Processing math: 100%

Your data matches 152 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000552
(load all 6 compositions to match this statistic)
Mapping
Mp00264: Graphs —delete endpoints⟶ Graphs
St000552: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => ([],1)
 => 0
([],2)
 => ([],2)
 => 0
([(0,1)],2)
 => ([],1)
 => 0
([],3)
 => ([],3)
 => 0
([(1,2)],3)
 => ([],2)
 => 0
([(0,2),(1,2)],3)
 => ([],1)
 => 0
([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 0
([],4)
 => ([],4)
 => 0
([(2,3)],4)
 => ([],3)
 => 0
([(1,3),(2,3)],4)
 => ([],2)
 => 0
([(0,3),(1,3),(2,3)],4)
 => ([],1)
 => 0
([(0,3),(1,2)],4)
 => ([],2)
 => 0
([(0,3),(1,2),(2,3)],4)
 => ([],1)
 => 0
([(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => 0
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,2)],3)
 => 0
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 0
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 0
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 0
([],5)
 => ([],5)
 => 0
([(3,4)],5)
 => ([],4)
 => 0
([(2,4),(3,4)],5)
 => ([],3)
 => 0
([(1,4),(2,4),(3,4)],5)
 => ([],2)
 => 0
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => 0
([(1,4),(2,3)],5)
 => ([],3)
 => 0
([(1,4),(2,3),(3,4)],5)
 => ([],2)
 => 0
([(0,1),(2,4),(3,4)],5)
 => ([],2)
 => 0
([(2,3),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => 0
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([],1)
 => 0
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => 0
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 0
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => 0
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 0
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 0
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 0
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 0
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 0
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 0
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([],1)
 => 0
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(2,3)],4)
 => 0
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,2)],3)
 => 0
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 0
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 0
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => 0
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 0
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 0
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 0
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 0
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => 0
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 0
Description
The number of cut vertices of a graph. A cut vertex is one whose deletion increases the number of connected components.
Matching statistic: St001330
Mapping
Mp00274: Graphs —block-cut tree⟶ Graphs
Mp00203: Graphs —cone⟶ Graphs
St001330: Graphs ⟶ ℤResult quality: 33% ●values known / values provided: 53%●distinct values known / distinct values provided: 33%
Values
([],1)
 => ([],1)
 => ([(0,1)],2)
 => 2 = 0 + 2
([],2)
 => ([],2)
 => ([(0,2),(1,2)],3)
 => 2 = 0 + 2
([(0,1)],2)
 => ([],1)
 => ([(0,1)],2)
 => 2 = 0 + 2
([],3)
 => ([],3)
 => ([(0,3),(1,3),(2,3)],4)
 => 2 = 0 + 2
([(1,2)],3)
 => ([],2)
 => ([(0,2),(1,2)],3)
 => 2 = 0 + 2
([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ? = 0 + 2
([(0,1),(0,2),(1,2)],3)
 => ([],1)
 => ([(0,1)],2)
 => 2 = 0 + 2
([],4)
 => ([],4)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2 = 0 + 2
([(2,3)],4)
 => ([],3)
 => ([(0,3),(1,3),(2,3)],4)
 => 2 = 0 + 2
([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0 + 2
([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0 + 2
([(0,3),(1,2)],4)
 => ([],2)
 => ([(0,2),(1,2)],3)
 => 2 = 0 + 2
([(0,3),(1,2),(2,3)],4)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ? = 0 + 2
([(1,2),(1,3),(2,3)],4)
 => ([],2)
 => ([(0,2),(1,2)],3)
 => 2 = 0 + 2
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ? = 0 + 2
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([],1)
 => ([(0,1)],2)
 => 2 = 0 + 2
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],1)
 => ([(0,1)],2)
 => 2 = 0 + 2
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],1)
 => ([(0,1)],2)
 => 2 = 0 + 2
([],5)
 => ([],5)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
([(3,4)],5)
 => ([],4)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2 = 0 + 2
([(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 2
([(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 2
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 2
([(1,4),(2,3)],5)
 => ([],3)
 => ([(0,3),(1,3),(2,3)],4)
 => 2 = 0 + 2
([(1,4),(2,3),(3,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 0 + 2
([(0,1),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0 + 2
([(2,3),(2,4),(3,4)],5)
 => ([],3)
 => ([(0,3),(1,3),(2,3)],4)
 => 2 = 0 + 2
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 0 + 2
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0 + 2
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0 + 2
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([],2)
 => ([(0,2),(1,2)],3)
 => 2 = 0 + 2
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ? = 0 + 2
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => ([(0,2),(1,2)],3)
 => 2 = 0 + 2
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ? = 0 + 2
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ? = 0 + 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([],1)
 => ([(0,1)],2)
 => 2 = 0 + 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([(0,1)],2)
 => 2 = 0 + 2
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => ([(0,6),(0,7),(1,5),(1,7),(2,3),(2,4),(2,7),(3,5),(3,7),(4,6),(4,7),(5,7),(6,7)],8)
 => ? = 0 + 2
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => ([(0,2),(1,2)],3)
 => 2 = 0 + 2
