Your data matches 3 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001109
Mapping
St001109: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => 1
([],2)
 => 1
([(0,1)],2)
 => 2
([],3)
 => 1
([(1,2)],3)
 => 4
([(0,2),(1,2)],3)
 => 2
([(0,1),(0,2),(1,2)],3)
 => 6
([],4)
 => 1
([(2,3)],4)
 => 8
([(1,3),(2,3)],4)
 => 4
([(0,3),(1,3),(2,3)],4)
 => 2
([(0,3),(1,2)],4)
 => 4
([(0,3),(1,2),(2,3)],4)
 => 2
([(1,2),(1,3),(2,3)],4)
 => 18
([(0,3),(1,2),(1,3),(2,3)],4)
 => 12
([(0,2),(0,3),(1,2),(1,3)],4)
 => 2
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 6
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 24
([],5)
 => 1
([(3,4)],5)
 => 16
([(2,4),(3,4)],5)
 => 8
([(1,4),(2,4),(3,4)],5)
 => 4
([(0,4),(1,4),(2,4),(3,4)],5)
 => 2
([(1,4),(2,3)],5)
 => 8
([(1,4),(2,3),(3,4)],5)
 => 4
([(0,1),(2,4),(3,4)],5)
 => 4
([(2,3),(2,4),(3,4)],5)
 => 54
([(0,4),(1,4),(2,3),(3,4)],5)
 => 2
([(1,4),(2,3),(2,4),(3,4)],5)
 => 36
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 24
([(1,3),(1,4),(2,3),(2,4)],5)
 => 4
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 2
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 18
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 24
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 12
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 6
([(0,4),(1,3),(2,3),(2,4)],5)
 => 2
([(0,1),(2,3),(2,4),(3,4)],5)
 => 36
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 24
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => 12
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 30
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 18
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => 6
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => 12
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 96
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 72
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 48
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => 12
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 6
Description
The number of proper colourings of a graph with as few colours as possible. By definition, this is the evaluation of the chromatic polynomial at the first nonnegative integer which is not a zero of the polynomial.
Matching statistic: St000514
(load all 2 compositions to match this statistic)
Mapping
Mp00037: Graphs —to partition of connected components⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
St000514: Integer partitions ⟶ ℤResult quality: 12% ●values known / values provided: 16%●distinct values known / distinct values provided: 12%
Values
([],1)
 => [1]
 => []
 => []
 => ? = 1
([],2)
 => [1,1]
 => [1]
 => [1]
 => ? ∊ {1,2}
([(0,1)],2)
 => [2]
 => []
 => []
 => ? ∊ {1,2}
([],3)
 => [1,1,1]
 => [1,1]
 => [2]
 => 2
([(1,2)],3)
 => [2,1]
 => [1]
 => [1]
 => ? ∊ {1,4,6}
([(0,2),(1,2)],3)
 => [3]
 => []
 => []
 => ? ∊ {1,4,6}
([(0,1),(0,2),(1,2)],3)
 => [3]
 => []
 => []
 => ? ∊ {1,4,6}
([],4)
 => [1,1,1,1]
 => [1,1,1]
 => [3]
 => 2
([(2,3)],4)
 => [2,1,1]
 => [1,1]
 => [2]
 => 2
([(1,3),(2,3)],4)
 => [3,1]
 => [1]
 => [1]
 => ? ∊ {1,4,4,6,8,12,18,24}
([(0,3),(1,3),(2,3)],4)
 => [4]
 => []
 => []
 => ? ∊ {1,4,4,6,8,12,18,24}
([(0,3),(1,2)],4)
 => [2,2]
 => [2]
 => [1,1]
 => 2
