Processing math: 100%

Your data matches 133 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001518
(load all 3 compositions to match this statistic)
Mapping
Mp00198: Posets —incomparability graph⟶ Graphs
Mp00117: Graphs —Ore closure⟶ Graphs
St001518: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => ([],1)
 => ([],1)
 => 1
([],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 1
([(0,1)],2)
 => ([],2)
 => ([],2)
 => 1
([],3)
 => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 1
([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 1
([(0,1),(0,2)],3)
 => ([(1,2)],3)
 => ([(1,2)],3)
 => 1
([(0,2),(2,1)],3)
 => ([],3)
 => ([],3)
 => 1
([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => ([(1,2)],3)
 => 1
([],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)
 => 1
([(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(1,2),(1,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,1),(0,2),(0,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => 1
([(0,2),(0,3),(3,1)],4)
 => ([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ([(2,3)],4)
 => 1
([(1,2),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => 1
([(0,3),(3,1),(3,2)],4)
 => ([(2,3)],4)
 => ([(2,3)],4)
 => 1
([(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,3),(1,3),(3,2)],4)
 => ([(2,3)],4)
 => ([(2,3)],4)
 => 1
([(0,3),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => 1
([(0,3),(1,2)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => 1
([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ([],4)
 => 1
([(0,3),(1,2),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => 1
([],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(3,4)],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),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(1,2),(1,3),(1,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,1),(0,2),(0,3),(0,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,2),(0,3),(0,4),(4,1)],5)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => 1
([(1,3),(1,4),(4,2)],5)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,3),(0,4),(4,1),(4,2)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(3,4)],5)
 => ([(3,4)],5)
 => 1
([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,4),(2,3)],5)
 => ([(1,4),(2,3)],5)
 => 1
([(2,3),(3,4)],5)
 => ([(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)
 => 1
([(1,4),(4,2),(4,3)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,4),(4,1),(4,2),(4,3)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => 1
([(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),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(1,4),(2,4),(4,3)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,4),(1,4),(4,2),(4,3)],5)
 => ([(1,4),(2,3)],5)
 => ([(1,4),(2,3)],5)
 => 1
([(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,4),(1,4),(2,4),(4,3)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,4),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
Description
The number of graphs with the same ordinary spectrum as the given graph.
Matching statistic: St000771
Mapping
Mp00206: Posets —antichains of maximal size⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
St000771: Graphs ⟶ ℤResult quality: 40% ●values known / values provided: 40%●distinct values known / distinct values provided: 50%
Values
([],1)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([],2)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,1)],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,2)],3)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,1),(0,2)],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1
([(0,2),(1,2)],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(1,2),(1,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,1),(0,2),(0,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,2),(0,3),(3,1)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,2),(2,3)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1
([(0,3),(3,1),(3,2)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(1,3),(3,2)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(1,2)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ? = 1
([(0,3),(1,2),(1,3)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? = 1
([(0,3),(1,2),(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,2),(1,3),(1,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,1),(0,2),(0,3),(0,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,2),(0,3),(0,4),(4,1)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,3),(1,4),(4,2)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,3),(0,4),(4,1),(4,2)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,2),(1,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ? = 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(2,3),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1
([(1,4),(4,2),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(4,1),(4,2),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,4),(2,4),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,4),(4,2),(4,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,4),(2,4),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,4),(2,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,4),(2,3),(4,2)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,3),(2,3),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(1,4),(2,3)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ? = 1
([(1,4),(2,3),(2,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1
([(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(3,4)],5)
 => ? = 1
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,4),(1,2),(1,4),(4,3)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? = 1
([(0,4),(1,2),(1,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,4),(1,2),(1,3),(1,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,2),(0,4),(3,1),(4,3)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1
([(0,4),(1,2),(1,3),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(0,4),(1,2),(1,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? = 1
([(0,3),(1,2),(1,4),(3,4)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(3,4)],5)
 => ? = 1
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1
([(1,4),(3,2),(4,3)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? = 2
([(0,3),(3,4),(4,1),(4,2)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,4),(1,2),(2,4),(4,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,3),(1,4),(4,2)],5)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(2,5),(3,4),(4,5)],6)
 => ? = 1
([(0,4),(3,2),(4,1),(4,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,4),(1,2),(2,3),(2,4)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? = 1
([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => ? = 1
([(0,3),(1,2),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ? = 1
([(0,4),(1,2),(2,3),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(4,5)],6)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(3,4),(3,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(2,3),(2,4),(2,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,2),(1,3),(1,4),(1,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,3),(1,4),(1,5),(5,2)],6)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 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
Mapping
Mp00206: Posets —antichains of maximal size⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
St000772: Graphs ⟶ ℤResult quality: 40% ●values known / values provided: 40%●distinct values known / distinct values provided: 50%
Values
([],1)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([],2)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,1)],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,2)],3)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,1),(0,2)],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1