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ? = 0 + 2
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ? = 1 + 2
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([],1)
 => ([(0,1)],2)
 => 2 = 0 + 2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([(0,1)],2)
 => 2 = 0 + 2
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([(0,1)],2)
 => 2 = 0 + 2
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ? = 0 + 2
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => ([(0,2),(1,2)],3)
 => 2 = 0 + 2
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ? = 0 + 2
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([(0,1)],2)
 => 2 = 0 + 2
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([],1)
 => ([(0,1)],2)
 => 2 = 0 + 2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([(0,1)],2)
 => 2 = 0 + 2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([(0,1)],2)
 => 2 = 0 + 2
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([(0,1)],2)
 => 2 = 0 + 2
([],6)
 => ([],6)
 => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
([(4,5)],6)
 => ([],5)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
([(3,5),(4,5)],6)
 => ([(3,5),(4,5)],6)
 => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 0 + 2
([(2,5),(3,5),(4,5)],6)
 => ([(2,5),(3,5),(4,5)],6)
 => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 0 + 2
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 0 + 2
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 0 + 2
([(2,5),(3,4)],6)
 => ([],4)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2 = 0 + 2
([(2,5),(3,4),(4,5)],6)
 => ([(2,6),(3,5),(4,5),(4,6)],7)
 => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
 => ? = 0 + 2
([(1,2),(3,5),(4,5)],6)
 => ([(2,4),(3,4)],5)
 => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 2
([(3,4),(3,5),(4,5)],6)
 => ([],4)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2 = 0 + 2
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 0 + 2
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 2
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,4),(3,4)],5)
 => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 2
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 0 + 2
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 2
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 2
([(2,4),(2,5),(3,4),(3,5)],6)
 => ([],3)
 => ([(0,3),(1,3),(2,3)],4)
 => 2 = 0 + 2
([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ? = 0 + 2
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0 + 2
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
 => ([(0,6),(0,8),(1,7),(1,8),(2,7),(2,8),(3,4),(3,5),(3,8),(4,6),(4,8),(5,7),(5,8),(6,8),(7,8)],9)
 => ? = 0 + 2
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],3)
 => ([(0,3),(1,3),(2,3)],4)
 => 2 = 0 + 2
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 0 + 2
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
 => ? = 0 + 2
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0 + 2
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0 + 2
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 0 + 2
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0 + 2
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],2)
 => ([(0,2),(1,2)],3)
 => 2 = 0 + 2
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ? = 0 + 2
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ? = 0 + 2
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],2)
 => ([(0,2),(1,2)],3)
 => 2 = 0 + 2
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ? = 0 + 2
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ? = 0 + 2
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],1)
 => ([(0,1)],2)
 => 2 = 0 + 2
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],1)
 => ([(0,1)],2)
 => 2 = 0 + 2
([(0,5),(1,4),(2,3)],6)
 => ([],3)
 => ([(0,3),(1,3),(2,3)],4)
 => 2 = 0 + 2
([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ([(0,8),(1,7),(1,8),(2,6),(2,8),(3,4),(3,5),(3,8),(4,6),(4,8),(5,7),(5,8),(6,8),(7,8)],9)
 => ? = 0 + 2
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 0 + 2
([(1,2),(3,4),(3,5),(4,5)],6)
 => ([],3)
 => ([(0,3),(1,3),(2,3)],4)
 => 2 = 0 + 2
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
 => ([(0,6),(0,8),(1,5),(1,8),(2,7),(2,8),(3,5),(3,7),(3,8),(4,6),(4,7),(4,8),(5,8),(6,8),(7,8)],9)
 => ? = 0 + 2
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 0 + 2
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([],2)
 => ([(0,2),(1,2)],3)
 => 2 = 0 + 2
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([],2)
 => ([(0,2),(1,2)],3)
 => 2 = 0 + 2
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],2)
 => ([(0,2),(1,2)],3)
 => 2 = 0 + 2
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],2)
 => ([(0,2),(1,2)],3)
 => 2 = 0 + 2
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],2)
 => ([(0,2),(1,2)],3)
 => 2 = 0 + 2
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],3)
 => ([(0,3),(1,3),(2,3)],4)
 => 2 = 0 + 2
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],1)
 => ([(0,1)],2)
 => 2 = 0 + 2
Description
The hat guessing number of a graph. Suppose that each vertex of a graph corresponds to a player, wearing a hat whose color is arbitrarily chosen from a set of q possible colors. Each player can see the hat colors of his neighbors, but not his own hat color. All of the players are asked to guess their own hat colors simultaneously, according to a predetermined guessing strategy and the hat colors they see, where no communication between them is allowed. The hat guessing number HG(G) of a graph G is the largest integer q such that there exists a guessing strategy guaranteeing at least one correct guess for any hat assignment of q possible colors. Because it suffices that a single player guesses correctly, the hat guessing number of a graph is the maximum of the hat guessing numbers of its connected components.