([(0,3),(1,2),(2,3)],4)
 => [4]
 => []
 => []
 => ? ∊ {1,4,4,6,8,12,18,24}
([(1,2),(1,3),(2,3)],4)
 => [3,1]
 => [1]
 => [1]
 => ? ∊ {1,4,4,6,8,12,18,24}
([(0,3),(1,2),(1,3),(2,3)],4)
 => [4]
 => []
 => []
 => ? ∊ {1,4,4,6,8,12,18,24}
([(0,2),(0,3),(1,2),(1,3)],4)
 => [4]
 => []
 => []
 => ? ∊ {1,4,4,6,8,12,18,24}
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [4]
 => []
 => []
 => ? ∊ {1,4,4,6,8,12,18,24}
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [4]
 => []
 => []
 => ? ∊ {1,4,4,6,8,12,18,24}
([],5)
 => [1,1,1,1,1]
 => [1,1,1,1]
 => [4]
 => 4
([(3,4)],5)
 => [2,1,1,1]
 => [1,1,1]
 => [3]
 => 2
([(2,4),(3,4)],5)
 => [3,1,1]
 => [1,1]
 => [2]
 => 2
([(1,4),(2,4),(3,4)],5)
 => [4,1]
 => [1]
 => [1]
 => ? ∊ {1,4,4,6,6,6,8,8,12,12,12,12,16,18,18,24,24,24,24,30,36,36,48,54,72,96,120}
([(0,4),(1,4),(2,4),(3,4)],5)
 => [5]
 => []
 => []
 => ? ∊ {1,4,4,6,6,6,8,8,12,12,12,12,16,18,18,24,24,24,24,30,36,36,48,54,72,96,120}
([(1,4),(2,3)],5)
 => [2,2,1]
 => [2,1]
 => [2,1]
 => 4
([(1,4),(2,3),(3,4)],5)
 => [4,1]
 => [1]
 => [1]
 => ? ∊ {1,4,4,6,6,6,8,8,12,12,12,12,16,18,18,24,24,24,24,30,36,36,48,54,72,96,120}
([(0,1),(2,4),(3,4)],5)
 => [3,2]
 => [2]
 => [1,1]
 => 2
([(2,3),(2,4),(3,4)],5)
 => [3,1,1]
 => [1,1]
 => [2]
 => 2
([(0,4),(1,4),(2,3),(3,4)],5)
 => [5]
 => []
 => []
 => ? ∊ {1,4,4,6,6,6,8,8,12,12,12,12,16,18,18,24,24,24,24,30,36,36,48,54,72,96,120}
([(1,4),(2,3),(2,4),(3,4)],5)
 => [4,1]
 => [1]
 => [1]
 => ? ∊ {1,4,4,6,6,6,8,8,12,12,12,12,16,18,18,24,24,24,24,30,36,36,48,54,72,96,120}
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => []
 => ? ∊ {1,4,4,6,6,6,8,8,12,12,12,12,16,18,18,24,24,24,24,30,36,36,48,54,72,96,120}
([(1,3),(1,4),(2,3),(2,4)],5)
 => [4,1]
 => [1]
 => [1]
 => ? ∊ {1,4,4,6,6,6,8,8,12,12,12,12,16,18,18,24,24,24,24,30,36,36,48,54,72,96,120}
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [5]
 => []
 => []
 => ? ∊ {1,4,4,6,6,6,8,8,12,12,12,12,16,18,18,24,24,24,24,30,36,36,48,54,72,96,120}
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [4,1]
 => [1]
 => [1]
 => ? ∊ {1,4,4,6,6,6,8,8,12,12,12,12,16,18,18,24,24,24,24,30,36,36,48,54,72,96,120}
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => []
 => ? ∊ {1,4,4,6,6,6,8,8,12,12,12,12,16,18,18,24,24,24,24,30,36,36,48,54,72,96,120}
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => []
 => ? ∊ {1,4,4,6,6,6,8,8,12,12,12,12,16,18,18,24,24,24,24,30,36,36,48,54,72,96,120}
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [5]
 => []
 => []
 => ? ∊ {1,4,4,6,6,6,8,8,12,12,12,12,16,18,18,24,24,24,24,30,36,36,48,54,72,96,120}
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => []
 => ? ∊ {1,4,4,6,6,6,8,8,12,12,12,12,16,18,18,24,24,24,24,30,36,36,48,54,72,96,120}
([(0,4),(1,3),(2,3),(2,4)],5)
 => [5]
 => []
 => []
 => ? ∊ {1,4,4,6,6,6,8,8,12,12,12,12,16,18,18,24,24,24,24,30,36,36,48,54,72,96,120}
([(0,1),(2,3),(2,4),(3,4)],5)
 => [3,2]
 => [2]
 => [1,1]
 => 2
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => [5]
 => []
 => []
 => ? ∊ {1,4,4,6,6,6,8,8,12,12,12,12,16,18,18,24,24,24,24,30,36,36,48,54,72,96,120}
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => [5]
 => []
 => []
 => ? ∊ {1,4,4,6,6,6,8,8,12,12,12,12,16,18,18,24,24,24,24,30,36,36,48,54,72,96,120}
