Processing math: 100%

Your data matches 22 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001140
(load all 2 compositions to match this statistic)
Mapping
Mp00251: Graphs —clique sizes⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
St001140: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => [1]
 => [1,0,1,0]
 => 0
([],2)
 => [1,1]
 => [1,0,1,1,0,0]
 => 0
([(0,1)],2)
 => [2]
 => [1,1,0,0,1,0]
 => 0
([],3)
 => [1,1,1]
 => [1,0,1,1,1,0,0,0]
 => 0
([(1,2)],3)
 => [2,1]
 => [1,0,1,0,1,0]
 => 0
([(0,2),(1,2)],3)
 => [2,2]
 => [1,1,0,0,1,1,0,0]
 => 0
([(0,1),(0,2),(1,2)],3)
 => [3]
 => [1,1,1,0,0,0,1,0]
 => 0
([],4)
 => [1,1,1,1]
 => [1,0,1,1,1,1,0,0,0,0]
 => 0
([(2,3)],4)
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => 0
([(1,3),(2,3)],4)
 => [2,2,1]
 => [1,0,1,0,1,1,0,0]
 => 0
([(0,3),(1,3),(2,3)],4)
 => [2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => 0
([(0,3),(1,2)],4)
 => [2,2]
 => [1,1,0,0,1,1,0,0]
 => 0
([(0,3),(1,2),(2,3)],4)
 => [2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => 0
([(1,2),(1,3),(2,3)],4)
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => 0
([(0,3),(1,2),(1,3),(2,3)],4)
 => [3,2]
 => [1,1,0,0,1,0,1,0]
 => 0
([(0,2),(0,3),(1,2),(1,3)],4)
 => [2,2,2,2]
 => [1,1,0,0,1,1,1,1,0,0,0,0]
 => 0
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => 0
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => 0
([],5)
 => [1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => 0
([(3,4)],5)
 => [2,1,1,1]
 => [1,0,1,1,1,0,1,0,0,0]
 => 0
([(2,4),(3,4)],5)
 => [2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => 0
([(1,4),(2,4),(3,4)],5)
 => [2,2,2,1]
 => [1,0,1,0,1,1,1,0,0,0]
 => 0
([(0,4),(1,4),(2,4),(3,4)],5)
 => [2,2,2,2]
 => [1,1,0,0,1,1,1,1,0,0,0,0]
 => 0
([(1,4),(2,3)],5)
 => [2,2,1]
 => [1,0,1,0,1,1,0,0]
 => 0
([(1,4),(2,3),(3,4)],5)
 => [2,2,2,1]
 => [1,0,1,0,1,1,1,0,0,0]
 => 0
([(0,1),(2,4),(3,4)],5)
 => [2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => 0
([(2,3),(2,4),(3,4)],5)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => [2,2,2,2]
 => [1,1,0,0,1,1,1,1,0,0,0,0]
 => 0
([(1,4),(2,3),(2,4),(3,4)],5)
 => [3,2,1]
 => [1,0,1,0,1,0,1,0]
 => 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,2,2]
 => [1,1,0,0,1,1,0,1,0,0]
 => 0
([(1,3),(1,4),(2,3),(2,4)],5)
 => [2,2,2,2,1]
 => [1,0,1,0,1,1,1,1,0,0,0,0]
 => 0
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,3,1]
 => [1,1,0,1,0,0,1,1,0,0]
 => 0
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [3,2,2]
 => [1,1,0,0,1,1,0,1,0,0]
 => 0
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,3,2]
 => [1,1,0,0,1,0,1,1,0,0]
 => 0
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,3,3]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 0
([(0,4),(1,3),(2,3),(2,4)],5)
 => [2,2,2,2]
 => [1,1,0,0,1,1,1,1,0,0,0,0]
 => 0
([(0,1),(2,3),(2,4),(3,4)],5)
 => [3,2]
 => [1,1,0,0,1,0,1,0]
 => 0
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => [3,2,2]
 => [1,1,0,0,1,1,0,1,0,0]
 => 0
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => 0
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [3,2,2,2]
 => [1,1,0,0,1,1,1,0,1,0,0,0]
 => 0
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,3,3]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 0
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => [3,3,2]
 => [1,1,0,0,1,0,1,1,0,0]
 => 0
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => 0
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => 0
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [4,3]
 => [1,1,1,0,0,0,1,0,1,0]
 => 0
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => [3,3,2,2]
 => [1,1,0,0,1,1,0,1,1,0,0,0]
 => 0
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [4,4]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => 0
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => 0
([(4,5)],6)
 => [2,1,1,1,1]
 => [1,0,1,1,1,1,0,1,0,0,0,0]
 => 0
([(3,5),(4,5)],6)
 => [2,2,1,1,1]
 => [1,0,1,1,1,0,1,1,0,0,0,0]
 => 0
Description
Number of indecomposable modules with projective and injective dimension at least two in the corresponding Nakayama algebra.
