Your data matches 2 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000171
(load all 2 compositions to match this statistic)
Mapping
St000171: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => 0
([],2)
 => 0
([(0,1)],2)
 => 1
([],3)
 => 0
([(1,2)],3)
 => 1
([(0,2),(1,2)],3)
 => 2
([(0,1),(0,2),(1,2)],3)
 => 2
([],4)
 => 0
([(2,3)],4)
 => 1
([(1,3),(2,3)],4)
 => 2
([(0,3),(1,3),(2,3)],4)
 => 3
([(0,3),(1,2)],4)
 => 1
([(0,3),(1,2),(2,3)],4)
 => 2
([(1,2),(1,3),(2,3)],4)
 => 2
([(0,3),(1,2),(1,3),(2,3)],4)
 => 3
([(0,2),(0,3),(1,2),(1,3)],4)
 => 2
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 3
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 3
([],5)
 => 0
([(3,4)],5)
 => 1
([(2,4),(3,4)],5)
 => 2
([(1,4),(2,4),(3,4)],5)
 => 3
([(0,4),(1,4),(2,4),(3,4)],5)
 => 4
([(1,4),(2,3)],5)
 => 1
([(1,4),(2,3),(3,4)],5)
 => 2
([(0,1),(2,4),(3,4)],5)
 => 2
([(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,4),(2,3),(3,4)],5)
 => 3
([(1,4),(2,3),(2,4),(3,4)],5)
 => 3
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 4
([(1,3),(1,4),(2,3),(2,4)],5)
 => 2
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 3
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 3
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 3
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4
([(0,4),(1,3),(2,3),(2,4)],5)
 => 2
([(0,1),(2,3),(2,4),(3,4)],5)
 => 2
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 3
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => 4
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 3
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => 4
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => 3
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => 3
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 4
Description
The degree of the graph. This is the maximal vertex degree of a graph.
Matching statistic: St001742
(load all 2 compositions to match this statistic)
Mapping
Mp00259: Graphs —vertex addition⟶ Graphs
St001742: Graphs ⟶ ℤResult quality: 4% ●values known / values provided: 4%●distinct values known / distinct values provided: 71%
Values
([],1)
 => ([],2)
 => 0
([],2)
 => ([],3)
 => 0
([(0,1)],2)
 => ([(1,2)],3)
 => 1
([],3)
 => ([],4)
 => 0
([(1,2)],3)
 => ([(2,3)],4)
 => 1
([(0,2),(1,2)],3)
 => ([(1,3),(2,3)],4)
 => 2
([(0,1),(0,2),(1,2)],3)
 => ([(1,2),(1,3),(2,3)],4)
 => 2
([],4)
 => ([],5)
 => 0
([(2,3)],4)
 => ([(3,4)],5)
 => 1
([(1,3),(2,3)],4)
 => ([(2,4),(3,4)],5)
 => 2
([(0,3),(1,3),(2,3)],4)
 => ([(1,4),(2,4),(3,4)],5)
 => 3
([(0,3),(1,2)],4)
 => ([(1,4),(2,3)],5)
 => 1
([(0,3),(1,2),(2,3)],4)
 => ([(1,4),(2,3),(3,4)],5)
 => 2
([(1,2),(1,3),(2,3)],4)
 => ([(2,3),(2,4),(3,4)],5)
 => 2
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => 3
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => 2
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
([],5)
 => ([],6)
 => 0
([(3,4)],5)
 => ([(4,5)],6)
 => 1
([(2,4),(3,4)],5)
 => ([(3,5),(4,5)],6)
 => 2
([(1,4),(2,4),(3,4)],5)
 => ([(2,5),(3,5),(4,5)],6)
 => 3
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => 4
([(1,4),(2,3)],5)
 => ([(2,5),(3,4)],6)
 => 1
([(1,4),(2,3),(3,4)],5)
 => ([(2,5),(3,4),(4,5)],6)
 => 2
([(0,1),(2,4),(3,4)],5)
 => ([(1,2),(3,5),(4,5)],6)
 => 2
([(2,3),(2,4),(3,4)],5)
 => ([(3,4),(3,5),(4,5)],6)
 => 2
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(1,5),(2,5),(3,4),(4,5)],6)
 => 3
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(2,5),(3,4),(3,5),(4,5)],6)
 => 3
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 4
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(2,4),(2,5),(3,4),(3,5)],6)
 => 2
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => 3
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => 3
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 4
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 3
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 4
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 2
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(3,4),(3,5),(4,5)],6)
 => 2
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => 3
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => 4
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => 2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => 3
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => 4
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => 3
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 4
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 4
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => 3
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 4
([],6)
 => ([],7)
 => ? = 0
([(4,5)],6)
 => ([(5,6)],7)
 => ? = 1
([(3,5),(4,5)],6)
 => ([(4,6),(5,6)],7)
 => ? = 2
([(2,5),(3,5),(4,5)],6)
 => ([(3,6),(4,6),(5,6)],7)
 => ? = 3
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(2,6),(3,6),(4,6),(5,6)],7)
 => ? = 4
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ? = 5
([(2,5),(3,4)],6)
 => ([(3,6),(4,5)],7)
 => ? = 1
([(2,5),(3,4),(4,5)],6)
 => ([(3,6),(4,5),(5,6)],7)
 => ? = 2
([(1,2),(3,5),(4,5)],6)
 => ([(2,3),(4,6),(5,6)],7)
 => ? = 2
([(3,4),(3,5),(4,5)],6)
 => ([(4,5),(4,6),(5,6)],7)
 => ? = 2
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(2,6),(3,6),(4,5),(5,6)],7)
 => ? = 3
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([(1,2),(3,6),(4,6),(5,6)],7)
 => ? = 3
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => ? = 4
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 4
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 5
([(2,4),(2,5),(3,4),(3,5)],6)
 => ([(3,5),(3,6),(4,5),(4,6)],7)
 => ? = 2
([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(1,6),(2,6),(3,5),(4,5)],7)
 => ? = 2
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7)
 => ? = 3
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ? = 3
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ? = 3
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => ? = 3
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
 => ? = 4
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 4
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ? = 4
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 5
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ? = 3
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => ? = 3
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ? = 4
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 4
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 4
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 5
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ? = 4
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 5
([(0,5),(1,4),(2,3)],6)
 => ([(1,6),(2,5),(3,4)],7)
 => ? = 1
([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(2,6),(3,5),(4,5),(4,6)],7)
 => ? = 2
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(1,2),(3,6),(4,5),(5,6)],7)
 => ? = 2
([(1,2),(3,4),(3,5),(4,5)],6)
 => ([(2,3),(4,5),(4,6),(5,6)],7)
 => ? = 2
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(1,6),(2,5),(3,4),(4,6),(5,6)],7)
 => ? = 3
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(2,5),(3,4),(3,6),(4,6),(5,6)],7)
 => ? = 3
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ? = 4
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ? = 4
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ? = 5
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(2,5),(2,6),(3,4),(3,6),(4,5)],7)
 => ? = 2
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
 => ? = 3
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ? = 3
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(1,6),(2,3),(2,5),(3,4),(4,6),(5,6)],7)
 => ? = 3
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
 => ? = 3
Description
The difference of the maximal and the minimal degree in a graph. The graph is regular if and only if this statistic is zero.