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => [5]
 => []
 => []
 => ? ∊ {1,4,4,6,6,6,8,8,12,12,12,12,16,18,18,24,24,24,24,30,36,36,48,54,72,96,120}
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => []
 => ? ∊ {1,4,4,6,6,6,8,8,12,12,12,12,16,18,18,24,24,24,24,30,36,36,48,54,72,96,120}
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => []
 => ? ∊ {1,4,4,6,6,6,8,8,12,12,12,12,16,18,18,24,24,24,24,30,36,36,48,54,72,96,120}
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => []
 => ? ∊ {1,4,4,6,6,6,8,8,12,12,12,12,16,18,18,24,24,24,24,30,36,36,48,54,72,96,120}
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [4,1]
 => [1]
 => [1]
 => ? ∊ {1,4,4,6,6,6,8,8,12,12,12,12,16,18,18,24,24,24,24,30,36,36,48,54,72,96,120}
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => []
 => ? ∊ {1,4,4,6,6,6,8,8,12,12,12,12,16,18,18,24,24,24,24,30,36,36,48,54,72,96,120}
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => []
 => ? ∊ {1,4,4,6,6,6,8,8,12,12,12,12,16,18,18,24,24,24,24,30,36,36,48,54,72,96,120}
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => [5]
 => []
 => []
 => ? ∊ {1,4,4,6,6,6,8,8,12,12,12,12,16,18,18,24,24,24,24,30,36,36,48,54,72,96,120}
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => [5]
 => []
 => []
 => ? ∊ {1,4,4,6,6,6,8,8,12,12,12,12,16,18,18,24,24,24,24,30,36,36,48,54,72,96,120}
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => []
 => ? ∊ {1,4,4,6,6,6,8,8,12,12,12,12,16,18,18,24,24,24,24,30,36,36,48,54,72,96,120}
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => [5]
 => []
 => []
 => ? ∊ {1,4,4,6,6,6,8,8,12,12,12,12,16,18,18,24,24,24,24,30,36,36,48,54,72,96,120}
([],6)
 => [1,1,1,1,1,1]
 => [1,1,1,1,1]
 => [5]
 => 4
([(4,5)],6)
 => [2,1,1,1,1]
 => [1,1,1,1]
 => [4]
 => 4
([(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => [3]
 => 2
([(2,5),(3,5),(4,5)],6)
 => [4,1,1]
 => [1,1]
 => [2]
 => 2
([(1,5),(2,5),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => ? ∊ {1,2,2,2,4,4,4,4,6,6,6,6,6,6,6,6,6,6,6,6,8,8,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,16,18,18,18,18,18,18,18,18,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,30,30,32,36,36,36,36,36,36,36,36,36,36,42,48,48,48,48,48,48,48,48,48,48,48,54,54,60,72,72,72,72,72,72,72,72,72,90,96,96,96,96,96,96,108,108,120,120,120,144,144,144,144,162,168,192,216,216,216,240,288,288,360,384,480,600,720}
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => [6]
 => []
 => []
 => ? ∊ {1,2,2,2,4,4,4,4,6,6,6,6,6,6,6,6,6,6,6,6,8,8,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,16,18,18,18,18,18,18,18,18,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,30,30,32,36,36,36,36,36,36,36,36,36,36,42,48,48,48,48,48,48,48,48,48,48,48,54,54,60,72,72,72,72,72,72,72,72,72,90,96,96,96,96,96,96,108,108,120,120,120,144,144,144,144,162,168,192,216,216,216,240,288,288,360,384,480,600,720}
([(2,5),(3,4)],6)
 => [2,2,1,1]
 => [2,1,1]
 => [3,1]
 => 4
([(2,5),(3,4),(4,5)],6)
 => [4,1,1]
 => [1,1]
 => [2]
 => 2
([(1,2),(3,5),(4,5)],6)
 => [3,2,1]
 => [2,1]
 => [2,1]
 => 4
([(3,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => [3]
 => 2
