Mp00147: Graphs —square⟶ Graphs
Mp00117: Graphs —Ore closure⟶ Graphs
St000260: Graphs ⟶ ℤResult quality: 46% ●values known / values provided: 46%●distinct values known / distinct values provided: 50%
Values
([],3)
 => ([],3)
 => ([],3)
 => ? = 3 - 2
([],4)
 => ([],4)
 => ([],4)
 => ? = 3 - 2
([(2,3)],4)
 => ([(2,3)],4)
 => ([(2,3)],4)
 => ? = 3 - 2
([],5)
 => ([],5)
 => ([],5)
 => ? = 3 - 2
([(3,4)],5)
 => ([(3,4)],5)
 => ([(3,4)],5)
 => ? = 3 - 2
([(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ? = 3 - 2
([(1,4),(2,3)],5)
 => ([(1,4),(2,3)],5)
 => ([(1,4),(2,3)],5)
 => ? = 3 - 2
([(1,4),(2,3),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 3 - 2
([(2,3),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ? = 3 - 2
([(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)
 => ? = 3 - 2
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 3 - 2
([],6)
 => ([],6)
 => ([],6)
 => ? = 2 - 2
([(4,5)],6)
 => ([(4,5)],6)
 => ([(4,5)],6)
 => ? = 3 - 2
([(3,5),(4,5)],6)
 => ([(3,4),(3,5),(4,5)],6)
 => ([(3,4),(3,5),(4,5)],6)
 => ? = 3 - 2
([(2,5),(3,5),(4,5)],6)
 => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 - 2
([(2,5),(3,4)],6)
 => ([(2,5),(3,4)],6)
 => ([(2,5),(3,4)],6)
 => ? = 3 - 2
([(2,5),(3,4),(4,5)],6)
 => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 - 2
([(1,2),(3,5),(4,5)],6)
 => ([(1,2),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(3,4),(3,5),(4,5)],6)
 => ? = 3 - 2
([(3,4),(3,5),(4,5)],6)
 => ([(3,4),(3,5),(4,5)],6)
 => ([(3,4),(3,5),(4,5)],6)
 => ? = 3 - 2
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(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)
 => ? = 3 - 2
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 - 2
([(2,4),(2,5),(3,4),(3,5)],6)
 => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 - 2
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(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)
 => ? = 3 - 2
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 - 2
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(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)
 => ? = 3 - 2
([(0,5),(1,4),(2,3)],6)
 => ([(0,5),(1,4),(2,3)],6)
 => ([(0,5),(1,4),(2,3)],6)
 => ? = 3 - 2
([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(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)
 => ? = 3 - 2
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(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)
 => ? = 3 - 2
([(1,2),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(3,4),(3,5),(4,5)],6)
 => ? = 3 - 2
([(0,5),(1,4),(2,3),(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),(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 = 3 - 2
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(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)
 => ? = 3 - 2
([(1,4),(1,5),(2,3),(2,5),(3,4)],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)
 => ? = 2 - 2
([(0,5),(1,4),(2,3),(2,4),(3,5),(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),(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 = 3 - 2
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 - 2
([(0,5),(1,2),(1,4),(2,3),(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),(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 = 3 - 2
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(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)
 => ? = 3 - 2
([(0,5),(1,4),(2,3),(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),(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 = 3 - 2
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],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 = 3 - 2
([(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)
 => ? = 3 - 2
([(0,4),(1,2),(1,3),(2,5),(3,5),(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),(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 = 3 - 2
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 - 2
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 - 2
([(0,4),(0,5),(1,2),(1,3),(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)],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 = 3 - 2
([(0,5),(1,2),(1,4),(2,3),(3,4),(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),(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 = 3 - 2
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(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),(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 = 3 - 2
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],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)
 => ([(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 = 3 - 2
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],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)
 => ([(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 = 3 - 2
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],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)
 => ([(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 = 3 - 2
([(5,6)],7)
 => ([(5,6)],7)
 => ([(5,6)],7)
 => ? = 2 - 2
([(4,6),(5,6)],7)
 => ([(4,5),(4,6),(5,6)],7)
 => ([(4,5),(4,6),(5,6)],7)
 => ? = 3 - 2
([(3,6),(4,6),(5,6)],7)
 => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 2
([(2,6),(3,6),(4,6),(5,6)],7)
 => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 2
([(3,6),(4,5)],7)
 => ([(3,6),(4,5)],7)
 => ([(3,6),(4,5)],7)
 => ? = 3 - 2
([(3,6),(4,5),(5,6)],7)
 => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 2
([(2,3),(4,6),(5,6)],7)
 => ([(2,3),(4,5),(4,6),(5,6)],7)
 => ([(2,3),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 2
([(4,5),(4,6),(5,6)],7)
 => ([(4,5),(4,6),(5,6)],7)
 => ([(4,5),(4,6),(5,6)],7)
 => ? = 3 - 2
([(2,6),(3,6),(4,5),(5,6)],7)
 => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 2
([(1,2),(3,6),(4,6),(5,6)],7)
