Your data matches 2 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000259
Mapping
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00129: Dyck paths —to 321-avoiding permutation (Billey-Jockusch-Stanley)⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000259: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => [1,0]
 => [1] => ([],1)
 => 0
[1,2] => [1,0,1,0]
 => [2,1] => ([(0,1)],2)
 => 1
[1,2,3] => [1,0,1,0,1,0]
 => [2,3,1] => ([(0,2),(1,2)],3)
 => 2
[2,3,1] => [1,1,0,1,0,0]
 => [3,1,2] => ([(0,2),(1,2)],3)
 => 2
[1,2,3,4] => [1,0,1,0,1,0,1,0]
 => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
 => 2
[1,3,4,2] => [1,0,1,1,0,1,0,0]
 => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
 => 3
[2,3,1,4] => [1,1,0,1,0,0,1,0]
 => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
 => 3
[2,3,4,1] => [1,1,0,1,0,1,0,0]
 => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2
[3,4,1,2] => [1,1,1,0,1,0,0,0]
 => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4)
 => 2
[3,4,2,1] => [1,1,1,0,1,0,0,0]
 => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4)
 => 2
[1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
 => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2
[1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0]
 => [2,3,5,1,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 3
[1,3,4,2,5] => [1,0,1,1,0,1,0,0,1,0]
 => [2,4,1,5,3] => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 4
[1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0]
 => [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 3
[1,4,5,2,3] => [1,0,1,1,1,0,1,0,0,0]
 => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 3
[1,4,5,3,2] => [1,0,1,1,1,0,1,0,0,0]
 => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 3
[2,3,1,4,5] => [1,1,0,1,0,0,1,0,1,0]
 => [3,1,4,5,2] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 3
[2,3,4,1,5] => [1,1,0,1,0,1,0,0,1,0]
 => [3,4,1,5,2] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 3
[2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0]
 => [3,4,5,1,2] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 2
[2,4,1,5,3] => [1,1,0,1,1,0,0,1,0,0]
 => [3,1,5,2,4] => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 4
[2,4,3,5,1] => [1,1,0,1,1,0,0,1,0,0]
 => [3,1,5,2,4] => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 4
[2,4,5,1,3] => [1,1,0,1,1,0,1,0,0,0]
 => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 3
[2,4,5,3,1] => [1,1,0,1,1,0,1,0,0,0]
 => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 3
[3,4,1,2,5] => [1,1,1,0,1,0,0,0,1,0]
 => [4,1,2,5,3] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 3
[3,4,1,5,2] => [1,1,1,0,1,0,0,1,0,0]
 => [4,1,5,2,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 3
[3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0]
 => [4,1,2,5,3] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 3
[3,4,2,5,1] => [1,1,1,0,1,0,0,1,0,0]
 => [4,1,5,2,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 3
[3,4,5,1,2] => [1,1,1,0,1,0,1,0,0,0]
 => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 2
[3,4,5,2,1] => [1,1,1,0,1,0,1,0,0,0]
 => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 2
[4,5,1,2,3] => [1,1,1,1,0,1,0,0,0,0]
 => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2
[4,5,1,3,2] => [1,1,1,1,0,1,0,0,0,0]
 => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2
[4,5,2,1,3] => [1,1,1,1,0,1,0,0,0,0]
 => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2
[4,5,2,3,1] => [1,1,1,1,0,1,0,0,0,0]
 => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2
[4,5,3,1,2] => [1,1,1,1,0,1,0,0,0,0]
 => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2
[4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0]
 => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2
[1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [2,3,4,5,6,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 2
[1,2,3,5,6,4] => [1,0,1,0,1,0,1,1,0,1,0,0]
 => [2,3,4,6,1,5] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => 3
[1,2,4,5,3,6] => [1,0,1,0,1,1,0,1,0,0,1,0]
 => [2,3,5,1,6,4] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => 4
[1,2,4,5,6,3] => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [2,3,5,6,1,4] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => 3
[1,2,5,6,3,4] => [1,0,1,0,1,1,1,0,1,0,0,0]
 => [2,3,6,1,4,5] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => 3
[1,2,5,6,4,3] => [1,0,1,0,1,1,1,0,1,0,0,0]
 => [2,3,6,1,4,5] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => 3