Matching statistic: St000259
(load all 3 compositions to match this statistic)
Mapping
Mp00264: Graphs —delete endpoints⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
Mp00111: Graphs —complement⟶ Graphs
St000259: Graphs ⟶ ℤResult quality: 12% ●values known / values provided: 12%●distinct values known / distinct values provided: 25%
Values
([],1)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([],2)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,1)],2)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([],3)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,2)],3)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,2),(1,2)],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([],4)
 => ([],4)
 => ([],1)
 => ([],1)
 => 0
([(2,3)],4)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,3),(2,3)],4)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(1,2)],4)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(1,2),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ? = 0
([],5)
 => ([],5)
 => ([],1)
 => ([],1)
 => 0
([(3,4)],5)
 => ([],4)
 => ([],1)
 => ([],1)
 => 0
([(2,4),(3,4)],5)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,4),(2,4),(3,4)],5)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(1,4),(2,3)],5)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,4),(2,3),(3,4)],5)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(2,4),(3,4)],5)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(2,3),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(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
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ? = 0
([(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)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ? = 0
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ? = 0
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ? = 0
([(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)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ? = 0
([(4,5)],6)
 => ([],5)
 => ([],1)
 => ([],1)
 => 0
([(3,5),(4,5)],6)
 => ([],4)
 => ([],1)
 => ([],1)
 => 0
([(2,5),(3,5),(4,5)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(2,5),(3,4)],6)
 => ([],4)
 => ([],1)
 => ([],1)
 => 0
([(2,5),(3,4),(4,5)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,2),(3,5),(4,5)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(3,4),(3,5),(4,5)],6)
 => ([(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 2
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 2
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,5),(1,5),(2,4),(3,4)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,5),(1,4),(2,3)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,5),(2,4),(3,4),(3,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(1,2),(3,4),(3,5),(4,5)],6)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(1,2),(1,5),(2,4),(3,4),(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)
 => ([],3)
 => ? = 1
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(3,6),(4,5)],7)
 => ([],5)
 => ([],1)
 => ([],1)
 => 0
([(2,3),(4,6),(5,6)],7)
 => ([],4)
 => ([],1)
 => ([],1)
 => 0
([(1,2),(3,6),(4,6),(5,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,6),(2,6),(3,5),(4,5)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,6),(2,5),(3,4)],7)
 => ([],4)
 => ([],1)
 => ([],1)
 => 0
([(1,2),(3,6),(4,5),(5,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(1,2),(4,6),(5,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
Description
The diameter of a connected graph. This is the greatest distance between any pair of vertices.