 => ([(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)
 => ? = 3 - 2
([(3,6),(4,5),(4,6),(5,6)],7)
 => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 2
([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => ([(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)
 => ? = 3 - 2
([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 - 2
([(1,6),(2,6),(3,5),(4,5)],7)
 => ([(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)
 => ? = 3 - 2
([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(1,4),(1,6),(2,3),(2,5),(2,6),(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)
 => ? = 3 - 2
([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 3 - 2
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
 => ([(0,3),(0,5),(1,2),(1,4),(1,6),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 3 - 2
([(0,6),(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 3 - 2
([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
 => ([(0,4),(0,5),(1,2),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 3 - 2
([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
 => ([(0,4),(0,6),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 3 - 2
([(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),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 3 - 2
([(0,6),(1,5),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(0,6),(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),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 3 - 2
([(0,6),(1,5),(2,3),(2,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 3 - 2
([(0,6),(1,6),(2,3),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 3 - 2
([(0,6),(1,4),(2,3),(2,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(0,6),(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),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 3 - 2
([(0,6),(1,2),(1,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 3 - 2
([(0,6),(1,4),(2,3),(3,5),(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),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 3 - 2
([(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(0,6),(1,2),(1,3),(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),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 3 - 2
([(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(5,6)],7)
 => ([(0,2),(0,6),(1,3),(1,4),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 3 - 2
([(0,5),(1,2),(1,3),(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),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 3 - 2
([(0,6),(1,5),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(0,5),(0,6),(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),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 3 - 2
([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5)],7)
 => ([(0,4),(0,5),(0,6),(1,2),(1,3),(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),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 3 - 2
([(0,6),(1,3),(1,5),(2,5),(2,6),(3,4),(4,5),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 3 - 2
([(0,1),(0,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 3 - 2
([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)
 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(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),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 3 - 2
([(0,6),(1,5),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(0,5),(0,6),(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),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 3 - 2
([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 3 - 2
([(0,5),(1,4),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 3 - 2
([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => ([(0,3),(0,6),(1,2),(1,5),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 3 - 2
([(0,4),(1,3),(2,5),(2,6),(3,5),(4,6),(5,6)],7)
 => ([(0,4),(0,6),(1,3),(1,5),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 3 - 2
([(0,6),(1,4),(2,3),(2,5),(3,5),(4,6),(5,6)],7)
 => ([(0,4),(0,6),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 3 - 2
([(0,5),(1,4),(1,5),(2,3),(2,6),(3,6),(4,6)],7)
 => ([(0,3),(0,5),(1,2),(1,4),(1,6),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 3 - 2
([(0,5),(1,4),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,3),(0,6),(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),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 3 - 2
([(0,4),(1,2),(1,6),(2,5),(3,5),(3,6),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 3 - 2
([(0,5),(1,2),(1,6),(2,6),(3,4),(3,6),(4,5),(5,6)],7)
 => ([(0,3),(0,5),(0,6),(1,2),(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),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 3 - 2
([(0,1),(0,5),(1,4),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 3 - 2
([(0,4),(1,3),(2,5),(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),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 3 - 2
([(0,5),(1,4),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 3 - 2
([(0,6),(1,2),(2,6),(3,4),(3,5),(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),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 3 - 2
([(0,4),(1,3),(2,5),(2,6),(3,5),(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),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 3 - 2
([(0,5),(1,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(0,6),(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),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 3 - 2
([(0,4),(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(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),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 3 - 2
Description
The radius of a connected graph. This is the minimum eccentricity of any vertex.