([(0,2),(1,2)],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(1,2),(1,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,1),(0,2),(0,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,2),(0,3),(3,1)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,2),(2,3)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1
([(0,3),(3,1),(3,2)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(1,3),(3,2)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(1,2)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ? = 1
([(0,3),(1,2),(1,3)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? = 1
([(0,3),(1,2),(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,2),(1,3),(1,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,1),(0,2),(0,3),(0,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,2),(0,3),(0,4),(4,1)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,3),(1,4),(4,2)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,3),(0,4),(4,1),(4,2)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,2),(1,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ? = 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(2,3),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1
([(1,4),(4,2),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(4,1),(4,2),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,4),(2,4),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,4),(4,2),(4,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,4),(2,4),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,4),(2,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,4),(2,3),(4,2)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,3),(2,3),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(1,4),(2,3)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ? = 1
([(1,4),(2,3),(2,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1
([(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(3,4)],5)
 => ? = 1
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,4),(1,2),(1,4),(4,3)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? = 1
([(0,4),(1,2),(1,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,4),(1,2),(1,3),(1,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,2),(0,4),(3,1),(4,3)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1
([(0,4),(1,2),(1,3),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(0,4),(1,2),(1,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? = 1
([(0,3),(1,2),(1,4),(3,4)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(3,4)],5)
 => ? = 1
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1
([(1,4),(3,2),(4,3)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? = 2
([(0,3),(3,4),(4,1),(4,2)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,4),(1,2),(2,4),(4,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,3),(1,4),(4,2)],5)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(2,5),(3,4),(4,5)],6)
 => ? = 1
([(0,4),(3,2),(4,1),(4,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,4),(1,2),(2,3),(2,4)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? = 1
([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => ? = 1
([(0,3),(1,2),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ? = 1
([(0,4),(1,2),(2,3),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(4,5)],6)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(3,4),(3,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(2,3),(2,4),(2,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,2),(1,3),(1,4),(1,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,3),(1,4),(1,5),(5,2)],6)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 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
Mapping
Mp00206: Posets —antichains of maximal size⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
St000777: Graphs ⟶ ℤResult quality: 40% ●values known / values provided: 40%●distinct values known / distinct values provided: 50%
Values
([],1)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([],2)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,1)],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,2)],3)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,1),(0,2)],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1
([(0,2),(1,2)],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(1,2),(1,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,1),(0,2),(0,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,2),(0,3),(3,1)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,2),(2,3)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1
([(0,3),(3,1),(3,2)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(1,3),(3,2)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(1,2)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ? = 1
([(0,3),(1,2),(1,3)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? = 1
([(0,3),(1,2),(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,2),(1,3),(1,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,1),(0,2),(0,3),(0,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,2),(0,3),(0,4),(4,1)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,3),(1,4),(4,2)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,3),(0,4),(4,1),(4,2)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,2),(1,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ? = 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(2,3),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1
([(1,4),(4,2),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(4,1),(4,2),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,4),(2,4),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,4),(4,2),(4,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,4),(2,4),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,4),(2,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,4),(2,3),(4,2)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,3),(2,3),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(1,4),(2,3)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ? = 1
([(1,4),(2,3),(2,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1
([(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(3,4)],5)
 => ? = 1
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,4),(1,2),(1,4),(4,3)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? = 1
([(0,4),(1,2),(1,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,4),(1,2),(1,3),(1,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,2),(0,4),(3,1),(4,3)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1
([(0,4),(1,2),(1,3),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(0,4),(1,2),(1,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? = 1
([(0,3),(1,2),(1,4),(3,4)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(3,4)],5)
 => ? = 1
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1
([(1,4),(3,2),(4,3)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? = 2
([(0,3),(3,4),(4,1),(4,2)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,4),(1,2),(2,4),(4,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,3),(1,4),(4,2)],5)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(2,5),(3,4),(4,5)],6)
 => ? = 1
([(0,4),(3,2),(4,1),(4,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,4),(1,2),(2,3),(2,4)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? = 1
([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => ? = 1
([(0,3),(1,2),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ? = 1
([(0,4),(1,2),(2,3),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(4,5)],6)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(3,4),(3,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(2,3),(2,4),(2,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,2),(1,3),(1,4),(1,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,3),(1,4),(1,5),(5,2)],6)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
Description
The number of distinct eigenvalues of the distance Laplacian of a connected graph.