Matching statistic: St000259
Mapping
Mp00274: Graphs —block-cut tree⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
Mp00111: Graphs —complement⟶ Graphs
St000259: Graphs ⟶ ℤResult quality: 33% ●values known / values provided: 53%●distinct values known / distinct values provided: 33%
Values
([],1)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([],2)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,1)],2)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([],3)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,2)],3)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,1),(0,2),(1,2)],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([],4)
 => ([],4)
 => ([],1)
 => ([],1)
 => 0
([(2,3)],4)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,3),(1,2)],4)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(1,2),(2,3)],4)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,2),(1,3),(2,3)],4)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([],5)
 => ([],5)
 => ([],1)
 => ([],1)
 => 0
([(3,4)],5)
 => ([],4)
 => ([],1)
 => ([],1)
 => 0
([(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,4),(2,3)],5)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,4),(2,3),(3,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,1),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(2,3),(2,4),(3,4)],5)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => ?
 => ?
 => ? = 0
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([],6)
 => ([],6)
 => ([],1)
 => ([],1)
 => 0
([(4,5)],6)
 => ([],5)
 => ([],1)
 => ([],1)
 => 0
([(3,5),(4,5)],6)
 => ([(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(2,5),(3,5),(4,5)],6)
 => ([(2,5),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(2,5),(3,4)],6)
 => ([],4)
 => ([],1)
 => ([],1)
 => 0
([(2,5),(3,4),(4,5)],6)
 => ([(2,6),(3,5),(4,5),(4,6)],7)
 => ?
 => ?
 => ? = 0
([(1,2),(3,5),(4,5)],6)
 => ([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(3,4),(3,5),(4,5)],6)
 => ([],4)
 => ([],1)
 => ([],1)
 => 0
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ?
 => ?
 => ? = 0
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ?
 => ?
 => ? = 0
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(2,4),(2,5),(3,4),(3,5)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
 => ?
 => ?
 => ? = 0
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => ?
 => ?
 => ? = 0
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,5),(1,4),(2,3)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ?
 => ?
 => ? = 0
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,2),(3,4),(3,5),(4,5)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
 => ?
 => ?
 => ? = 0
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
Description
The diameter of a connected graph. This is the greatest distance between any pair of vertices.
Matching statistic: St000260
Mapping
Mp00274: Graphs —block-cut tree⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
Mp00111: Graphs —complement⟶ Graphs
St000260: Graphs ⟶ ℤResult quality: 33% ●values known / values provided: 53%●distinct values known / distinct values provided: 33%
Values
([],1)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([],2)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,1)],2)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([],3)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,2)],3)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,1),(0,2),(1,2)],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([],4)
 => ([],4)
 => ([],1)
 => ([],1)
 => 0
([(2,3)],4)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,3),(1,2)],4)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(1,2),(2,3)],4)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,2),(1,3),(2,3)],4)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([],5)
 => ([],5)
 => ([],1)
 => ([],1)
 => 0
([(3,4)],5)
 => ([],4)
 => ([],1)
 => ([],1)
 => 0
([(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,4),(2,3)],5)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,4),(2,3),(3,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,1),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(2,3),(2,4),(3,4)],5)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => ?
 => ?
 => ? = 0
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([],6)
 => ([],6)
 => ([],1)
 => ([],1)
 => 0
([(4,5)],6)
 => ([],5)
 => ([],1)
 => ([],1)
 => 0
([(3,5),(4,5)],6)
 => ([(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(2,5),(3,5),(4,5)],6)
 => ([(2,5),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(2,5),(3,4)],6)
 => ([],4)
 => ([],1)
 => ([],1)
 => 0
([(2,5),(3,4),(4,5)],6)
 => ([(2,6),(3,5),(4,5),(4,6)],7)
 => ?