Matching statistic: St000260
(load all 3 compositions to match this statistic)
Mapping
Mp00264: Graphs —delete endpoints⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
Mp00111: Graphs —complement⟶ Graphs
St000260: Graphs ⟶ ℤResult quality: 12% ●values known / values provided: 12%●distinct values known / distinct values provided: 25%
Values
([],1)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([],2)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,1)],2)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([],3)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,2)],3)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,2),(1,2)],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([],4)
 => ([],4)
 => ([],1)
 => ([],1)
 => 0
([(2,3)],4)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,3),(2,3)],4)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(1,2)],4)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(1,2),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ? = 0
([],5)
 => ([],5)
 => ([],1)
 => ([],1)
 => 0
([(3,4)],5)
 => ([],4)
 => ([],1)
 => ([],1)
 => 0
([(2,4),(3,4)],5)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,4),(2,4),(3,4)],5)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(1,4),(2,3)],5)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,4),(2,3),(3,4)],5)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(2,4),(3,4)],5)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(2,3),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(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
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ? = 0
([(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)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ? = 0
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ? = 0
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ? = 0
([(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)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ? = 0
([(4,5)],6)
 => ([],5)
 => ([],1)
 => ([],1)
 => 0
([(3,5),(4,5)],6)
 => ([],4)
 => ([],1)
 => ([],1)
 => 0
([(2,5),(3,5),(4,5)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(2,5),(3,4)],6)
 => ([],4)
 => ([],1)
 => ([],1)
 => 0
([(2,5),(3,4),(4,5)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,2),(3,5),(4,5)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(3,4),(3,5),(4,5)],6)
 => ([(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 2
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 2
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,5),(1,5),(2,4),(3,4)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,5),(1,4),(2,3)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,5),(2,4),(3,4),(3,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(1,2),(3,4),(3,5),(4,5)],6)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(1,2),(1,5),(2,4),(3,4),(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)
 => ([],3)
 => ? = 1
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(3,6),(4,5)],7)
 => ([],5)
 => ([],1)
 => ([],1)
 => 0
([(2,3),(4,6),(5,6)],7)
 => ([],4)
 => ([],1)
 => ([],1)
 => 0
([(1,2),(3,6),(4,6),(5,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,6),(2,6),(3,5),(4,5)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,6),(2,5),(3,4)],7)
 => ([],4)
 => ([],1)
 => ([],1)
 => 0
([(1,2),(3,6),(4,5),(5,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(1,2),(4,6),(5,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
Description
The radius of a connected graph. This is the minimum eccentricity of any vertex.
Matching statistic: St000302
(load all 3 compositions to match this statistic)
Mapping
Mp00264: Graphs —delete endpoints⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
Mp00111: Graphs —complement⟶ Graphs
St000302: Graphs ⟶ ℤResult quality: 12% ●values known / values provided: 12%●distinct values known / distinct values provided: 25%
Values
([],1)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([],2)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,1)],2)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([],3)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,2)],3)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,2),(1,2)],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([],4)
 => ([],4)
 => ([],1)
 => ([],1)
 => 0
([(2,3)],4)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,3),(2,3)],4)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(1,2)],4)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(1,2),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ? = 0
([],5)
 => ([],5)
 => ([],1)
 => ([],1)
 => 0
([(3,4)],5)
 => ([],4)
 => ([],1)
 => ([],1)
 => 0
([(2,4),(3,4)],5)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,4),(2,4),(3,4)],5)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(1,4),(2,3)],5)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,4),(2,3),(3,4)],5)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(2,4),(3,4)],5)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(2,3),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(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
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ? = 0
([(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)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ? = 0
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ? = 0
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ? = 0
([(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)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ? = 0
([(4,5)],6)
 => ([],5)
 => ([],1)
 => ([],1)
 => 0
([(3,5),(4,5)],6)
 => ([],4)
 => ([],1)
 => ([],1)
 => 0
([(2,5),(3,5),(4,5)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(2,5),(3,4)],6)
 => ([],4)
 => ([],1)
 => ([],1)
 => 0
([(2,5),(3,4),(4,5)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,2),(3,5),(4,5)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(3,4),(3,5),(4,5)],6)
 => ([(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 2
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 2
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,5),(1,5),(2,4),(3,4)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,5),(1,4),(2,3)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,5),(2,4),(3,4),(3,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(1,2),(3,4),(3,5),(4,5)],6)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(1,2),(1,5),(2,4),(3,4),(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)
 => ([],3)
 => ? = 1
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(3,6),(4,5)],7)
 => ([],5)
 => ([],1)
 => ([],1)
 => 0
([(2,3),(4,6),(5,6)],7)
 => ([],4)
 => ([],1)
 => ([],1)
 => 0
([(1,2),(3,6),(4,6),(5,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,6),(2,6),(3,5),(4,5)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,6),(2,5),(3,4)],7)
 => ([],4)
 => ([],1)
 => ([],1)
 => 0
([(1,2),(3,6),(4,5),(5,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(1,2),(4,6),(5,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
Description
The determinant of the distance matrix of a connected graph.