Matching statistic: St001645
Mapping
Mp00206: Posets —antichains of maximal size⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
St001645: Graphs ⟶ ℤResult quality: 40% ●values known / values provided: 40%●distinct values known / distinct values provided: 50%
Values
([],1)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([],2)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,1)],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,2)],3)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,1),(0,2)],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1
([(0,2),(1,2)],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(1,2),(1,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,1),(0,2),(0,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,2),(0,3),(3,1)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,2),(2,3)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1
([(0,3),(3,1),(3,2)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(1,3),(3,2)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(1,2)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ? = 1
([(0,3),(1,2),(1,3)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? = 1
([(0,3),(1,2),(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,2),(1,3),(1,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,1),(0,2),(0,3),(0,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,2),(0,3),(0,4),(4,1)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,3),(1,4),(4,2)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,3),(0,4),(4,1),(4,2)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,2),(1,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ? = 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(2,3),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1
([(1,4),(4,2),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(4,1),(4,2),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,4),(2,4),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,4),(4,2),(4,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,4),(2,4),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,4),(2,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,4),(2,3),(4,2)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,3),(2,3),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,4),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(1,4),(2,3)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ? = 1
([(1,4),(2,3),(2,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1
([(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(3,4)],5)
 => ? = 1
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,4),(1,2),(1,4),(4,3)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? = 1
([(0,4),(1,2),(1,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,4),(1,2),(1,3),(1,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,2),(0,4),(3,1),(4,3)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1
([(0,4),(1,2),(1,3),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(0,4),(1,2),(1,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? = 1
([(0,3),(1,2),(1,4),(3,4)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(3,4)],5)
 => ? = 1
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1
([(1,4),(3,2),(4,3)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? = 2
([(0,3),(3,4),(4,1),(4,2)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,4),(1,2),(2,4),(4,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,3),(1,4),(4,2)],5)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(2,5),(3,4),(4,5)],6)
 => ? = 1
([(0,4),(3,2),(4,1),(4,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,4),(1,2),(2,3),(2,4)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? = 1
([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => ? = 1
([(0,3),(1,2),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ? = 1
([(0,4),(1,2),(2,3),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(4,5)],6)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(3,4),(3,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(2,3),(2,4),(2,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,2),(1,3),(1,4),(1,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,3),(1,4),(1,5),(5,2)],6)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
Description
The pebbling number of a connected graph.