 => ?
 => ? = 0
([(1,2),(3,5),(4,5)],6)
 => ([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(3,4),(3,5),(4,5)],6)
 => ([],4)
 => ([],1)
 => ([],1)
 => 0
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ?
 => ?
 => ? = 0
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ?
 => ?
 => ? = 0
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(2,4),(2,5),(3,4),(3,5)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
 => ?
 => ?
 => ? = 0
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => ?
 => ?
 => ? = 0
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,5),(1,4),(2,3)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ?
 => ?
 => ? = 0
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,2),(3,4),(3,5),(4,5)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
 => ?
 => ?
 => ? = 0
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
Description
The radius of a connected graph. This is the minimum eccentricity of any vertex.
Matching statistic: St000302
Mapping
Mp00274: Graphs —block-cut tree⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
Mp00111: Graphs —complement⟶ Graphs
St000302: Graphs ⟶ ℤResult quality: 33% ●values known / values provided: 53%●distinct values known / distinct values provided: 33%
Values
([],1)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([],2)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,1)],2)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([],3)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,2)],3)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,1),(0,2),(1,2)],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([],4)
 => ([],4)
 => ([],1)
 => ([],1)
 => 0
([(2,3)],4)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,3),(1,2)],4)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(1,2),(2,3)],4)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,2),(1,3),(2,3)],4)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([],5)
 => ([],5)
 => ([],1)
 => ([],1)
 => 0
([(3,4)],5)
 => ([],4)
 => ([],1)
 => ([],1)
 => 0
([(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,4),(2,3)],5)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,4),(2,3),(3,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,1),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(2,3),(2,4),(3,4)],5)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => ?
 => ?
 => ? = 0
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([],6)
 => ([],6)
 => ([],1)
 => ([],1)
 => 0
([(4,5)],6)
 => ([],5)
 => ([],1)
 => ([],1)
 => 0
([(3,5),(4,5)],6)
 => ([(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(2,5),(3,5),(4,5)],6)
 => ([(2,5),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(2,5),(3,4)],6)
 => ([],4)
 => ([],1)
 => ([],1)
 => 0
([(2,5),(3,4),(4,5)],6)
 => ([(2,6),(3,5),(4,5),(4,6)],7)
 => ?
 => ?
 => ? = 0
([(1,2),(3,5),(4,5)],6)
 => ([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(3,4),(3,5),(4,5)],6)
 => ([],4)
 => ([],1)
 => ([],1)
 => 0
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ?
 => ?
 => ? = 0
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ?
 => ?
 => ? = 0
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(2,4),(2,5),(3,4),(3,5)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
 => ?
 => ?
 => ? = 0
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => ?
 => ?
 => ? = 0
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,5),(1,4),(2,3)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ?
 => ?
 => ? = 0
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,2),(3,4),(3,5),(4,5)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
 => ?
 => ?
 => ? = 0
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
Description
The determinant of the distance matrix of a connected graph.
Matching statistic: St000466
Mapping
Mp00274: Graphs —block-cut tree⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
Mp00111: Graphs —complement⟶ Graphs
St000466: Graphs ⟶ ℤResult quality: 33% ●values known / values provided: 53%●distinct values known / distinct values provided: 33%
Values
([],1)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([],2)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,1)],2)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([],3)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,2)],3)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,1),(0,2),(1,2)],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([],4)
 => ([],4)
 => ([],1)
 => ([],1)
 => 0
([(2,3)],4)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,3),(1,2)],4)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(1,2),(2,3)],4)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,2),(1,3),(2,3)],4)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([],5)
 => ([],5)
 => ([],1)
 => ([],1)
 => 0
([(3,4)],5)
 => ([],4)
 => ([],1)
 => ([],1)
 => 0
([(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,4),(2,3)],5)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,4),(2,3),(3,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,1),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(2,3),(2,4),(3,4)],5)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => ?
 => ?
 => ? = 0
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([],6)
 => ([],6)
 => ([],1)
 => ([],1)
 => 0
([(4,5)],6)
 => ([],5)
 => ([],1)
 => ([],1)
 => 0
([(3,5),(4,5)],6)
 => ([(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(2,5),(3,5),(4,5)],6)
 => ([(2,5),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(2,5),(3,4)],6)
 => ([],4)
 => ([],1)
 => ([],1)
 => 0
([(2,5),(3,4),(4,5)],6)
 => ([(2,6),(3,5),(4,5),(4,6)],7)
 => ?
 => ?
 => ? = 0
([(1,2),(3,5),(4,5)],6)
 => ([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(3,4),(3,5),(4,5)],6)
 => ([],4)
 => ([],1)
 => ([],1)
 => 0
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ?
