- FindStat

Your data matches 45 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)

Matching statistic: St000376

Mapping

Mp00276: Graphs —to edge-partition of biconnected components⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00028: Dyck paths —reverse⟶ Dyck paths
St000376: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

([(0,2),(1,2)],3)
 => [1,1]
 => [1,1,0,0]
 => [1,1,0,0]
 => 0
([(0,1),(0,2),(1,2)],3)
 => [3]
 => [1,0,1,0,1,0]
 => [1,0,1,0,1,0]
 => 0
([(1,3),(2,3)],4)
 => [1,1]
 => [1,1,0,0]
 => [1,1,0,0]
 => 0
([(0,3),(1,3),(2,3)],4)
 => [1,1,1]
 => [1,1,0,1,0,0]
 => [1,1,0,1,0,0]
 => 0
([(0,3),(1,2)],4)
 => [1,1]
 => [1,1,0,0]
 => [1,1,0,0]
 => 0
([(0,3),(1,2),(2,3)],4)
 => [1,1,1]
 => [1,1,0,1,0,0]
 => [1,1,0,1,0,0]
 => 0
([(1,2),(1,3),(2,3)],4)
 => [3]
 => [1,0,1,0,1,0]
 => [1,0,1,0,1,0]
 => 0
([(0,3),(1,2),(1,3),(2,3)],4)
 => [3,1]
 => [1,0,1,0,1,1,0,0]
 => [1,1,0,0,1,0,1,0]
 => 0
([(0,2),(0,3),(1,2),(1,3)],4)
 => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => 0
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [5]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => 0
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => 0
([(2,4),(3,4)],5)
 => [1,1]
 => [1,1,0,0]
 => [1,1,0,0]
 => 0
([(1,4),(2,4),(3,4)],5)
 => [1,1,1]
 => [1,1,0,1,0,0]
 => [1,1,0,1,0,0]
 => 0
([(0,4),(1,4),(2,4),(3,4)],5)
 => [1,1,1,1]
 => [1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0]
 => 1
([(1,4),(2,3)],5)
 => [1,1]
 => [1,1,0,0]
 => [1,1,0,0]
 => 0
([(1,4),(2,3),(3,4)],5)
 => [1,1,1]
 => [1,1,0,1,0,0]
 => [1,1,0,1,0,0]
 => 0
([(0,1),(2,4),(3,4)],5)
 => [1,1,1]
 => [1,1,0,1,0,0]
 => [1,1,0,1,0,0]
 => 0
([(2,3),(2,4),(3,4)],5)
 => [3]
 => [1,0,1,0,1,0]
 => [1,0,1,0,1,0]
 => 0
([(0,4),(1,4),(2,3),(3,4)],5)
 => [1,1,1,1]
 => [1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0]
 => 1
([(1,4),(2,3),(2,4),(3,4)],5)
 => [3,1]
 => [1,0,1,0,1,1,0,0]
 => [1,1,0,0,1,0,1,0]
 => 0
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => [3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => 0
([(1,3),(1,4),(2,3),(2,4)],5)
 => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => 0
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => 0
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => 0
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => 0
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [5,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0]
 => 0
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => 0
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [7]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => 0
([(0,4),(1,3),(2,3),(2,4)],5)
 => [1,1,1,1]
 => [1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0]
 => 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => [3,1]
 => [1,0,1,0,1,1,0,0]
 => [1,1,0,0,1,0,1,0]
 => 0
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => [3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => 0
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => [3,3]
 => [1,1,1,0,1,0,0,0]
 => [1,1,1,0,1,0,0,0]
 => 0
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => [5]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => 0
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => 0
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => [7]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => 0
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => [5,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0]
 => 0
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => 0
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [6,1]
 => [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,0]
 => 0
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [8]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => 0
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => [7]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => 0
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => [8]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => 0
([(3,5),(4,5)],6)
 => [1,1]
 => [1,1,0,0]
 => [1,1,0,0]
 => 0
([(2,5),(3,5),(4,5)],6)
 => [1,1,1]
 => [1,1,0,1,0,0]
 => [1,1,0,1,0,0]
 => 0
([(1,5),(2,5),(3,5),(4,5)],6)
 => [1,1,1,1]
 => [1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0]
 => 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => [1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 2
([(2,5),(3,4)],6)
 => [1,1]
 => [1,1,0,0]
 => [1,1,0,0]
 => 0
([(2,5),(3,4),(4,5)],6)
 => [1,1,1]
 => [1,1,0,1,0,0]
 => [1,1,0,1,0,0]
 => 0
([(1,2),(3,5),(4,5)],6)
 => [1,1,1]
 => [1,1,0,1,0,0]
 => [1,1,0,1,0,0]
 => 0
([(3,4),(3,5),(4,5)],6)
 => [3]
 => [1,0,1,0,1,0]
 => [1,0,1,0,1,0]
 => 0
([(1,5),(2,5),(3,4),(4,5)],6)
 => [1,1,1,1]
 => [1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0]
 => 1

Description

The bounce deficit of a Dyck path. For a Dyck path

$D$ of semilength

$n$ , this is defined as

$\binom{n}{2} - \operatorname{area}(D) - \operatorname{bounce}(D).$ The zeta map [[Mp00032]] sends this statistic to the dinv deficit [[St000369]], both are thus equidistributed.