Matching statistic: St000259
Mapping
Mp00206: Posets —antichains of maximal size⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
St000259: Graphs ⟶ ℤResult quality: 40% ●values known / values provided: 40%●distinct values known / distinct values provided: 50%
Values
([],1)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([],2)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,1)],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,2)],3)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,1),(0,2)],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(0,2),(1,2)],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(1,2),(1,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,1),(0,2),(0,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,2),(0,3),(3,1)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,2),(2,3)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(0,3),(3,1),(3,2)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(1,3),(3,2)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(1,2)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ? = 1 - 1
([(0,3),(1,2),(1,3)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? = 1 - 1
([(0,3),(1,2),(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,2),(1,3),(1,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,1),(0,2),(0,3),(0,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,2),(0,3),(0,4),(4,1)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,3),(1,4),(4,2)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,3),(0,4),(4,1),(4,2)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,2),(1,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ? = 1 - 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(2,3),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(1,4),(4,2),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(4,1),(4,2),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,4),(2,4),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(1,4),(4,2),(4,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(1,4),(2,4),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(1,4),(2,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(1,4),(2,3),(4,2)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(1,3),(2,3),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(1,4),(2,3)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ? = 1 - 1
([(1,4),(2,3),(2,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(3,4)],5)
 => ? = 1 - 1
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,4),(1,2),(1,4),(4,3)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? = 1 - 1
([(0,4),(1,2),(1,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,4),(1,2),(1,3),(1,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,2),(0,4),(3,1),(4,3)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(0,4),(1,2),(1,3),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(0,4),(1,2),(1,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? = 1 - 1
([(0,3),(1,2),(1,4),(3,4)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(3,4)],5)
 => ? = 1 - 1
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(1,4),(3,2),(4,3)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? = 2 - 1
([(0,3),(3,4),(4,1),(4,2)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,4),(1,2),(2,4),(4,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,3),(1,4),(4,2)],5)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(2,5),(3,4),(4,5)],6)
 => ? = 1 - 1
([(0,4),(3,2),(4,1),(4,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,4),(1,2),(2,3),(2,4)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? = 1 - 1
([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => ? = 1 - 1
([(0,3),(1,2),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ? = 1 - 1
([(0,4),(1,2),(2,3),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(4,5)],6)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(3,4),(3,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(2,3),(2,4),(2,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,2),(1,3),(1,4),(1,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,3),(1,4),(1,5),(5,2)],6)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
Description
The diameter of a connected graph. This is the greatest distance between any pair of vertices.
Matching statistic: St000260
Mapping
Mp00206: Posets —antichains of maximal size⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
St000260: Graphs ⟶ ℤResult quality: 40% ●values known / values provided: 40%●distinct values known / distinct values provided: 50%
Values
([],1)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([],2)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,1)],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,2)],3)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,1),(0,2)],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(0,2),(1,2)],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(1,2),(1,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,1),(0,2),(0,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,2),(0,3),(3,1)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,2),(2,3)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(0,3),(3,1),(3,2)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(1,3),(3,2)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(1,2)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ? = 1 - 1
([(0,3),(1,2),(1,3)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? = 1 - 1
([(0,3),(1,2),(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,2),(1,3),(1,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,1),(0,2),(0,3),(0,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,2),(0,3),(0,4),(4,1)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,3),(1,4),(4,2)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,3),(0,4),(4,1),(4,2)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,2),(1,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ? = 1 - 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(2,3),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(1,4),(4,2),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(4,1),(4,2),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,4),(2,4),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(1,4),(4,2),(4,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(1,4),(2,4),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(1,4),(2,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(1,4),(2,3),(4,2)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(1,3),(2,3),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(1,4),(2,3)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ? = 1 - 1
([(1,4),(2,3),(2,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(3,4)],5)
 => ? = 1 - 1
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,4),(1,2),(1,4),(4,3)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? = 1 - 1
([(0,4),(1,2),(1,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,4),(1,2),(1,3),(1,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,2),(0,4),(3,1),(4,3)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(0,4),(1,2),(1,3),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(0,4),(1,2),(1,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? = 1 - 1
([(0,3),(1,2),(1,4),(3,4)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(3,4)],5)
 => ? = 1 - 1
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(1,4),(3,2),(4,3)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? = 2 - 1
([(0,3),(3,4),(4,1),(4,2)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,4),(1,2),(2,4),(4,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,3),(1,4),(4,2)],5)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(2,5),(3,4),(4,5)],6)
 => ? = 1 - 1
([(0,4),(3,2),(4,1),(4,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,4),(1,2),(2,3),(2,4)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? = 1 - 1
([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => ? = 1 - 1
([(0,3),(1,2),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ? = 1 - 1
([(0,4),(1,2),(2,3),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(4,5)],6)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(3,4),(3,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(2,3),(2,4),(2,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,2),(1,3),(1,4),(1,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,3),(1,4),(1,5),(5,2)],6)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
Description
The radius of a connected graph. This is the minimum eccentricity of any vertex.