([(1,5),(2,5),(3,4),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => ? ∊ {1,2,2,2,4,4,4,4,6,6,6,6,6,6,6,6,6,6,6,6,8,8,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,16,18,18,18,18,18,18,18,18,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,30,30,32,36,36,36,36,36,36,36,36,36,36,42,48,48,48,48,48,48,48,48,48,48,48,54,54,60,72,72,72,72,72,72,72,72,72,90,96,96,96,96,96,96,108,108,120,120,120,144,144,144,144,162,168,192,216,216,216,240,288,288,360,384,480,600,720}
([(0,1),(2,5),(3,5),(4,5)],6)
 => [4,2]
 => [2]
 => [1,1]
 => 2
([(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1,1]
 => [1,1]
 => [2]
 => 2
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => [6]
 => []
 => []
 => ? ∊ {1,2,2,2,4,4,4,4,6,6,6,6,6,6,6,6,6,6,6,6,8,8,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,16,18,18,18,18,18,18,18,18,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,30,30,32,36,36,36,36,36,36,36,36,36,36,42,48,48,48,48,48,48,48,48,48,48,48,54,54,60,72,72,72,72,72,72,72,72,72,90,96,96,96,96,96,96,108,108,120,120,120,144,144,144,144,162,168,192,216,216,216,240,288,288,360,384,480,600,720}
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => ? ∊ {1,2,2,2,4,4,4,4,6,6,6,6,6,6,6,6,6,6,6,6,8,8,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,16,18,18,18,18,18,18,18,18,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,30,30,32,36,36,36,36,36,36,36,36,36,36,42,48,48,48,48,48,48,48,48,48,48,48,54,54,60,72,72,72,72,72,72,72,72,72,90,96,96,96,96,96,96,108,108,120,120,120,144,144,144,144,162,168,192,216,216,216,240,288,288,360,384,480,600,720}
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => [6]
 => []
 => []
 => ? ∊ {1,2,2,2,4,4,4,4,6,6,6,6,6,6,6,6,6,6,6,6,8,8,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,16,18,18,18,18,18,18,18,18,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,30,30,32,36,36,36,36,36,36,36,36,36,36,42,48,48,48,48,48,48,48,48,48,48,48,54,54,60,72,72,72,72,72,72,72,72,72,90,96,96,96,96,96,96,108,108,120,120,120,144,144,144,144,162,168,192,216,216,216,240,288,288,360,384,480,600,720}
([(2,4),(2,5),(3,4),(3,5)],6)
 => [4,1,1]
 => [1,1]
 => [2]
 => 2
([(0,5),(1,5),(2,4),(3,4)],6)
 => [3,3]
 => [3]
 => [1,1,1]
 => 8
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => ? ∊ {1,2,2,2,4,4,4,4,6,6,6,6,6,6,6,6,6,6,6,6,8,8,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,16,18,18,18,18,18,18,18,18,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,30,30,32,36,36,36,36,36,36,36,36,36,36,42,48,48,48,48,48,48,48,48,48,48,48,54,54,60,72,72,72,72,72,72,72,72,72,90,96,96,96,96,96,96,108,108,120,120,120,144,144,144,144,162,168,192,216,216,216,240,288,288,360,384,480,600,720}
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => [6]
 => []
 => []
 => ? ∊ {1,2,2,2,4,4,4,4,6,6,6,6,6,6,6,6,6,6,6,6,8,8,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,16,18,18,18,18,18,18,18,18,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,30,30,32,36,36,36,36,36,36,36,36,36,36,42,48,48,48,48,48,48,48,48,48,48,48,54,54,60,72,72,72,72,72,72,72,72,72,90,96,96,96,96,96,96,108,108,120,120,120,144,144,144,144,162,168,192,216,216,216,240,288,288,360,384,480,600,720}
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1,1]
 => [1,1]
 => [2]
 => 2
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => [5,1]
 => [1]
 => [1]