 => ?
 => ? = 0
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ?
 => ?
 => ? = 0
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(2,4),(2,5),(3,4),(3,5)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
 => ?
 => ?
 => ? = 0
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => ?
 => ?
 => ? = 0
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,5),(1,4),(2,3)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ?
 => ?
 => ? = 0
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,2),(3,4),(3,5),(4,5)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
 => ?
 => ?
 => ? = 0
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
Description
The Gutman (or modified Schultz) index of a connected graph. This is ∑{u,v}⊆Vd(u)d(v)d(u,v) where d(u) is the degree of vertex u and d(u,v) is the distance between vertices u and v. For trees on n vertices, the modified Schultz index is related to the Wiener index via S∗(T)=4W(T)−(n−1)(2n−1) [1].
Matching statistic: St000467
Mapping
Mp00274: Graphs —block-cut tree⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
Mp00111: Graphs —complement⟶ Graphs
St000467: Graphs ⟶ ℤResult quality: 33% ●values known / values provided: 53%●distinct values known / distinct values provided: 33%
Values
([],1)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([],2)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,1)],2)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([],3)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,2)],3)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,1),(0,2),(1,2)],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([],4)
 => ([],4)
 => ([],1)
 => ([],1)
 => 0
([(2,3)],4)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,3),(1,2)],4)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(1,2),(2,3)],4)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,2),(1,3),(2,3)],4)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([],5)
 => ([],5)
 => ([],1)
 => ([],1)
 => 0
([(3,4)],5)
 => ([],4)
 => ([],1)
 => ([],1)
 => 0
([(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,4),(2,3)],5)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,4),(2,3),(3,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,1),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(2,3),(2,4),(3,4)],5)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => ?
 => ?
 => ? = 0
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([],6)
 => ([],6)
 => ([],1)
 => ([],1)
 => 0
([(4,5)],6)
 => ([],5)
 => ([],1)
 => ([],1)
 => 0
([(3,5),(4,5)],6)
 => ([(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(2,5),(3,5),(4,5)],6)
 => ([(2,5),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(2,5),(3,4)],6)
 => ([],4)
 => ([],1)
 => ([],1)
 => 0
([(2,5),(3,4),(4,5)],6)
 => ([(2,6),(3,5),(4,5),(4,6)],7)
 => ?
 => ?
 => ? = 0
([(1,2),(3,5),(4,5)],6)
 => ([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(3,4),(3,5),(4,5)],6)
 => ([],4)
 => ([],1)
 => ([],1)
 => 0
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ?
 => ?
 => ? = 0
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ?
 => ?
 => ? = 0
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(2,4),(2,5),(3,4),(3,5)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
 => ?
 => ?
 => ? = 0
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => ?
 => ?
 => ? = 0
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,5),(1,4),(2,3)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ?
 => ?
 => ? = 0
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,2),(3,4),(3,5),(4,5)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
 => ?
 => ?
 => ? = 0
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
Description
The hyper-Wiener index of a connected graph. This is ∑{u,v}⊆Vd(u,v)+d(u,v)2.
Matching statistic: St000771
Mapping
Mp00274: Graphs —block-cut tree⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
Mp00111: Graphs —complement⟶ Graphs
St000771: Graphs ⟶ ℤResult quality: 33% ●values known / values provided: 53%●distinct values known / distinct values provided: 33%
Values
([],1)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([],2)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,1)],2)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([],3)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,2)],3)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,1),(0,2),(1,2)],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([],4)
 => ([],4)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(2,3)],4)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,3),(1,2)],4)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,3),(1,2),(2,3)],4)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(1,2),(1,3),(2,3)],4)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([],5)
 => ([],5)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(3,4)],5)
 => ([],4)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(1,4),(2,3)],5)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,4),(2,3),(3,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,1),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(2,3),(2,4),(3,4)],5)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => ?
 => ?
 => ? = 0 + 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 + 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([],6)
 => ([],6)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(4,5)],6)
 => ([],5)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(3,5),(4,5)],6)
 => ([(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(2,5),(3,5),(4,5)],6)
 => ([(2,5),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(2,5),(3,4)],6)
 => ([],4)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(2,5),(3,4),(4,5)],6)
 => ([(2,6),(3,5),(4,5),(4,6)],7)
 => ?
 => ?
 => ? = 0 + 1
([(1,2),(3,5),(4,5)],6)
 => ([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(3,4),(3,5),(4,5)],6)
 => ([],4)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ?
 => ?
 => ? = 0 + 1
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ?
 => ?