Matching statistic: St000302
Mapping
Mp00206: Posets —antichains of maximal size⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
St000302: Graphs ⟶ ℤResult quality: 40% ●values known / values provided: 40%●distinct values known / distinct values provided: 50%
Values
([],1)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([],2)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,1)],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,2)],3)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,1),(0,2)],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(0,2),(1,2)],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(1,2),(1,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,1),(0,2),(0,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,2),(0,3),(3,1)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,2),(2,3)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(0,3),(3,1),(3,2)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(1,3),(3,2)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(1,2)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ? = 1 - 1
([(0,3),(1,2),(1,3)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? = 1 - 1
([(0,3),(1,2),(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,2),(1,3),(1,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,1),(0,2),(0,3),(0,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,2),(0,3),(0,4),(4,1)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,3),(1,4),(4,2)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,3),(0,4),(4,1),(4,2)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,2),(1,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ? = 1 - 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(2,3),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(1,4),(4,2),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(4,1),(4,2),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,4),(2,4),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(1,4),(4,2),(4,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(1,4),(2,4),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(1,4),(2,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(1,4),(2,3),(4,2)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(1,3),(2,3),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(1,4),(2,3)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ? = 1 - 1
([(1,4),(2,3),(2,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(3,4)],5)
 => ? = 1 - 1
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,4),(1,2),(1,4),(4,3)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? = 1 - 1
([(0,4),(1,2),(1,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,4),(1,2),(1,3),(1,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,2),(0,4),(3,1),(4,3)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(0,4),(1,2),(1,3),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(0,4),(1,2),(1,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? = 1 - 1
([(0,3),(1,2),(1,4),(3,4)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(3,4)],5)
 => ? = 1 - 1
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(1,4),(3,2),(4,3)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? = 2 - 1
([(0,3),(3,4),(4,1),(4,2)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,4),(1,2),(2,4),(4,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,3),(1,4),(4,2)],5)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(2,5),(3,4),(4,5)],6)
 => ? = 1 - 1
([(0,4),(3,2),(4,1),(4,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,4),(1,2),(2,3),(2,4)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? = 1 - 1
([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => ? = 1 - 1
([(0,3),(1,2),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ? = 1 - 1
([(0,4),(1,2),(2,3),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(4,5)],6)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(3,4),(3,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(2,3),(2,4),(2,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,2),(1,3),(1,4),(1,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,3),(1,4),(1,5),(5,2)],6)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
Description
The determinant of the distance matrix of a connected graph.