Matching statistic: St000466
(load all 3 compositions to match this statistic)
Mapping
Mp00264: Graphs —delete endpoints⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
Mp00111: Graphs —complement⟶ Graphs
St000466: Graphs ⟶ ℤResult quality: 12% ●values known / values provided: 12%●distinct values known / distinct values provided: 25%
Values
([],1)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([],2)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,1)],2)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([],3)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,2)],3)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,2),(1,2)],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([],4)
 => ([],4)
 => ([],1)
 => ([],1)
 => 0
([(2,3)],4)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,3),(2,3)],4)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(1,2)],4)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(1,2),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ? = 0
([],5)
 => ([],5)
 => ([],1)
 => ([],1)
 => 0
([(3,4)],5)
 => ([],4)
 => ([],1)
 => ([],1)
 => 0
([(2,4),(3,4)],5)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,4),(2,4),(3,4)],5)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(1,4),(2,3)],5)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,4),(2,3),(3,4)],5)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(2,4),(3,4)],5)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(2,3),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(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
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ? = 0
([(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)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ? = 0
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ? = 0
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ? = 0
([(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)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ? = 0
([(4,5)],6)
 => ([],5)
 => ([],1)
 => ([],1)
 => 0
([(3,5),(4,5)],6)
 => ([],4)
 => ([],1)
 => ([],1)
 => 0
([(2,5),(3,5),(4,5)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(2,5),(3,4)],6)
 => ([],4)
 => ([],1)
 => ([],1)
 => 0
([(2,5),(3,4),(4,5)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,2),(3,5),(4,5)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(3,4),(3,5),(4,5)],6)
 => ([(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 2
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 2
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,5),(1,5),(2,4),(3,4)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,5),(1,4),(2,3)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,5),(2,4),(3,4),(3,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(1,2),(3,4),(3,5),(4,5)],6)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(1,2),(1,5),(2,4),(3,4),(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)
 => ([],3)
 => ? = 1
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(3,6),(4,5)],7)
 => ([],5)
 => ([],1)
 => ([],1)
 => 0
([(2,3),(4,6),(5,6)],7)
 => ([],4)
 => ([],1)
 => ([],1)
 => 0
([(1,2),(3,6),(4,6),(5,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,6),(2,6),(3,5),(4,5)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,6),(2,5),(3,4)],7)
 => ([],4)
 => ([],1)
 => ([],1)
 => 0
([(1,2),(3,6),(4,5),(5,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(1,2),(4,6),(5,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
Description
The Gutman (or modified Schultz) index of a connected graph. This is ∑{u,v}⊆Vd(u)d(v)d(u,v) where d(u) is the degree of vertex u and d(u,v) is the distance between vertices u and v. For trees on n vertices, the modified Schultz index is related to the Wiener index via S∗(T)=4W(T)−(n−1)(2n−1) [1].