 => ? ∊ {1,2,2,2,4,4,4,4,6,6,6,6,6,6,6,6,6,6,6,6,8,8,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,16,18,18,18,18,18,18,18,18,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,30,30,32,36,36,36,36,36,36,36,36,36,36,42,48,48,48,48,48,48,48,48,48,48,48,54,54,60,72,72,72,72,72,72,72,72,72,90,96,96,96,96,96,96,108,108,120,120,120,144,144,144,144,162,168,192,216,216,216,240,288,288,360,384,480,600,720}
([(0,5),(1,4),(2,3)],6)
 => [2,2,2]
 => [2,2]
 => [2,2]
 => 16
([(0,1),(2,5),(3,4),(4,5)],6)
 => [4,2]
 => [2]
 => [1,1]
 => 2
([(1,2),(3,4),(3,5),(4,5)],6)
 => [3,2,1]
 => [2,1]
 => [2,1]
 => 4
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,2]
 => [2]
 => [1,1]
 => 2
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => [4,2]
 => [2]
 => [1,1]
 => 2
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => [3,3]
 => [3]
 => [1,1,1]
 => 8
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,2]
 => [2]
 => [1,1]
 => 2
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,1,1]
 => [1,1]
 => [2]
 => 2
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => [3,3]
 => [3]
 => [1,1,1]
 => 8
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => [4,2]
 => [2]
 => [1,1]
 => 2
Description
The number of invariant simple graphs when acting with a permutation of given cycle type.
Matching statistic: St001645
Mapping
Mp00243: Graphs —weak duplicate order⟶ Posets
Mp00074: Posets —to graph⟶ Graphs
Mp00157: Graphs —connected complement⟶ Graphs
St001645: Graphs ⟶ ℤResult quality: 9% ●values known / values provided: 10%●distinct values known / distinct values provided: 9%
Values
([],1)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([],2)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(0,1)],2)
 => ([],2)
 => ([],2)
 => ([],2)
 => ? = 2
([],3)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 4
([(0,2),(1,2)],3)
 => ([],2)
 => ([],2)
 => ([],2)
 => ? ∊ {2,6}
([(0,1),(0,2),(1,2)],3)
 => ([],3)
 => ([],3)
 => ([],3)
 => ? ∊ {2,6}
([],4)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(2,3)],4)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 4
([(1,3),(2,3)],4)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 4
([(0,3),(1,3),(2,3)],4)
 => ([],2)
 => ([],2)
 => ([],2)
 => ? ∊ {2,2,2,6,8,12,18,24}
([(0,3),(1,2)],4)
 => ([],4)
 => ([],4)
 => ([],4)
 => ? ∊ {2,2,2,6,8,12,18,24}
([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => ? ∊ {2,2,2,6,8,12,18,24}
([(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ? ∊ {2,2,2,6,8,12,18,24}
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ? ∊ {2,2,2,6,8,12,18,24}
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([],2)
 => ([],2)
 => ([],2)
 => ? ∊ {2,2,2,6,8,12,18,24}
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],3)
 => ([],3)
 => ([],3)
 => ? ∊ {2,2,2,6,8,12,18,24}
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],4)
 => ([],4)
 => ([],4)
 => ? ∊ {2,2,2,6,8,12,18,24}
([],5)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 4
([(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 4
([(1,4),(2,4),(3,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 4
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([],2)
 => ([],2)
 => ([],2)
 => ? ∊ {2,2,2,2,2,6,6,6,8,8,12,12,12,12,16,18,18,24,24,24,24,30,36,36,48,54,72,96,120}