Matching statistic: St000466
Mapping
Mp00206: Posets —antichains of maximal size⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
St000466: Graphs ⟶ ℤResult quality: 40% ●values known / values provided: 40%●distinct values known / distinct values provided: 50%
Values
([],1)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([],2)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,1)],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,2)],3)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,1),(0,2)],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(0,2),(1,2)],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(1,2),(1,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,1),(0,2),(0,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,2),(0,3),(3,1)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,2),(2,3)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(0,3),(3,1),(3,2)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(1,3),(3,2)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(1,2)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ? = 1 - 1
([(0,3),(1,2),(1,3)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? = 1 - 1
([(0,3),(1,2),(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,2),(1,3),(1,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,1),(0,2),(0,3),(0,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,2),(0,3),(0,4),(4,1)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,3),(1,4),(4,2)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,3),(0,4),(4,1),(4,2)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,2),(1,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ? = 1 - 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(2,3),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(1,4),(4,2),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(4,1),(4,2),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,4),(2,4),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(1,4),(4,2),(4,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(1,4),(2,4),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(1,4),(2,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(1,4),(2,3),(4,2)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(1,3),(2,3),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(1,4),(2,3)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ? = 1 - 1
([(1,4),(2,3),(2,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(3,4)],5)
 => ? = 1 - 1
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,4),(1,2),(1,4),(4,3)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? = 1 - 1
([(0,4),(1,2),(1,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,4),(1,2),(1,3),(1,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,2),(0,4),(3,1),(4,3)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(0,4),(1,2),(1,3),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(0,4),(1,2),(1,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? = 1 - 1
([(0,3),(1,2),(1,4),(3,4)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(3,4)],5)
 => ? = 1 - 1
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(1,4),(3,2),(4,3)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? = 2 - 1
([(0,3),(3,4),(4,1),(4,2)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,4),(1,2),(2,4),(4,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,3),(1,4),(4,2)],5)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(2,5),(3,4),(4,5)],6)
 => ? = 1 - 1
([(0,4),(3,2),(4,1),(4,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,4),(1,2),(2,3),(2,4)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? = 1 - 1
([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => ? = 1 - 1
([(0,3),(1,2),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ? = 1 - 1
([(0,4),(1,2),(2,3),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(4,5)],6)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(3,4),(3,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(2,3),(2,4),(2,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,2),(1,3),(1,4),(1,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,3),(1,4),(1,5),(5,2)],6)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
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
Mapping
Mp00206: Posets —antichains of maximal size⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
St000467: Graphs ⟶ ℤResult quality: 40% ●values known / values provided: 40%●distinct values known / distinct values provided: 50%
Values
([],1)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([],2)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,1)],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,2)],3)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,1),(0,2)],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(0,2),(1,2)],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(1,2),(1,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,1),(0,2),(0,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,2),(0,3),(3,1)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,2),(2,3)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(0,3),(3,1),(3,2)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(1,3),(3,2)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(1,2)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ? = 1 - 1
([(0,3),(1,2),(1,3)],4)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? = 1 - 1
([(0,3),(1,2),(2,3)],4)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,2),(1,3),(1,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,1),(0,2),(0,3),(0,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,2),(0,3),(0,4),(4,1)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,3),(1,4),(4,2)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,3),(0,4),(4,1),(4,2)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,2),(1,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ? = 1 - 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(2,3),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(1,4),(4,2),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(4,1),(4,2),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,4),(2,4),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(1,4),(4,2),(4,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(1,4),(2,4),(4,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(1,4),(2,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(1,4),(2,3),(4,2)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(1,3),(2,3),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,4),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(1,4),(2,3)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ? = 1 - 1
([(1,4),(2,3),(2,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(3,4)],5)
 => ? = 1 - 1
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,4),(1,2),(1,4),(4,3)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? = 1 - 1
([(0,4),(1,2),(1,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,4),(1,2),(1,3),(1,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,2),(0,4),(3,1),(4,3)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(0,4),(1,2),(1,3),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(0,4),(1,2),(1,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? = 1 - 1
([(0,3),(1,2),(1,4),(3,4)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(3,4)],5)
 => ? = 1 - 1
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(1,4),(3,2),(4,3)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? = 2 - 1
([(0,3),(3,4),(4,1),(4,2)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,4),(1,2),(2,4),(4,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,3),(1,4),(4,2)],5)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(2,5),(3,4),(4,5)],6)
 => ? = 1 - 1
([(0,4),(3,2),(4,1),(4,3)],5)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,4),(1,2),(2,3),(2,4)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => ? = 1 - 1
([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => ? = 1 - 1
([(0,3),(1,2),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => ? = 1 - 1
([(0,4),(1,2),(2,3),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => ? = 1 - 1
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(4,5)],6)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(3,4),(3,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(2,3),(2,4),(2,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,2),(1,3),(1,4),(1,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(1,3),(1,4),(1,5),(5,2)],6)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 - 1
Description
The hyper-Wiener index of a connected graph. This is ∑{u,v}⊆Vd(u,v)+d(u,v)2.