The following 216 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St000771The largest multiplicity of a distance Laplacian eigenvalue in a connected graph. St000772The multiplicity of the largest distance Laplacian eigenvalue in a connected graph. St000777The number of distinct eigenvalues of the distance Laplacian of a connected graph. St001645The pebbling number of a connected graph. St000259The diameter of a connected graph. St000302The determinant of the distance matrix of a connected graph. St000466The Gutman (or modified Schultz) index of a connected graph. St000467The hyper-Wiener index of a connected graph. St000264The girth of a graph, which is not a tree. St000464The Schultz index of a connected graph. St001545The second Elser number of a connected graph. St001704The size of the largest multi-subset-intersection of the deck of a graph with the deck of another graph. St000456The monochromatic index of a connected graph. St001118The acyclic chromatic index of a graph. St001281The normalized isoperimetric number of a graph. St000699The toughness times the least common multiple of 1,. St000968We make a CNakayama algebra out of the LNakayama algebra (corresponding to the Dyck path) [c0,c1,...,cn−1] by adding c0 to cn−1. St001256Number of simple reflexive modules that are 2-stable reflexive. St001204Call a CNakayama algebra (a Nakayama algebra with a cyclic quiver) with Kupisch series L=[c0,c1,...,cn−1] such that n=c0<ci for all i>0 a special CNakayama algebra. St001103The number of words with multiplicities of the letters given by the partition, avoiding the consecutive pattern 123. St000882The number of connected components of short braid edges in the graph of braid moves of a permutation. St001195The global dimension of the algebra A/AfA of the corresponding Nakayama algebra A with minimal left faithful projective-injective module Af. St000879The number of long braid edges in the graph of braid moves of a permutation. St001908The number of semistandard tableaux of distinct weight whose maximal entry is the length of the partition. St001890The maximum magnitude of the Möbius function of a poset. St001637The number of (upper) dissectors of a poset. St000205Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and partition weight. St000206Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and integer composition weight. St001570The minimal number of edges to add to make a graph Hamiltonian. St001359The number of permutations in the equivalence class of a permutation obtained by taking inverses of cycles. St001738The minimal order of a graph which is not an induced subgraph of the given graph. St000056The decomposition (or block) number of a permutation. St000286The number of connected components of the complement of a graph. St000486The number of cycles of length at least 3 of a permutation. St000694The number of affine bounded permutations that project to a given permutation. St000788The number of nesting-similar perfect matchings of a perfect matching. St001174The Gorenstein dimension of the algebra A/I when I is the tilting module corresponding to the permutation in the Auslander algebra of K[x]/(xn). St001208The number of connected components of the quiver of A/T when T is the 1-tilting module corresponding to the permutation in the Auslander algebra A of K[x]/(xn). St001272The number of graphs with the same degree sequence. St001322The size of a minimal independent dominating set in a graph. St001333The cardinality of a minimal edge-isolating set of a graph. St001339The irredundance number of a graph. St001340The cardinality of a minimal non-edge isolating set of a graph. St001354The number of series nodes in the modular decomposition of a graph. St001363The Euler characteristic of a graph according to Knill. St001393The induced matching number of a graph. St001461The number of topologically connected components of the chord diagram of a permutation. St001463The number of distinct columns in the nullspace of a graph. St001496The number of graphs with the same Laplacian spectrum as the given graph. St001518The number of graphs with the same ordinary spectrum as the given graph. St001590The crossing number of a perfect matching. St001765The number of connected components of the friends and strangers graph. St001830The chord expansion number of a perfect matching. St001832The number of non-crossing perfect matchings in the chord expansion of a perfect matching. St001859The number of factors of the Stanley symmetric function associated with a permutation. St000096The number of spanning trees of a graph. St000221The number of strong fixed points of a permutation. St000261The edge connectivity of a graph. St000262The vertex connectivity of a graph. St000274The number of perfect matchings of a graph. St000276The size of the preimage of the map 'to graph' from Ordered trees to Graphs. St000279The size of the preimage of the map 'cycle-as-one-line notation' from Permutations to Permutations. St000303The determinant of the product of the incidence matrix and its transpose of a graph divided by 4. St000310The minimal degree of a vertex of a graph. St000327The number of cover relations in a poset. St000375The number of non weak exceedences of a permutation that are mid-points of a decreasing subsequence of length 3. St000623The number of occurrences of the pattern 52341 in a permutation. St000689The maximal n such that the minimal generator-cogenerator module in the LNakayama algebra of a Dyck path is n-rigid. St000787The number of flips required to make a perfect matching noncrossing. St001001The number of indecomposable modules with projective and injective dimension equal to the global dimension of the Nakayama algebra corresponding to the Dyck path. St001292The injective dimension of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path. St001305The number of induced cycles on four vertices in a graph. St001307The number of induced stars on four vertices in a graph. St001314The