([(1,4),(2,3)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ? ∊ {2,2,2,2,2,6,6,6,8,8,12,12,12,12,16,18,18,24,24,24,24,30,36,36,48,54,72,96,120}
([(1,4),(2,3),(3,4)],5)
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ? ∊ {2,2,2,2,2,6,6,6,8,8,12,12,12,12,16,18,18,24,24,24,24,30,36,36,48,54,72,96,120}
([(0,1),(2,4),(3,4)],5)
 => ([],4)
 => ([],4)
 => ([],4)
 => ? ∊ {2,2,2,2,2,6,6,6,8,8,12,12,12,12,16,18,18,24,24,24,24,30,36,36,48,54,72,96,120}
([(2,3),(2,4),(3,4)],5)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ? ∊ {2,2,2,2,2,6,6,6,8,8,12,12,12,12,16,18,18,24,24,24,24,30,36,36,48,54,72,96,120}
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => ? ∊ {2,2,2,2,2,6,6,6,8,8,12,12,12,12,16,18,18,24,24,24,24,30,36,36,48,54,72,96,120}
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ? ∊ {2,2,2,2,2,6,6,6,8,8,12,12,12,12,16,18,18,24,24,24,24,30,36,36,48,54,72,96,120}
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ? ∊ {2,2,2,2,2,6,6,6,8,8,12,12,12,12,16,18,18,24,24,24,24,30,36,36,48,54,72,96,120}
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 4
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => ? ∊ {2,2,2,2,2,6,6,6,8,8,12,12,12,12,16,18,18,24,24,24,24,30,36,36,48,54,72,96,120}
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ? ∊ {2,2,2,2,2,6,6,6,8,8,12,12,12,12,16,18,18,24,24,24,24,30,36,36,48,54,72,96,120}
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ? ∊ {2,2,2,2,2,6,6,6,8,8,12,12,12,12,16,18,18,24,24,24,24,30,36,36,48,54,72,96,120}
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ? ∊ {2,2,2,2,2,6,6,6,8,8,12,12,12,12,16,18,18,24,24,24,24,30,36,36,48,54,72,96,120}
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([],2)
 => ([],2)
 => ([],2)
 => ? ∊ {2,2,2,2,2,6,6,6,8,8,12,12,12,12,16,18,18,24,24,24,24,30,36,36,48,54,72,96,120}
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],3)
 => ([],3)
 => ([],3)
 => ? ∊ {2,2,2,2,2,6,6,6,8,8,12,12,12,12,16,18,18,24,24,24,24,30,36,36,48,54,72,96,120}
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(2,3),(2,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => ? ∊ {2,2,2,2,2,6,6,6,8,8,12,12,12,12,16,18,18,24,24,24,24,30,36,36,48,54,72,96,120}
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ([],5)
 => ([],5)
 => ? ∊ {2,2,2,2,2,6,6,6,8,8,12,12,12,12,16,18,18,24,24,24,24,30,36,36,48,54,72,96,120}
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(3,4)],5)
 => ([(3,4)],5)
 => ([(3,4)],5)
 => ? ∊ {2,2,2,2,2,6,6,6,8,8,12,12,12,12,16,18,18,24,24,24,24,30,36,36,48,54,72,96,120}
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([],5)
 => ([],5)
 => ([],5)
 => ? ∊ {2,2,2,2,2,6,6,6,8,8,12,12,12,12,16,18,18,24,24,24,24,30,36,36,48,54,72,96,120}
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([],5)
 => ([],5)
 => ([],5)
 => ? ∊ {2,2,2,2,2,6,6,6,8,8,12,12,12,12,16,18,18,24,24,24,24,30,36,36,48,54,72,96,120}
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3)],5)
 => ([(1,4),(2,3)],5)
 => ([(1,4),(2,3)],5)
 => ? ∊ {2,2,2,2,2,6,6,6,8,8,12,12,12,12,16,18,18,24,24,24,24,30,36,36,48,54,72,96,120}
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3)],5)
 => ([(1,4),(2,3)],5)
 => ([(1,4),(2,3)],5)
 => ? ∊ {2,2,2,2,2,6,6,6,8,8,12,12,12,12,16,18,18,24,24,24,24,30,36,36,48,54,72,96,120}