The following 123 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St000908The length of the shortest maximal antichain in a poset. St001301The first Betti number of the order complex associated with the poset. St001634The trace of the Coxeter matrix of the incidence algebra of a poset. St000914The sum of the values of the Möbius function of a poset. St000284The Plancherel distribution on integer partitions. St000704The number of semistandard tableaux on a given integer partition with minimal maximal entry. St000901The cube of the number of standard Young tableaux with shape given by the partition. St001128The exponens consonantiae of a partition. St000936The number of even values of the symmetric group character corresponding to the partition. St000938The number of zeros of the symmetric group character corresponding to the partition. St000940The number of characters of the symmetric group whose value on the partition is zero. St001124The multiplicity of the standard representation in the Kronecker square corresponding to a partition. St001681The number of inclusion-wise minimal subsets of a lattice, whose meet is the bottom element. St001719The number of shortest chains of small intervals from the bottom to the top in a lattice. St001881The number of factors of a lattice as a Cartesian product of lattices. St001677The number of non-degenerate subsets of a lattice whose meet is the bottom element. St001845The number of join irreducibles minus the rank of a lattice. St000455The second largest eigenvalue of a graph if it is integral. St001496The number of graphs with the same Laplacian spectrum as the given graph. St001307The number of induced stars on four vertices in a graph. 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. 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. St001195The global dimension of the algebra A/AfA of the corresponding Nakayama algebra A with minimal left faithful projective-injective module Af. St000322The skewness of a graph. St001820The size of the image of the pop stack sorting operator. St001846The number of elements which do not have a complement in the lattice. St001578The minimal number of edges to add or remove to make a graph a line graph. St001877Number of indecomposable injective modules with projective dimension 2. St001001The number of indecomposable modules with projective and injective dimension equal to the global dimension of the Nakayama algebra corresponding to the Dyck path. 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. St001875The number of simple modules with projective dimension at most 1. St000689The maximal n such that the minimal generator-cogenerator module in the LNakayama algebra of a Dyck path is n-rigid. St001314The number of tilting modules of arbitrary projective dimension that have no simple modules as a direct summand in the corresponding Nakayama algebra. St001879The number of indecomposable summands of the top of the first syzygy of the dual of the regular module in the incidence algebra of the lattice. St001880The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice. St000264The girth of a graph, which is not a tree. St001613The binary logarithm of the size of the center of a lattice. St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset. St001493The number of simple modules with maximal even projective dimension in the corresponding Nakayama algebra. St001292The injective dimension of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path. St001256Number of simple reflexive modules that are 2-stable reflexive. St001289The vector space dimension of the n-fold tensor product of D(A), where n is maximal such that this n-fold tensor product is nonzero. St001021Sum of the differences between projective and codominant dimension of the non-projective indecomposable injective modules in the Nakayama algebra corresponding to the Dyck path. St001089Number of indecomposable projective non-injective modules minus the number of indecomposable projective non-injective modules with dominant dimension equal to the injective dimension in the corresponding Nakayama algebra. St001193The dimension of Ext1A(A/AeA,A) in the corresponding Nakayama algebra A such that eA is a minimal faithful projective-injective module. St001204Call a CNakayama algebra (a Nakayama algebra with a cyclic quiver) with Kupisch series L=[c0,c1,...,cn−1] such that n=c0<ci for all i>0 a special CNakayama algebra. St001216The number of indecomposable injective modules in the corresponding Nakayama algebra that have non-vanishing second Ext-group with the regular module. St001221The number of simple modules in the corresponding LNakayama algebra that have 2 dimensional second Extension group with the regular module. St001222Number of simple modules in the corresponding LNakayama algebra that have a unique 2-extension with the regular module. St001229The vector space dimension of the first extension group between the Jacobson radical J and J^2. St001230The number of simple modules with injective dimension equal to the dominant dimension equal to one and the dual property. St001264The smallest index i such that the i-th simple module has projective dimension