 => ? = 0 + 1
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(2,4),(2,5),(3,4),(3,5)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
 => ?
 => ?
 => ? = 0 + 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => ?
 => ?
 => ? = 0 + 1
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,5),(1,4),(2,3)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ?
 => ?
 => ? = 0 + 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(1,2),(3,4),(3,5),(4,5)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
 => ?
 => ?
 => ? = 0 + 1
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
Description
The largest multiplicity of a distance Laplacian eigenvalue in a connected graph. The distance Laplacian of a graph is the (symmetric) matrix with row and column sums 0, which has the negative distances between two vertices as its off-diagonal entries. This statistic is the largest multiplicity of an eigenvalue. For example, the cycle on four vertices has distance Laplacian (4−1−2−1−14−1−2−2−14−1−1−2−14). Its eigenvalues are 0,4,4,6, so the statistic is 2. The path on four vertices has eigenvalues 0,4.7…,6,9.2… and therefore statistic 1.
Matching statistic: St000772
Mapping
Mp00274: Graphs —block-cut tree⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
Mp00111: Graphs —complement⟶ Graphs
St000772: Graphs ⟶ ℤResult quality: 33% ●values known / values provided: 53%●distinct values known / distinct values provided: 33%
Values
([],1)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([],2)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,1)],2)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([],3)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,2)],3)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,1),(0,2),(1,2)],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([],4)
 => ([],4)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(2,3)],4)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,3),(1,2)],4)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,3),(1,2),(2,3)],4)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(1,2),(1,3),(2,3)],4)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([],5)
 => ([],5)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(3,4)],5)
 => ([],4)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(1,4),(2,3)],5)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,4),(2,3),(3,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,1),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(2,3),(2,4),(3,4)],5)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => ?
 => ?
 => ? = 0 + 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 + 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([],6)
 => ([],6)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(4,5)],6)
 => ([],5)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(3,5),(4,5)],6)
 => ([(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(2,5),(3,5),(4,5)],6)
 => ([(2,5),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(2,5),(3,4)],6)
 => ([],4)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(2,5),(3,4),(4,5)],6)
 => ([(2,6),(3,5),(4,5),(4,6)],7)
 => ?
 => ?
 => ? = 0 + 1
([(1,2),(3,5),(4,5)],6)
 => ([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(3,4),(3,5),(4,5)],6)
 => ([],4)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ?
 => ?
 => ? = 0 + 1
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ?
 => ?
 => ? = 0 + 1
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(2,4),(2,5),(3,4),(3,5)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
 => ?
 => ?
 => ? = 0 + 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => ?
 => ?
 => ? = 0 + 1
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,5),(1,4),(2,3)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ?
 => ?
 => ? = 0 + 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(1,2),(3,4),(3,5),(4,5)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
 => ?
 => ?
 => ? = 0 + 1
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
Description
The multiplicity of the largest distance Laplacian eigenvalue in a connected graph. The distance Laplacian of a graph is the (symmetric) matrix with row and column sums 0, which has the negative distances between two vertices as its off-diagonal entries. This statistic is the largest multiplicity of an eigenvalue. For example, the cycle on four vertices has distance Laplacian (4−1−2−1−14−1−2−2−14−1−1−2−14). Its eigenvalues are 0,4,4,6, so the statistic is 1. The path on four vertices has eigenvalues 0,4.7…,6,9.2… and therefore also statistic 1. The graphs with statistic n−1, n−2 and n−3 have been characterised, see [1].
Matching statistic: St000777
Mapping
Mp00274: Graphs —block-cut tree⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
Mp00111: Graphs —complement⟶ Graphs
St000777: Graphs ⟶ ℤResult quality: 33% ●values known / values provided: 53%●distinct values known / distinct values provided: 33%
Values
([],1)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([],2)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,1)],2)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([],3)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,2)],3)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,1),(0,2),(1,2)],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([],4)
 => ([],4)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(2,3)],4)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,3),(1,2)],4)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,3),(1,2),(2,3)],4)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(1,2),(1,3),(2,3)],4)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([],5)
 => ([],5)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(3,4)],5)
 => ([],4)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(1,4),(2,3)],5)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,4),(2,3),(3,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,1),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(2,3),(2,4),(3,4)],5)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => ?
 => ?
 => ? = 0 + 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 + 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([],6)
 => ([],6)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(4,5)],6)
 => ([],5)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(3,5),(4,5)],6)
 => ([(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(2,5),(3,5),(4,5)],6)
 => ([(2,5),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(2,5),(3,4)],6)
 => ([],4)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(2,5),(3,4),(4,5)],6)
 => ([(2,6),(3,5),(4,5),(4,6)],7)
 => ?