Matching statistic: St001330

Mapping

Mp00274: Graphs —block-cut tree⟶ Graphs
Mp00203: Graphs —cone⟶ Graphs
St001330: Graphs ⟶ ℤResult quality: 17% ●values known / values provided: 25%●distinct values known / distinct values provided: 17%

Values

([(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
([(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
([(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)
 => ? = 1 + 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)
 => ? = 1 + 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)
 => ? = 1 + 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)
 => ? = 0 + 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
([(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)
 => ? = 1 + 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)
 => ? = 2 + 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)
 => ? = 1 + 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)
 => ? = 1 + 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)
 => ? = 2 + 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)
 => ? = 1 + 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)
 => ? = 1 + 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)
 => ? = 2 + 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)
 => ? = 2 + 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)
 => ? = 1 + 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
([(0,5),(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)
 => ? = 1 + 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)
 => ? = 1 + 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)
 => ? = 2 + 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
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)
 => ([],1)
 => ([(0,1)],2)
 => 2 = 0 + 2
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],1)
 => ([(0,1)],2)
 => 2 = 0 + 2
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],2)
 => ([(0,2),(1,2)],3)
 => 2 = 0 + 2
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],2)
 => ([(0,2),(1,2)],3)
 => 2 = 0 + 2
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([],2)
 => ([(0,2),(1,2)],3)
 => 2 = 0 + 2
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => ([],1)
 => ([(0,1)],2)
 => 2 = 0 + 2
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
 => ([],1)
 => ([(0,1)],2)
 => 2 = 0 + 2
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([],1)
 => ([(0,1)],2)
 => 2 = 0 + 2
([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],1)
 => ([(0,1)],2)
 => 2 = 0 + 2
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([],1)
 => ([(0,1)],2)
 => 2 = 0 + 2
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],1)
 => ([(0,1)],2)
 => 2 = 0 + 2
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => ([],2)
 => ([(0,2),(1,2)],3)
 => 2 = 0 + 2
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],2)
 => ([(0,2),(1,2)],3)
 => 2 = 0 + 2
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],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: 17% ●values known / values provided: 25%●distinct values known / distinct values provided: 17%

Values

([(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
([(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
([(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)
 => ? = 1
([(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)
 => ? = 1
([(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)
 => ?
 => ?
 => ? = 1
([(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)
 => ? = 0
([(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
([(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)
 => ? = 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)
 => ? = 2
([(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)
 => ?
 => ?
 => ? = 1
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(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)
 => ?
 => ?
 => ? = 2
([(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)
 => ? = 1
([(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)
 => ? = 1
([(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)
 => ?
 => ?
 => ? = 2
([(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)
 => ?
 => ?
 => ? = 2
([(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)
 => ? = 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
([(1,4),(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
([(0,5),(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)
 => ?
 => ?
 => ? = 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(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)
 => ?
 => ?
 => ? = 2
([(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
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],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: 17% ●values known / values provided: 25%●distinct values known / distinct values provided: 17%

Values

([(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
([(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
([(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)
 => ? = 1
([(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)
 => ? = 1
([(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)
 => ?
 => ?
 => ? = 1
([(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)
 => ? = 0
([(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
([(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)
 => ? = 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)
 => ? = 2
([(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)
 => ?
 => ?
 => ? = 1
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(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)
 => ?
 => ?
 => ? = 2
([(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)
 => ? = 1
([(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)
 => ? = 1
([(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)
 => ?
 => ?
 => ? = 2
([(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)
 => ?
 => ?
 => ? = 2
([(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)
 => ? = 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
([(1,4),(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
([(0,5),(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)
 => ?
 => ?
 => ? = 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(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)
 => ?
 => ?
 => ? = 2
([(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
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],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: 17% ●values known / values provided: 25%●distinct values known / distinct values provided: 17%