equal to the global dimension of the corresponding Nakayama algebra. St001274The number of indecomposable injective modules with projective dimension equal to two. St001275The projective dimension of the second term in a minimal injective coresolution of the regular module. St001695The natural comajor index of a standard Young tableau. St001698The comajor index of a standard tableau minus the weighted size of its shape. St001699The major index of a standard tableau minus the weighted size of its shape. St001712The number of natural descents of a standard Young tableau. St001462The number of factors of a standard tableaux under concatenation. St001621The number of atoms of a lattice. St001198The number of simple modules in the algebra eAe with projective dimension at most 1 in the corresponding Nakayama algebra A with minimal faithful projective-injective module eA. St001206The maximal dimension of an indecomposable projective eAe-module (that is the height of the corresponding Dyck path) of the corresponding Nakayama algebra with minimal faithful projective-injective module eA. St000699The toughness times the least common multiple of 1,. St000181The number of connected components of the Hasse diagram for the poset. St000266The number of spanning subgraphs of a graph with the same connected components. St000267The number of maximal spanning forests contained in a graph. St000773The multiplicity of the largest Laplacian eigenvalue in a graph. St000775The multiplicity of the largest eigenvalue in a graph. St000785The number of distinct colouring schemes of a graph. St001272The number of graphs with the same degree sequence. St001316The domatic number of a graph. St001395The number of strictly unfriendly partitions of a graph. St001475The evaluation of the Tutte polynomial of the graph at (x,y) equal to (1,0). St001476The evaluation of the Tutte polynomial of the graph at (x,y) equal to (1,-1). St001546The number of monomials in the Tutte polynomial of a graph. St000283The size of the preimage of the map 'to graph' from Binary trees to Graphs. St000323The minimal crossing number of a graph. St000351The determinant of the adjacency matrix of a graph. St000368The Altshuler-Steinberg determinant of a graph. St000370The genus of a graph. St000379The number of Hamiltonian cycles in a graph. St000403The Szeged index minus the Wiener index of a graph. St000636The hull number of a graph. St000637The length of the longest cycle in a graph. St000671The maximin edge-connectivity for choosing a subgraph. St000948The chromatic discriminant of a graph. St001029The size of the core of a graph. St001069The coefficient of the monomial xy of the Tutte polynomial of the graph. St001109The number of proper colourings of a graph with as few colours as possible. St001119The length of a shortest maximal path in a graph. St001271The competition number of a graph. St001281The normalized isoperimetric number of a graph. St001305The number of induced cycles on four vertices in a graph. St001309The number of four-cliques in a graph. St001310The number of induced diamond graphs in a graph. St001311The cyclomatic number of a graph. St001317The minimal number of occurrences of the forest-pattern in a linear ordering of the vertices of the graph. St001320The minimal number of occurrences of the path-pattern in a linear ordering of the vertices of the graph. St001323The independence gap of a graph. St001324The minimal number of occurrences of the chordal-pattern in a linear ordering of the vertices of the graph. St001325The minimal number of occurrences of the comparability-pattern in a linear ordering of the vertices of the graph. St001326The minimal number of occurrences of the interval-pattern in a linear ordering of the vertices of the graph. St001328The minimal number of occurrences of the bipartite-pattern in a linear ordering of the vertices of the graph. St001329The minimal number of occurrences of the outerplanar pattern in a linear ordering of the vertices of the graph. St001331The size of the minimal feedback vertex set. St001334The minimal number of occurrences of the 3-colorable pattern in a linear ordering of the vertices of the graph. St001335The cardinality of a minimal cycle-isolating set of a graph. St001336The minimal number of vertices in a graph whose complement is triangle-free. St001357The maximal degree of a regular spanning subgraph of a graph. St001367The smallest number which does not occur as degree of a vertex in a graph. St001638The book thickness of a graph. St001654The monophonic hull number of a graph. St001689The number of celebrities in a graph. St001702The absolute value of the determinant of the adjacency matrix of a graph. St001736The total number of cycles in a graph. St001793The difference between the clique number and the chromatic number of a graph. St001794Half the number of sets of vertices in a graph which are dominating and non-blocking. St001795The binary logarithm of the evaluation of the Tutte polynomial of the graph at (x,y) equal to (-1,-1). St001796The absolute value of the quotient of the Tutte polynomial of the graph at (1,1) and (-1,-1). St001797The number of overfull subgraphs of a graph.