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3)],5)
 => ([(0,1),(2,4),(3,4)],5)
 => ([(0,1),(2,4),(3,4)],5)
 => ? ∊ {2,2,2,2,2,6,6,6,8,8,12,12,12,12,16,18,18,24,24,24,24,30,36,36,48,54,72,96,120}
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ? ∊ {2,2,2,2,2,6,6,6,8,8,12,12,12,12,16,18,18,24,24,24,24,30,36,36,48,54,72,96,120}
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => ? ∊ {2,2,2,2,2,6,6,6,8,8,12,12,12,12,16,18,18,24,24,24,24,30,36,36,48,54,72,96,120}
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => ? ∊ {2,2,2,2,2,6,6,6,8,8,12,12,12,12,16,18,18,24,24,24,24,30,36,36,48,54,72,96,120}
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => ? ∊ {2,2,2,2,2,6,6,6,8,8,12,12,12,12,16,18,18,24,24,24,24,30,36,36,48,54,72,96,120}
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([],3)
 => ([],3)
 => ([],3)
 => ? ∊ {2,2,2,2,2,6,6,6,8,8,12,12,12,12,16,18,18,24,24,24,24,30,36,36,48,54,72,96,120}
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],4)
 => ([],4)
 => ([],4)
 => ? ∊ {2,2,2,2,2,6,6,6,8,8,12,12,12,12,16,18,18,24,24,24,24,30,36,36,48,54,72,96,120}
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([],5)
 => ([],5)
 => ([],5)
 => ? ∊ {2,2,2,2,2,6,6,6,8,8,12,12,12,12,16,18,18,24,24,24,24,30,36,36,48,54,72,96,120}
([],6)
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
([(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 4
([(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 4
([(2,5),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 4
([(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 4
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([],2)
 => ([],2)
 => ([],2)
 => ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,6,6,6,8,8,8,8,8,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,16,16,18,18,18,18,18,18,18,18,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,30,30,32,36,36,36,36,36,36,36,36,36,36,42,48,48,48,48,48,48,48,48,48,48,48,54,54,60,72,72,72,72,72,72,72,72,72,90,96,96,96,96,96,96,108,108,120,120,120,144,144,144,144,162,168,192,216,216,216,240,288,288,360,384,480,600,720}
([(2,5),(3,4)],6)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,6,6,6,8,8,8,8,8,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,16,16,18,18,18,18,18,18,18,18,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,30,30,32,36,36,36,36,36,36,36,36,36,36,42,48,48,48,48,48,48,48,48,48,48,48,54,54,60,72,72,72,72,72,72,72,72,72,90,96,96,96,96,96,96,108,108,120,120,120,144,144,144,144,162,168,192,216,216,216,240,288,288,360,384,480,600,720}
([(2,5),(3,4),(4,5)],6)
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,6,6,6,8,8,8,8,8,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,16,16,18,18,18,18,18,18,18,18,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,30,30,32,36,36,36,36,36,36,36,36,36,36,42,48,48,48,48,48,48,48,48,48,48,48,54,54,60,72,72,72,72,72,72,72,72,72,90,96,96,96,96,96,96,108,108,120,120,120,144,144,144,144,162,168,192,216,216,216,240,288,288,360,384,480,600,720}
([(1,2),(3,5),(4,5)],6)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,6,6,6,8,8,8,8,8,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,16,16,18,18,18,18,18,18,18,18,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,30,30,32,36,36,36,36,36,36,36,36,36,36,42,48,48,48,48,48,48,48,48,48,48,48,54,54,60,72,72,72,72,72,72,72,72,72,90,96,96,96,96,96,96,108,108,120,120,120,144,144,144,144,162,168,192,216,216,216,240,288,288,360,384,480,600,720}