Values

([(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
([(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
([(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)
 => ? = 1
([(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)
 => ? = 1
([(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)
 => ?
 => ?
 => ? = 1
([(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)
 => ? = 0
([(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
([(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)
 => ? = 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)
 => ? = 2
([(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)
 => ?
 => ?
 => ? = 1
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(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)
 => ?
 => ?
 => ? = 2
([(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)
 => ? = 1
([(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)
 => ? = 1
([(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)
 => ?
 => ?
 => ? = 2
([(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)
 => ?
 => ?
 => ? = 2
([(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)
 => ? = 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
([(1,4),(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
([(0,5),(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)
 => ?
 => ?
 => ? = 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(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)
 => ?
 => ?
 => ? = 2
([(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
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],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: 17% ●values known / values provided: 25%●distinct values known / distinct values provided: 17%

Values

([(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
([(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
([(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)
 => ? = 1
([(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)
 => ? = 1
([(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)
 => ?
 => ?
 => ? = 1
([(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)
 => ? = 0
([(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
([(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)
 => ? = 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)
 => ? = 2
([(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)
 => ?
 => ?
 => ? = 1
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(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)
 => ?
 => ?
 => ? = 2
([(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)
 => ? = 1
([(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)
 => ? = 1
([(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)
 => ?
 => ?
 => ? = 2
([(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)
 => ?
 => ?
 => ? = 2
([(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)
 => ? = 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
([(1,4),(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
([(0,5),(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)
 => ?
 => ?
 => ? = 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(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)
 => ?
 => ?
 => ? = 2
([(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
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0

Description

The Gutman (or modified Schultz) index of a connected graph. This is

$\sum_{\{u,v\}\subseteq V} d(u)d(v)d(u,v)$ 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

$S^\ast(T)=4W(T)-(n-1)(2n-1)$ [1].

Matching statistic: St000467

Mapping

Mp00274: Graphs —block-cut tree⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
Mp00111: Graphs —complement⟶ Graphs
St000467: Graphs ⟶ ℤResult quality: 17% ●values known / values provided: 25%●distinct values known / distinct values provided: 17%

Values

([(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
([(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
([(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)
 => ? = 1
([(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)
 => ? = 1
([(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)
 => ?
 => ?
 => ? = 1
([(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)
 => ? = 0
([(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
([(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)
 => ? = 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)
 => ? = 2
([(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)
 => ?
 => ?
 => ? = 1
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(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)
 => ?
 => ?
 => ? = 2
([(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)
 => ? = 1
([(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)
 => ? = 1
([(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)
 => ?
 => ?
 => ? = 2
([(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)
 => ?
 => ?
 => ? = 2
([(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)
 => ? = 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
([(1,4),(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
([(0,5),(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)
 => ?
 => ?
 => ? = 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1
([(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)
 => ?
 => ?
 => ? = 2
([(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
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 0
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 0

Description

The hyper-Wiener index of a connected graph. This is

$\sum_{\{u,v\}\subseteq V} d(u,v)+d(u,v)^2.$

Matching statistic: St000771

Mapping

Mp00274: Graphs —block-cut tree⟶ Graphs
Mp00154: Graphs —core⟶ Graphs
Mp00111: Graphs —complement⟶ Graphs
St000771: Graphs ⟶ ℤResult quality: 17% ●values known / values provided: 25%●distinct values known / distinct values provided: 17%

Values

([(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
([(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
([(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)
 => ? = 1 + 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)
 => ? = 1 + 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)
 => ?
 => ?
 => ? = 1 + 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)
 => ? = 0 + 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
([(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)
 => ? = 1 + 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)
 => ? = 2 + 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)
 => ?
 => ?
 => ? = 1 + 1
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 + 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)
 => ?
 => ?
 => ? = 2 + 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)
 => ? = 1 + 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)
 => ? = 1 + 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)
 => ?
 => ?
 => ? = 2 + 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)
 => ?
 => ?
 => ? = 2 + 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)
 => ? = 1 + 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
([(0,5),(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)
 => ?
 => ?
 => ? = 1 + 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 + 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)
 => ?
 => ?
 => ? = 2 + 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
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],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

$\left(\begin{array}{rrrr} 4 & -1 & -2 & -1 \\ -1 & 4 & -1 & -2 \\ -2 & -1 & 4 & -1 \\ -1 & -2 & -1 & 4 \end{array}\right).$ Its eigenvalues are

$0,4,4,6$ , so the statistic is

$2$ . The path on four vertices has eigenvalues

$0, 4.7\dots, 6, 9.2\dots$ 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: 17% ●values known / values provided: 25%●distinct values known / distinct values provided: 17%