 => ?
 => ? = 0 + 1
([(1,2),(3,5),(4,5)],6)
 => ([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(3,4),(3,5),(4,5)],6)
 => ([],4)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ?
 => ?
 => ? = 0 + 1
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ?
 => ?
 => ? = 0 + 1
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(2,4),(2,5),(3,4),(3,5)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
 => ?
 => ?
 => ? = 0 + 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => ?
 => ?
 => ? = 0 + 1
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,5),(1,4),(2,3)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)
 => ?
 => ?
 => ? = 0 + 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(1,2),(3,4),(3,5),(4,5)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
 => ?
 => ?
 => ? = 0 + 1
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 0 + 1
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],3)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
Description
The number of distinct eigenvalues of the distance Laplacian of a connected graph.
The following 142 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St001645The pebbling number of a connected graph. St001846The number of elements which do not have a complement in the lattice. St001719The number of shortest chains of small intervals from the bottom to the top in a lattice. St001820The size of the image of the pop stack sorting operator. St000264The girth of a graph, which is not a tree. St001001The number of indecomposable modules with projective and injective dimension equal to the global dimension of the Nakayama algebra corresponding to the Dyck path. St001322The size of a minimal independent dominating set in a graph. St001339The irredundance number of a graph. St001363The Euler characteristic of a graph according to Knill. St000447The number of pairs of vertices of a graph with distance 3. St001256Number of simple reflexive modules that are 2-stable reflexive. 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. St001113Number of indecomposable projective non-injective modules with reflexive Auslander-Reiten sequences in the corresponding Nakayama algebra. St001140Number of indecomposable modules with projective and injective dimension at least two in the corresponding Nakayama algebra. St001163The number of simple modules with dominant dimension at least three 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. St001219Number of simple modules S in the corresponding Nakayama algebra such that the Auslander-Reiten sequence ending at S has the property that all modules in the exact sequence are reflexive. St001264The smallest index i such that the i-th simple module has projective dimension equal to the global dimension of 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. St001493The number of simple modules with maximal even projective dimension in the corresponding Nakayama algebra. 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. St000287The number of connected components of a graph. St001518The number of graphs with the same ordinary spectrum as the given graph. St001314The number of tilting modules of arbitrary projective dimension that have no simple modules as a direct summand in the corresponding Nakayama algebra. St001722The number of minimal chains with small intervals between a binary word and the top element. St001570The minimal number of edges to add to make a graph Hamiltonian. St001435The number of missing boxes in the first row. St001438The number of missing boxes of a skew partition. St001487The number of inner corners of a skew partition. St001490The number of connected components of a skew partition. St000068The number of minimal elements in a poset. St001845The number of join irreducibles minus the rank of a lattice. St001651The Frankl number of a lattice. St000221The number of strong fixed points of a permutation. St000279The size of the preimage of the map 'cycle-as-one-line notation' from Permutations to Permutations. St000375The number of non weak exceedences of a permutation that are mid-points of a decreasing subsequence of length 3. St000623The number of occurrences of the pattern 52341 in a permutation. St000689The maximal n such that the minimal generator-cogenerator module in the LNakayama algebra of a Dyck path is n-rigid. St000787The number of flips required to make a perfect matching noncrossing. St001381The fertility of a permutation. St001444The rank of the skew-symmetric form which is non-zero on crossing arcs of a perfect matching. St001466The number of transpositions swapping cyclically adjacent numbers in a permutation. St001549The number of restricted non-inversions between exceedances. St001551The number of restricted non-inversions between exceedances where the rightmost exceedance is linked. St001552The number of inversions between excedances and fixed points of a permutation. St001663The number of occurrences of the Hertzsprung pattern 132 in a permutation. St001810The number of fixed points of a permutation smaller than its largest moved point. St001811The Castelnuovo-Mumford regularity of a permutation. St001837The number of occurrences of a 312 pattern in the restricted growth word of a perfect matching. St001850The number of Hecke atoms of a permutation. St000056The decomposition (or block) number of a permutation. St000486The number of cycles of length at least 3 of a permutation. St000694The number of affine bounded permutations that project to a given permutation. St000788The number of nesting-similar perfect matchings of a perfect matching. St001174The Gorenstein dimension of the algebra A/I when I is the tilting module corresponding to the permutation in the Auslander algebra of K[x]/(xn). St001208The number of connected components of the quiver of A/T when T is the 1-tilting module corresponding to the permutation in the Auslander algebra A of K[x]/(xn). St001461The number of topologically connected components of the chord diagram of a permutation. St001590The crossing number of a perfect matching. St001830The chord expansion number of a perfect