number of tilting modules of arbitrary projective dimension that have no simple modules as a direct summand in the corresponding Nakayama algebra. St001347The number of pairs of vertices of a graph having the same neighbourhood. St001367The smallest number which does not occur as degree of a vertex in a graph. St001381The fertility of a permutation. St001444The rank of the skew-symmetric form which is non-zero on crossing arcs of a perfect matching. St001466The number of transpositions swapping cyclically adjacent numbers in a permutation. St001479The number of bridges of a graph. St001549The number of restricted non-inversions between exceedances. St001551The number of restricted non-inversions between exceedances where the rightmost exceedance is linked. St001552The number of inversions between excedances and fixed points of a permutation. St001575The minimal number of edges to add or remove to make a graph edge transitive. St001578The minimal number of edges to add or remove to make a graph a line graph. St001663The number of occurrences of the Hertzsprung pattern 132 in a permutation. St001668The number of points of the poset minus the width of the poset. St001703The villainy of a graph. St001810The number of fixed points of a permutation smaller than its largest moved point. St001811The Castelnuovo-Mumford regularity of a permutation. St001837The number of occurrences of a 312 pattern in the restricted growth word of a perfect matching. St001850The number of Hecke atoms of a permutation. St000511The number of invariant subsets when acting with a permutation of given cycle type. St000003The number of standard Young tableaux of the partition. St000159The number of distinct parts of the integer partition. St000160The multiplicity of the smallest part of a partition. St000278The size of the preimage of the map 'to partition' from Integer compositions to Integer partitions. St000284The Plancherel distribution on integer partitions. St000346The number of coarsenings of a partition. St000388The number of orbits of vertices of a graph under automorphisms. St000473The number of parts of a partition that are strictly bigger than the number of ones. St000480The number of lower covers of a partition in dominance order. St000533The minimum of the number of parts and the size of the first part of an integer partition. St000548The number of different non-empty partial sums of an integer partition. St000553The number of blocks of a graph. St000618The number of self-evacuating tableaux of given shape. St000704The number of semistandard tableaux on a given integer partition with minimal maximal entry. St000706The product of the factorials of the multiplicities of an integer partition. St000759The smallest missing part in an integer partition. St000775The multiplicity of the largest eigenvalue in a graph. St000785The number of distinct colouring schemes of a graph. St000810The sum of the entries in the column specified by the partition of the change of basis matrix from powersum symmetric functions to monomial symmetric functions. St000813The number of zero-one matrices with weakly decreasing column sums and row sums given by the partition. St000814The sum of the entries in the column specified by the partition of the change of basis matrix from elementary symmetric functions to Schur symmetric functions. St000897The number of different multiplicities of parts of an integer partition. St000901The cube of the number of standard Young tableaux with shape given by the partition. St000916The packing number of a graph. St000993The multiplicity of the largest part of an integer partition. St001121The multiplicity of the irreducible representation indexed by the partition in the Kronecker square corresponding to the partition. St001128The exponens consonantiae of a partition. St001282The number of graphs with the same chromatic polynomial. St001432The order dimension of the partition. St001562The value of the complete homogeneous symmetric function evaluated at 1. St001563The value of the power-sum symmetric function evaluated at 1. St001564The value of the forgotten symmetric functions when all variables set to 1. St001740The number of graphs with the same symmetric edge polytope as the given graph. St001775The degree of the minimal polynomial of the largest eigenvalue of a graph. St001951The number of factors in the disjoint direct product decomposition of the automorphism group of a graph. St000212The number of standard Young tableaux for an integer partition such that no two consecutive entries appear in the same row. St000311The number of vertices of odd degree in a graph. St000322The skewness of a graph. St000323The minimal crossing number of a graph. St000370The genus of a graph. St000447The number of pairs of vertices of a graph with distance 3. St000449The number of pairs of vertices of a graph with distance 4. St000475The number of parts equal to 1 in a partition. St000481The number of upper covers of a partition in dominance order. St000506The number of standard desarrangement tableaux of shape equal to the given partition. St000513The number of invariant subsets of size 2 when acting with a permutation of given cycle type. St000552The number of cut vertices of a graph. St000567The sum of the products of all pairs of parts. St000749The smallest integer d such that the restriction of the representation corresponding to a partition of n to the symmetric group on n-d letters has a constituent of odd degree. St000929The constant term of the character polynomial of an integer partition. St000936The number of even values of the symmetric group character corresponding to the partition. St000938The number of zeros of the symmetric group character corresponding to the partition. St001091The number of parts in an integer partition whose next smaller part has the same size. St001097The coefficient of the monomial symmetric function indexed by the partition in the formal group law for linear orders. St001098The