Matching statistic: St000467
(load all 3 compositions to match this statistic)
Mapping
Mp00264: Graphs —delete endpoints⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
Mp00111: Graphs —complement⟶ Graphs
St000467: Graphs ⟶ ℤResult quality: 12% ●values known / values provided: 12%●distinct values known / distinct values provided: 25%
Values
([],1)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([],2)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,1)],2)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([],3)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,2)],3)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,2),(1,2)],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([],4)
 => ([],4)
 => ([],1)
 => ([],1)
 => 0
([(2,3)],4)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,3),(2,3)],4)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(1,2)],4)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(1,2),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ? = 0
([],5)
 => ([],5)
 => ([],1)
 => ([],1)
 => 0
([(3,4)],5)
 => ([],4)
 => ([],1)
 => ([],1)
 => 0
([(2,4),(3,4)],5)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,4),(2,4),(3,4)],5)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(1,4),(2,3)],5)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,4),(2,3),(3,4)],5)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(2,4),(3,4)],5)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(2,3),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(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
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ? = 0
([(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)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ? = 0
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ? = 0
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ? = 0
([(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)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ? = 0
([(4,5)],6)
 => ([],5)
 => ([],1)
 => ([],1)
 => 0
([(3,5),(4,5)],6)
 => ([],4)
 => ([],1)
 => ([],1)
 => 0
([(2,5),(3,5),(4,5)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(2,5),(3,4)],6)
 => ([],4)
 => ([],1)
 => ([],1)
 => 0
([(2,5),(3,4),(4,5)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,2),(3,5),(4,5)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(3,4),(3,5),(4,5)],6)
 => ([(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 2
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 2
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,5),(1,5),(2,4),(3,4)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,5),(1,4),(2,3)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,5),(2,4),(3,4),(3,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(1,2),(3,4),(3,5),(4,5)],6)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(1,2),(1,5),(2,4),(3,4),(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)
 => ([],3)
 => ? = 1
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0
([(3,6),(4,5)],7)
 => ([],5)
 => ([],1)
 => ([],1)
 => 0
([(2,3),(4,6),(5,6)],7)
 => ([],4)
 => ([],1)
 => ([],1)
 => 0
([(1,2),(3,6),(4,6),(5,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,6),(2,6),(3,5),(4,5)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,6),(2,5),(3,4)],7)
 => ([],4)
 => ([],1)
 => ([],1)
 => 0
([(1,2),(3,6),(4,5),(5,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(1,2),(4,6),(5,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
Description
The hyper-Wiener index of a connected graph. This is ∑{u,v}⊆Vd(u,v)+d(u,v)2.
Matching statistic: St000771
(load all 3 compositions to match this statistic)
Mapping
Mp00264: Graphs —delete endpoints⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
Mp00111: Graphs —complement⟶ Graphs
St000771: Graphs ⟶ ℤResult quality: 12% ●values known / values provided: 12%●distinct values known / distinct values provided: 25%
Values
([],1)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([],2)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,1)],2)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([],3)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,2)],3)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,2),(1,2)],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([],4)
 => ([],4)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(2,3)],4)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,3),(2,3)],4)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,3),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,3),(1,2)],4)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,3),(1,2),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ? = 0 + 1
([],5)
 => ([],5)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(3,4)],5)
 => ([],4)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(2,4),(3,4)],5)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,4),(2,4),(3,4)],5)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,4),(2,3)],5)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,4),(2,3),(3,4)],5)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,1),(2,4),(3,4)],5)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(2,3),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 + 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 + 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(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
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ? = 0 + 1
([(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)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ? = 0 + 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ? = 0 + 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ? = 0 + 1
([(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)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ? = 0 + 1
([(4,5)],6)
 => ([],5)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(3,5),(4,5)],6)
 => ([],4)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(2,5),(3,5),(4,5)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(2,5),(3,4)],6)
 => ([],4)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(2,5),(3,4),(4,5)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,2),(3,5),(4,5)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(3,4),(3,5),(4,5)],6)
 => ([(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 2 + 1
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 2 + 1
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 + 1
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,5),(1,5),(2,4),(3,4)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 + 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 + 1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 + 1
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,5),(1,4),(2,3)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,5),(2,4),(3,4),(3,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,2),(3,4),(3,5),(4,5)],6)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 + 1
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 + 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(1,2),(1,5),(2,4),(3,4),(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)
 => ([],3)
 => ? = 1 + 1
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 + 1
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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
([(3,6),(4,5)],7)
 => ([],5)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(2,3),(4,6),(5,6)],7)
 => ([],4)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,2),(3,6),(4,6),(5,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,6),(2,6),(3,5),(4,5)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,6),(2,5),(3,4)],7)
 => ([],4)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,2),(3,6),(4,5),(5,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,3),(1,2),(4,6),(5,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
Description
The largest multiplicity of a distance Laplacian eigenvalue in a connected graph. The distance Laplacian of a graph is the (symmetric) matrix with row and column sums 0, which has the negative distances between two vertices as its off-diagonal entries. This statistic is the largest multiplicity of an eigenvalue. For example, the cycle on four vertices has distance Laplacian (4−1−2−1−14−1−2−2−14−1−1−2−14). Its eigenvalues are 0,4,4,6, so the statistic is 2. The path on four vertices has eigenvalues 0,4.7…,6,9.2… and therefore statistic 1.