([(3,4),(3,5),(4,5)],6)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,6,6,6,8,8,8,8,8,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,16,16,18,18,18,18,18,18,18,18,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,30,30,32,36,36,36,36,36,36,36,36,36,36,42,48,48,48,48,48,48,48,48,48,48,48,54,54,60,72,72,72,72,72,72,72,72,72,90,96,96,96,96,96,96,108,108,120,120,120,144,144,144,144,162,168,192,216,216,216,240,288,288,360,384,480,600,720}
([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,6,6,6,8,8,8,8,8,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,16,16,18,18,18,18,18,18,18,18,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,30,30,32,36,36,36,36,36,36,36,36,36,36,42,48,48,48,48,48,48,48,48,48,48,48,54,54,60,72,72,72,72,72,72,72,72,72,90,96,96,96,96,96,96,108,108,120,120,120,144,144,144,144,162,168,192,216,216,216,240,288,288,360,384,480,600,720}
([(0,1),(2,5),(3,5),(4,5)],6)
 => ([],4)
 => ([],4)
 => ([],4)
 => ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,6,6,6,8,8,8,8,8,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,16,16,18,18,18,18,18,18,18,18,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,30,30,32,36,36,36,36,36,36,36,36,36,36,42,48,48,48,48,48,48,48,48,48,48,48,54,54,60,72,72,72,72,72,72,72,72,72,90,96,96,96,96,96,96,108,108,120,120,120,144,144,144,144,162,168,192,216,216,216,240,288,288,360,384,480,600,720}
([(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,6,6,6,8,8,8,8,8,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,16,16,18,18,18,18,18,18,18,18,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,30,30,32,36,36,36,36,36,36,36,36,36,36,42,48,48,48,48,48,48,48,48,48,48,48,54,54,60,72,72,72,72,72,72,72,72,72,90,96,96,96,96,96,96,108,108,120,120,120,144,144,144,144,162,168,192,216,216,216,240,288,288,360,384,480,600,720}
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,6,6,6,8,8,8,8,8,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,16,16,18,18,18,18,18,18,18,18,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,30,30,32,36,36,36,36,36,36,36,36,36,36,42,48,48,48,48,48,48,48,48,48,48,48,54,54,60,72,72,72,72,72,72,72,72,72,90,96,96,96,96,96,96,108,108,120,120,120,144,144,144,144,162,168,192,216,216,216,240,288,288,360,384,480,600,720}
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ? ∊ {2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,6,6,6,6,6,6,6,6,6,6,8,8,8,8,8,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,16,16,18,18,18,18,18,18,18,18,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,30,30,32,36,36,36,36,36,36,36,36,36,36,42,48,48,48,48,48,48,48,48,48,48,48,54,54,60,72,72,72,72,72,72,72,72,72,90,96,96,96,96,96,96,108,108,120,120,120,144,144,144,144,162,168,192,216,216,216,240,288,288,360,384,480,600,720}
([(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 4
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 4
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => 6
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 6
Description
The pebbling number of a connected graph.