coefficient times the product of the factorials of the parts of the monomial symmetric function indexed by the partition in the formal group law for vertex labelled trees. St001099The coefficient times the product of the factorials of the parts of the monomial symmetric function indexed by the partition in the formal group law for leaf labelled binary trees. St001100The coefficient times the product of the factorials of the parts of the monomial symmetric function indexed by the partition in the formal group law for leaf labelled trees. St001101The coefficient times the product of the factorials of the parts of the monomial symmetric function indexed by the partition in the formal group law for increasing trees. St001122The multiplicity of the sign representation in the Kronecker square corresponding to a partition. St001123The multiplicity of the dual of the standard representation in the Kronecker square corresponding to a partition. St001309The number of four-cliques in a graph. St001323The independence gap of a graph. St001334The minimal number of occurrences of the 3-colorable pattern in a linear ordering of the vertices of the graph. St001350Half of the Albertson index of a graph. St001351The Albertson index of a graph. St001395The number of strictly unfriendly partitions of a graph. St001521Half the total irregularity of a graph. St001522The total irregularity of a graph. St001574The minimal number of edges to add or remove to make a graph regular. St001576The minimal number of edges to add or remove to make a graph vertex transitive. St001646The number of edges that can be added without increasing the maximal degree of a graph. St001647The number of edges that can be added without increasing the clique number. St001689The number of celebrities in a graph. St001692The number of vertices with higher degree than the average degree in a graph. St001708The number of pairs of vertices of different degree in a graph. St001742The difference of the maximal and the minimal degree in a graph. St001826The maximal number of leaves on a vertex of a graph. St000735The last entry on the main diagonal of a standard tableau. St000693The modular (standard) major index of a standard tableau. St000318The number of addable cells of the Ferrers diagram of an integer partition. St000049The number of set partitions whose sorted block sizes correspond to the partition. St000146The Andrews-Garvan crank of a partition. St000256The number of parts from which one can substract 2 and still get an integer partition. St000275Number of permutations whose sorted list of non zero multiplicities of the Lehmer code is the given partition. St000781The number of proper colouring schemes of a Ferrers diagram. St000783The side length of the largest staircase partition fitting into a partition. St001442The number of standard Young tableaux whose major index is divisible by the size of a given integer partition. St001568The smallest positive integer that does not appear twice in the partition. St000143The largest repeated part of a partition. St000185The weighted size of a partition. St000225Difference between largest and smallest parts in a partition. St001124The multiplicity of the standard representation in the Kronecker square corresponding to a partition. St001214The aft of an integer partition. St001440The number of standard Young tableaux whose major index is congruent one modulo the size of a given integer partition. St001198The number of simple modules in the algebra eAe with projective dimension at most 1 in the corresponding Nakayama algebra A with minimal faithful projective-injective module eA. St001206The maximal dimension of an indecomposable projective eAe-module (that is the height of the corresponding Dyck path) of the corresponding Nakayama algebra with minimal faithful projective-injective module eA. St001162The minimum jump of a permutation. St001217The projective dimension of the indecomposable injective module I[n-2] in the corresponding Nakayama algebra with simples enumerated from 0 to n-1. St001257The dominant dimension of the double dual of A/J when A is the corresponding Nakayama algebra with Jacobson radical J. St001344The neighbouring number of a permutation. St001493The number of simple modules with maximal even projective dimension in the corresponding Nakayama algebra. St001719The number of shortest chains of small intervals from the bottom to the top in a lattice. St001722The number of minimal chains with small intervals between a binary word and the top element. St001820The size of the image of the pop stack sorting operator. St001881The number of factors of a lattice as a Cartesian product of lattices. St000406The number of occurrences of the pattern 3241 in a permutation. St001113Number of indecomposable projective non-injective modules with reflexive Auslander-Reiten sequences in the corresponding Nakayama algebra. St001159Number of simple modules with dominant dimension equal to the global dimension in the corresponding Nakayama algebra. St001615The number of join prime elements of a lattice. St001846The number of elements which do not have a complement in the lattice. St001616The number of neutral elements in a lattice. St001720The minimal length of a chain of small intervals in a lattice. St001754The number of tolerances of a finite lattice. St001613The binary logarithm of the size of the center of a lattice. St001617The dimension of the space of valuations of a lattice. St001630The global dimension of the incidence algebra of the lattice over the rational numbers. St001875The number of simple modules with projective dimension at most 1. St001877Number of indecomposable injective modules with projective dimension 2. St001878The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L. St000657The smallest part of an integer composition. St000312The number of leaves in a graph. St000383The last part of an integer composition. St001490The number of connected components of a skew partition.