Matching statistic: St000772
(load all 3 compositions to match this statistic)
Mapping
Mp00264: Graphs —delete endpoints⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
Mp00111: Graphs —complement⟶ Graphs
St000772: Graphs ⟶ ℤResult quality: 12% ●values known / values provided: 12%●distinct values known / distinct values provided: 25%
Values
([],1)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([],2)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,1)],2)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([],3)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,2)],3)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,2),(1,2)],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([],4)
 => ([],4)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(2,3)],4)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,3),(2,3)],4)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,3),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,3),(1,2)],4)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,3),(1,2),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ? = 0 + 1
([],5)
 => ([],5)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(3,4)],5)
 => ([],4)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(2,4),(3,4)],5)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,4),(2,4),(3,4)],5)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,4),(2,3)],5)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,4),(2,3),(3,4)],5)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,1),(2,4),(3,4)],5)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(2,3),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 + 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 + 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(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
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ? = 0 + 1
([(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)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ? = 0 + 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ? = 0 + 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ? = 0 + 1
([(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)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ? = 0 + 1
([(4,5)],6)
 => ([],5)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(3,5),(4,5)],6)
 => ([],4)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(2,5),(3,5),(4,5)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(2,5),(3,4)],6)
 => ([],4)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(2,5),(3,4),(4,5)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,2),(3,5),(4,5)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(3,4),(3,5),(4,5)],6)
 => ([(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 2 + 1
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 2 + 1
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 + 1
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,5),(1,5),(2,4),(3,4)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 + 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 + 1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 + 1
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,5),(1,4),(2,3)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,5),(2,4),(3,4),(3,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,2),(3,4),(3,5),(4,5)],6)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 + 1
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 + 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(1,2),(1,5),(2,4),(3,4),(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)
 => ([],3)
 => ? = 1 + 1
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 + 1
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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
([(3,6),(4,5)],7)
 => ([],5)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(2,3),(4,6),(5,6)],7)
 => ([],4)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,2),(3,6),(4,6),(5,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,6),(2,6),(3,5),(4,5)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,6),(2,5),(3,4)],7)
 => ([],4)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,2),(3,6),(4,5),(5,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,3),(1,2),(4,6),(5,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
Description
The multiplicity of the largest distance Laplacian eigenvalue in a connected graph. The distance Laplacian of a graph is the (symmetric) matrix with row and column sums 0, which has the negative distances between two vertices as its off-diagonal entries. This statistic is the largest multiplicity of an eigenvalue. For example, the cycle on four vertices has distance Laplacian (4−1−2−1−14−1−2−2−14−1−1−2−14). Its eigenvalues are 0,4,4,6, so the statistic is 1. The path on four vertices has eigenvalues 0,4.7…,6,9.2… and therefore also statistic 1. The graphs with statistic n−1, n−2 and n−3 have been characterised, see [1].
Matching statistic: St000777
(load all 3 compositions to match this statistic)
Mapping
Mp00264: Graphs —delete endpoints⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
Mp00111: Graphs —complement⟶ Graphs
St000777: Graphs ⟶ ℤResult quality: 12% ●values known / values provided: 12%●distinct values known / distinct values provided: 25%
Values
([],1)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([],2)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,1)],2)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([],3)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,2)],3)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,2),(1,2)],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([],4)
 => ([],4)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(2,3)],4)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,3),(2,3)],4)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,3),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,3),(1,2)],4)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,3),(1,2),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ? = 0 + 1
([],5)
 => ([],5)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(3,4)],5)
 => ([],4)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(2,4),(3,4)],5)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,4),(2,4),(3,4)],5)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,4),(2,3)],5)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,4),(2,3),(3,4)],5)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,1),(2,4),(3,4)],5)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(2,3),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 + 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 + 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(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
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ? = 0 + 1
([(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)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ? = 0 + 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ? = 0 + 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ? = 0 + 1
([(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)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ? = 0 + 1
([(4,5)],6)
 => ([],5)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(3,5),(4,5)],6)
 => ([],4)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(2,5),(3,5),(4,5)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(2,5),(3,4)],6)
 => ([],4)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(2,5),(3,4),(4,5)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,2),(3,5),(4,5)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(3,4),(3,5),(4,5)],6)
 => ([(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 2 + 1
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 2 + 1
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 + 1
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,5),(1,5),(2,4),(3,4)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 + 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 + 1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 + 1
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,5),(1,4),(2,3)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,5),(2,4),(3,4),(3,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,2),(3,4),(3,5),(4,5)],6)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 + 1
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 + 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(1,2),(1,5),(2,4),(3,4),(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)
 => ([],3)
 => ? = 1 + 1
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 + 1
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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
([(3,6),(4,5)],7)
 => ([],5)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(2,3),(4,6),(5,6)],7)
 => ([],4)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,2),(3,6),(4,6),(5,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,6),(2,6),(3,5),(4,5)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,6),(2,5),(3,4)],7)
 => ([],4)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,2),(3,6),(4,5),(5,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,3),(1,2),(4,6),(5,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
Description
The number of distinct eigenvalues of the distance Laplacian of a connected graph.