[1,3,4,2,5,6] => [1,0,1,1,0,1,0,0,1,0,1,0]
 => [2,4,1,5,6,3] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => 4
[1,3,4,5,2,6] => [1,0,1,1,0,1,0,1,0,0,1,0]
 => [2,4,5,1,6,3] => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => 4
[1,3,4,5,6,2] => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [2,4,5,6,1,3] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 3
[1,3,5,2,6,4] => [1,0,1,1,0,1,1,0,0,1,0,0]
 => [2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => 5
[1,3,5,4,6,2] => [1,0,1,1,0,1,1,0,0,1,0,0]
 => [2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => 5
[1,3,5,6,2,4] => [1,0,1,1,0,1,1,0,1,0,0,0]
 => [2,4,6,1,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => 3
[1,3,5,6,4,2] => [1,0,1,1,0,1,1,0,1,0,0,0]
 => [2,4,6,1,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => 3
[1,4,5,2,3,6] => [1,0,1,1,1,0,1,0,0,0,1,0]
 => [2,5,1,3,6,4] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => 4
[1,4,5,2,6,3] => [1,0,1,1,1,0,1,0,0,1,0,0]
 => [2,5,1,6,3,4] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
 => 4
Description
The diameter of a connected graph. This is the greatest distance between any pair of vertices.
Matching statistic: St000454
Mapping
Mp00068: Permutations —Simion-Schmidt map⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Mp00011: Binary trees —to graph⟶ Graphs
St000454: Graphs ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 43%
Values
[1] => [1] => [.,.]
 => ([],1)
 => 0
[1,2] => [1,2] => [.,[.,.]]
 => ([(0,1)],2)
 => 1
[1,2,3] => [1,3,2] => [.,[[.,.],.]]
 => ([(0,2),(1,2)],3)
 => ? = 2
[2,3,1] => [2,3,1] => [[.,.],[.,.]]
 => ([(0,2),(1,2)],3)
 => ? = 2
[1,2,3,4] => [1,4,3,2] => [.,[[[.,.],.],.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 2
[1,3,4,2] => [1,4,3,2] => [.,[[[.,.],.],.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 3
[2,3,1,4] => [2,4,1,3] => [[.,.],[[.,.],.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 3
[2,3,4,1] => [2,4,3,1] => [[.,.],[[.,.],.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 2
[3,4,1,2] => [3,4,1,2] => [[.,[.,.]],[.,.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 2
[3,4,2,1] => [3,4,2,1] => [[[.,.],.],[.,.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 2
[1,2,3,4,5] => [1,5,4,3,2] => [.,[[[[.,.],.],.],.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 2
[1,2,4,5,3] => [1,5,4,3,2] => [.,[[[[.,.],.],.],.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 3
[1,3,4,2,5] => [1,5,4,3,2] => [.,[[[[.,.],.],.],.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 4
[1,3,4,5,2] => [1,5,4,3,2] => [.,[[[[.,.],.],.],.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 3
[1,4,5,2,3] => [1,5,4,3,2] => [.,[[[[.,.],.],.],.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 3
[1,4,5,3,2] => [1,5,4,3,2] => [.,[[[[.,.],.],.],.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 3
[2,3,1,4,5] => [2,5,1,4,3] => [[.,.],[[[.,.],.],.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 3
[2,3,4,1,5] => [2,5,4,1,3] => [[.,.],[[[.,.],.],.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 3
[2,3,4,5,1] => [2,5,4,3,1] => [[.,.],[[[.,.],.],.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 2
[2,4,1,5,3] => [2,5,1,4,3] => [[.,.],[[[.,.],.],.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 4
[2,4,3,5,1] => [2,5,4,3,1] => [[.,.],[[[.,.],.],.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 4
[2,4,5,1,3] => [2,5,4,1,3] => [[.,.],[[[.,.],.],.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 3
[2,4,5,3,1] => [2,5,4,3,1] => [[.,.],[[[.,.],.],.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 3
[3,4,1,2,5] => [3,5,1,4,2] => [[.,[.,.]],[[.,.],.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 3
[3,4,1,5,2] => [3,5,1,4,2] => [[.,[.,.]],[[.,.],.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 3
[3,4,2,1,5] => [3,5,2,1,4] => [[[.,.],.],[[.,.],.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 3
[3,4,2,5,1] => [3,5,2,4,1] => [[[.,.],.],[[.,.],.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 3
[3,4,5,1,2] => [3,5,4,1,2] => [[.,[.,.]],[[.,.],.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 2
[3,4,5,2,1] => [3,5,4,2,1] => [[[.,.],.],[[.,.],.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 2
[4,5,1,2,3] => [4,5,1,3,2] => [[.,[[.,.],.]],[.,.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 2
[4,5,1,3,2] => [4,5,1,3,2] => [[.,[[.,.],.]],[.,.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 2
[4,5,2,1,3] => [4,5,2,1,3] => [[[.,.],[.,.]],[.,.]]