matching. St001832The number of non-crossing perfect matchings in the chord expansion of a perfect matching. St001859The number of factors of the Stanley symmetric function associated with a permutation. St001359The number of permutations in the equivalence class of a permutation obtained by taking inverses of cycles. St001195The global dimension of the algebra A/AfA of the corresponding Nakayama algebra A with minimal left faithful projective-injective module Af. St001890The maximum magnitude of the Möbius function of a poset. St000175Degree of the polynomial counting the number of semistandard Young tableaux when stretching the shape. St000205Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and partition weight. St000206Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and integer composition weight. St000225Difference between largest and smallest parts in a partition. St000749The smallest integer d such that the restriction of the representation corresponding to a partition of n to the symmetric group on n-d letters has a constituent of odd degree. St001175The size of a partition minus the hook length of the base cell. St001178Twelve times the variance of the major index among all standard Young tableaux of a partition. St001586The number of odd parts smaller than the largest even part in an integer partition. St000618The number of self-evacuating tableaux of given shape. St000781The number of proper colouring schemes of a Ferrers diagram. St001432The order dimension of the partition. St001609The number of coloured trees such that the multiplicities of colours are given by a partition. St001780The order of promotion on the set of standard tableaux of given shape. St001899The total number of irreducible representations contained in the higher Lie character for an integer partition. St001900The number of distinct irreducible representations contained in the higher Lie character for an integer partition. St001901The largest multiplicity of an irreducible representation contained in the higher Lie character for an integer partition. St001908The number of semistandard tableaux of distinct weight whose maximal entry is the length of the partition. St001913The number of preimages of an integer partition in Bulgarian solitaire. St001924The number of cells in an integer partition whose arm and leg length coincide. St001936The number of transitive factorisations of a permutation of given cycle type into star transpositions. St000143The largest repeated part of a partition. St000185The weighted size of a partition. St001214The aft of an integer partition. St001440The number of standard Young tableaux whose major index is congruent one modulo the size of a given integer partition. St000049The number of set partitions whose sorted block sizes correspond to the partition. St000275Number of permutations whose sorted list of non zero multiplicities of the Lehmer code is the given partition. St000783The side length of the largest staircase partition fitting into a partition. St001442The number of standard Young tableaux whose major index is divisible by the size of a given integer partition. St000318The number of addable cells of the Ferrers diagram of an integer partition. St001124The multiplicity of the standard representation in the Kronecker square corresponding to a partition. St001568The smallest positive integer that does not appear twice in the partition. St001325The minimal number of occurrences of the comparability-pattern in a linear ordering of the vertices of the graph. St001367The smallest number which does not occur as degree of a vertex in a graph. St001479The number of bridges of a graph. St001103The number of words with multiplicities of the letters given by the partition, avoiding the consecutive pattern 123. St001333The cardinality of a minimal edge-isolating set of a graph. St001340The cardinality of a minimal non-edge isolating set of a graph. St001496The number of graphs with the same Laplacian spectrum as the given graph. 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. St001877Number of indecomposable injective modules with projective dimension 2. St001703The villainy of a graph. St001738The minimal order of a graph which is not an induced subgraph of the given graph. St001301The first Betti number of the order complex associated with the poset. St000181The number of connected components of the Hasse diagram for the poset. St000908The length of the shortest maximal antichain in a poset. St001634The trace of the Coxeter matrix of the incidence algebra of a poset. 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. St001236The dominant dimension of the corresponding Comp-Nakayama algebra. St000699The toughness times the least common multiple of 1,. 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. St000941The number of characters of the symmetric group whose value on the partition is even. St000284The Plancherel distribution on integer partitions. St000698The number of 2-rim hooks removed from an integer partition to obtain its associated 2-core. 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. St000514The number of invariant simple graphs when acting with a permutation of given cycle type. St000515The number of invariant set partitions when acting with a permutation of given cycle type. St000449The number of pairs of vertices of a graph with distance 4. St001095The number of non-isomorphic posets with precisely one further covering relation. St001793The difference between the clique number and the chromatic number of a graph. St000553The number of blocks of a graph. St000775The multiplicity of the largest eigenvalue in a graph. St000914The sum of the values of the Möbius function of a poset. St001562The value of the complete homogeneous symmetric function evaluated at 1. St001563The value of the power-sum symmetric function evaluated at 1. St001564The value of the forgotten symmetric functions when all variables set to 1. St001739The number of graphs with the same edge polytope as the given graph. St001740The number of graphs with the same symmetric edge polytope as the given graph.