Matching statistic: St001645
(load all 3 compositions to match this statistic)
Mapping
Mp00264: Graphs —delete endpoints⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
Mp00111: Graphs —complement⟶ Graphs
St001645: Graphs ⟶ ℤResult quality: 12% ●values known / values provided: 12%●distinct values known / distinct values provided: 25%
Values
([],1)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([],2)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,1)],2)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([],3)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,2)],3)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,2),(1,2)],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([],4)
 => ([],4)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(2,3)],4)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,3),(2,3)],4)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,3),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,3),(1,2)],4)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,3),(1,2),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ? = 0 + 1
([],5)
 => ([],5)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(3,4)],5)
 => ([],4)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(2,4),(3,4)],5)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,4),(2,4),(3,4)],5)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,4),(2,3)],5)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,4),(2,3),(3,4)],5)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,1),(2,4),(3,4)],5)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(2,3),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 + 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 + 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(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
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ? = 0 + 1
([(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)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ? = 0 + 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ? = 0 + 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ? = 0 + 1
([(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)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ? = 0 + 1
([(4,5)],6)
 => ([],5)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(3,5),(4,5)],6)
 => ([],4)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(2,5),(3,5),(4,5)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(2,5),(3,4)],6)
 => ([],4)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(2,5),(3,4),(4,5)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,2),(3,5),(4,5)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(3,4),(3,5),(4,5)],6)
 => ([(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 2 + 1
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 2 + 1
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 + 1
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,5),(1,5),(2,4),(3,4)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 + 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 + 1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 + 1
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,5),(1,4),(2,3)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,5),(2,4),(3,4),(3,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,2),(3,4),(3,5),(4,5)],6)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 + 1
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 + 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(1,2),(1,5),(2,4),(3,4),(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)
 => ([],3)
 => ? = 1 + 1
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 1 + 1
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ? = 0 + 1
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(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
([(3,6),(4,5)],7)
 => ([],5)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(2,3),(4,6),(5,6)],7)
 => ([],4)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,2),(3,6),(4,6),(5,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,6),(2,6),(3,5),(4,5)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,6),(2,5),(3,4)],7)
 => ([],4)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,2),(3,6),(4,5),(5,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,3),(1,2),(4,6),(5,6)],7)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
Description
The pebbling number of a connected graph.
The following 12 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St001845The number of join irreducibles minus the rank of a lattice. St001846The number of elements which do not have a complement in the lattice. St001719The number of shortest chains of small intervals from the bottom to the top in a lattice. St001820The size of the image of the pop stack sorting operator. St001877Number of indecomposable injective modules with projective dimension 2. St001630The global dimension of the incidence algebra of the lattice over the rational numbers. St001878The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L. St001371The length of the longest Yamanouchi prefix of a binary word. St001730The number of times the path corresponding to a binary word crosses the base line. 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). St001236The dominant dimension of the corresponding Comp-Nakayama algebra. St001195The global dimension of the algebra A/AfA of the corresponding Nakayama algebra A with minimal left faithful projective-injective module Af.