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ? = 2
[4,5,2,3,1] => [4,5,2,3,1] => [[[.,.],[.,.]],[.,.]]
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ? = 2
[4,5,3,1,2] => [4,5,3,1,2] => [[[.,[.,.]],.],[.,.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 2
[4,5,3,2,1] => [4,5,3,2,1] => [[[[.,.],.],.],[.,.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 2
[1,2,3,4,5,6] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 2
[1,2,3,5,6,4] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 3
[1,2,4,5,3,6] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 4
[1,2,4,5,6,3] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 3
[1,2,5,6,3,4] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 3
[1,2,5,6,4,3] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 3
[1,3,4,2,5,6] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 4
[1,3,4,5,2,6] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 4
[1,3,4,5,6,2] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 3
[1,3,5,2,6,4] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 5
[1,3,5,4,6,2] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 5
[1,3,5,6,2,4] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 3
[1,3,5,6,4,2] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 3
[1,4,5,2,3,6] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 4
[1,4,5,2,6,3] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 4
[1,4,5,3,2,6] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 4
[1,4,5,3,6,2] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 4
[6,7,3,1,2,4,5] => [6,7,3,1,5,4,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2
[6,7,3,1,2,5,4] => [6,7,3,1,5,4,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2
[6,7,3,1,4,2,5] => [6,7,3,1,5,4,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2
[6,7,3,1,4,5,2] => [6,7,3,1,5,4,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2
[6,7,3,1,5,2,4] => [6,7,3,1,5,4,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2
[6,7,3,1,5,4,2] => [6,7,3,1,5,4,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2
[6,7,3,2,1,4,5] => [6,7,3,2,1,5,4] => [[[[.,.],.],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2
[6,7,3,2,1,5,4] => [6,7,3,2,1,5,4] => [[[[.,.],.],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2
[6,7,3,2,4,1,5] => [6,7,3,2,5,1,4] => [[[[.,.],.],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2
[6,7,3,2,4,5,1] => [6,7,3,2,5,4,1] => [[[[.,.],.],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2
[6,7,3,2,5,1,4] => [6,7,3,2,5,1,4] => [[[[.,.],.],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2
[6,7,3,2,5,4,1] => [6,7,3,2,5,4,1] => [[[[.,.],.],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2
[6,7,3,4,1,2,5] => [6,7,3,5,1,4,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2
[6,7,3,4,1,5,2] => [6,7,3,5,1,4,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2
[6,7,3,4,2,1,5] => [6,7,3,5,2,1,4] => [[[[.,.],.],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2
[6,7,3,4,2,5,1] => [6,7,3,5,2,4,1] => [[[[.,.],.],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2
[6,7,3,4,5,1,2] => [6,7,3,5,4,1,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2
[6,7,3,4,5,2,1] => [6,7,3,5,4,2,1] => [[[[.,.],.],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2
[6,7,3,5,1,2,4] => [6,7,3,5,1,4,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2
[6,7,3,5,1,4,2] => [6,7,3,5,1,4,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2
[6,7,3,5,2,1,4] => [6,7,3,5,2,1,4] => [[[[.,.],.],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2
[6,7,3,5,2,4,1] => [6,7,3,5,2,4,1] => [[[[.,.],.],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2
[6,7,3,5,4,1,2] => [6,7,3,5,4,1,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2
[6,7,3,5,4,2,1] => [6,7,3,5,4,2,1] => [[[[.,.],.],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2
Description
The largest eigenvalue of a graph if it is integral. If a graph is $d$-regular, then its largest eigenvalue equals $d$. One can show that the largest eigenvalue always lies between the average degree and the maximal degree. This statistic is undefined if the largest eigenvalue of the graph is not integral.