Values

([(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
([(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
([(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)
 => ? = 1 + 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)
 => ? = 1 + 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)
 => ?
 => ?
 => ? = 1 + 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)
 => ? = 0 + 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
([(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)
 => ? = 1 + 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)
 => ? = 2 + 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)
 => ?
 => ?
 => ? = 1 + 1
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 + 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)
 => ?
 => ?
 => ? = 2 + 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)
 => ? = 1 + 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)
 => ? = 1 + 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)
 => ?
 => ?
 => ? = 2 + 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)
 => ?
 => ?
 => ? = 2 + 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)
 => ? = 1 + 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
([(0,5),(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)
 => ?
 => ?
 => ? = 1 + 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 + 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)
 => ?
 => ?
 => ? = 2 + 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
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],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

$\left(\begin{array}{rrrr} 4 & -1 & -2 & -1 \\ -1 & 4 & -1 & -2 \\ -2 & -1 & 4 & -1 \\ -1 & -2 & -1 & 4 \end{array}\right).$ Its eigenvalues are

$0,4,4,6$ , so the statistic is

$1$ . The path on four vertices has eigenvalues

$0, 4.7\dots, 6, 9.2\dots$ 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: 17% ●values known / values provided: 25%●distinct values known / distinct values provided: 17%

Values

([(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
([(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
([(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)
 => ? = 1 + 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)
 => ? = 1 + 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)
 => ?
 => ?
 => ? = 1 + 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)
 => ? = 0 + 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
([(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)
 => ? = 1 + 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)
 => ? = 2 + 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)
 => ?
 => ?
 => ? = 1 + 1
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 + 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)
 => ?
 => ?
 => ? = 2 + 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)
 => ? = 1 + 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)
 => ? = 1 + 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)
 => ?
 => ?
 => ? = 2 + 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)
 => ?
 => ?
 => ? = 2 + 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)
 => ? = 1 + 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
([(0,5),(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)
 => ?
 => ?
 => ? = 1 + 1
([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,1)],2)
 => ([],2)
 => ? = 1 + 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)
 => ?
 => ?
 => ? = 2 + 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
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([],2)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1 = 0 + 1

Description

The number of distinct eigenvalues of the distance Laplacian of a connected graph.

The following 35 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. St001845The number of join irreducibles minus the rank of a lattice. St001846The number of elements which do not have a complement in the lattice. St001719The number of shortest chains of small intervals from the bottom to the top in a lattice. St001820The size of the image of the pop stack sorting operator. St001720The minimal length of a chain of small intervals in a lattice. St001568The smallest positive integer that does not appear twice in the partition. St001626The number of maximal proper sublattices of a lattice. St000264The girth of a graph, which is not a tree. St001618The cardinality of the Frattini sublattice of a lattice. St001140Number of indecomposable modules with projective and injective dimension at least two in the corresponding Nakayama algebra. St001193The dimension of

$Ext_A^1(A/AeA,A)$ in the corresponding Nakayama algebra

$A$ such that

$eA$ is a minimal faithful projective-injective module. St001292The injective dimension of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path. St001314The number of tilting modules of arbitrary projective dimension that have no simple modules as a direct summand in the corresponding Nakayama algebra. St001435The number of missing boxes in the first row. St001438The number of missing boxes of a skew partition. St001006Number of simple modules with projective dimension equal to the global dimension of the Nakayama algebra corresponding to the Dyck path. St001013Number of indecomposable injective modules with codominant dimension equal to the global dimension in the Nakayama algebra corresponding to the Dyck path. St001188The number of simple modules

$S$ with grade

$\inf \{ i \geq 0 | Ext^i(S,A) \neq 0 \}$ at least two in the Nakayama algebra

$A$ corresponding to the Dyck path. St001191Number of simple modules

$S$ with

$Ext_A^i(S,A)=0$ for all

$i=0,1,...,g-1$ in the corresponding Nakayama algebra

$A$ with global dimension

$g$ . St001212The number of simple modules in the corresponding Nakayama algebra that have non-zero second Ext-group with the regular module. St001244The number of simple modules of projective dimension one that are not 1-regular for the Nakayama algebra associated to a Dyck path. St001256Number of simple reflexive modules that are 2-stable reflexive. St001481The minimal height of a peak of a Dyck path. St001487The number of inner corners of a skew partition. St001490The number of connected components of a skew partition. St001493The number of simple modules with maximal even projective dimension in the corresponding Nakayama algebra. St001507The sum of projective dimension of simple modules with even projective dimension divided by 2 in the LNakayama algebra corresponding to Dyck paths. St001722The number of minimal chains with small intervals between a binary word and the top element. St001165Number of simple modules with even projective dimension in the corresponding Nakayama algebra. 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

$eA$ . St001239The largest vector space dimension of the double dual of a simple module in the corresponding Nakayama algebra. St001473The absolute value of the sum of all entries of the Coxeter matrix of the corresponding LNakayama algebra. St001001The number of indecomposable modules with projective and injective dimension equal to the global dimension of the Nakayama algebra corresponding to the Dyck path.