searching the database
Your data matches 2 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
(click to perform a complete search on your data)
Matching statistic: St000259
Mp00068: Permutations —Simion-Schmidt map⟶ Permutations
Mp00088: Permutations —Kreweras complement⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000259: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00088: Permutations —Kreweras complement⟶ 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] => [1] => ([],1)
=> 0
[1,2] => [1,2] => [2,1] => ([(0,1)],2)
=> 1
[2,1,3] => [2,1,3] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> 1
[3,1,2] => [3,1,2] => [3,1,2] => ([(0,2),(1,2)],3)
=> 2
[2,3,1,4] => [2,4,1,3] => [4,2,1,3] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 2
[2,4,1,3] => [2,4,1,3] => [4,2,1,3] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 2
[3,2,1,4] => [3,2,1,4] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 1
[3,4,1,2] => [3,4,1,2] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4)
=> 2
[4,1,2,3] => [4,1,3,2] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
=> 3
[4,1,3,2] => [4,1,3,2] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
=> 3
[4,2,1,3] => [4,2,1,3] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 2
[4,3,1,2] => [4,3,1,2] => [4,1,3,2] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 2
[2,3,1,4,5] => [2,5,1,4,3] => [4,2,1,5,3] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> 3
[2,3,1,5,4] => [2,5,1,4,3] => [4,2,1,5,3] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> 3
[2,3,4,1,5] => [2,5,4,1,3] => [5,2,1,4,3] => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> 2
[2,3,5,1,4] => [2,5,4,1,3] => [5,2,1,4,3] => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> 2
[2,4,1,3,5] => [2,5,1,4,3] => [4,2,1,5,3] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> 3
[2,4,1,5,3] => [2,5,1,4,3] => [4,2,1,5,3] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> 3
[2,4,3,1,5] => [2,5,4,1,3] => [5,2,1,4,3] => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> 2
[2,4,5,1,3] => [2,5,4,1,3] => [5,2,1,4,3] => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> 2
[2,5,1,3,4] => [2,5,1,4,3] => [4,2,1,5,3] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> 3
[2,5,1,4,3] => [2,5,1,4,3] => [4,2,1,5,3] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> 3
[2,5,3,1,4] => [2,5,4,1,3] => [5,2,1,4,3] => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> 2
[2,5,4,1,3] => [2,5,4,1,3] => [5,2,1,4,3] => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> 2
[3,2,4,1,5] => [3,2,5,1,4] => [5,3,2,1,4] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[3,2,5,1,4] => [3,2,5,1,4] => [5,3,2,1,4] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[3,4,1,2,5] => [3,5,1,4,2] => [4,1,2,5,3] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> 3
[3,4,1,5,2] => [3,5,1,4,2] => [4,1,2,5,3] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> 3
[3,4,2,1,5] => [3,5,2,1,4] => [5,4,2,1,3] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[3,4,5,1,2] => [3,5,4,1,2] => [5,1,2,4,3] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[3,5,1,2,4] => [3,5,1,4,2] => [4,1,2,5,3] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> 3
[3,5,1,4,2] => [3,5,1,4,2] => [4,1,2,5,3] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> 3
[3,5,2,1,4] => [3,5,2,1,4] => [5,4,2,1,3] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[3,5,4,1,2] => [3,5,4,1,2] => [5,1,2,4,3] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[4,1,2,3,5] => [4,1,5,3,2] => [3,1,5,2,4] => ([(0,4),(1,3),(2,3),(2,4)],5)
=> 4
[4,1,2,5,3] => [4,1,5,3,2] => [3,1,5,2,4] => ([(0,4),(1,3),(2,3),(2,4)],5)
=> 4
[4,1,3,2,5] => [4,1,5,3,2] => [3,1,5,2,4] => ([(0,4),(1,3),(2,3),(2,4)],5)
=> 4
[4,1,3,5,2] => [4,1,5,3,2] => [3,1,5,2,4] => ([(0,4),(1,3),(2,3),(2,4)],5)
=> 4
[4,1,5,2,3] => [4,1,5,3,2] => [3,1,5,2,4] => ([(0,4),(1,3),(2,3),(2,4)],5)
=> 4
[4,1,5,3,2] => [4,1,5,3,2] => [3,1,5,2,4] => ([(0,4),(1,3),(2,3),(2,4)],5)
=> 4
[4,2,3,1,5] => [4,2,5,1,3] => [5,3,1,2,4] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[4,2,5,1,3] => [4,2,5,1,3] => [5,3,1,2,4] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[4,3,2,1,5] => [4,3,2,1,5] => [5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
[4,3,5,1,2] => [4,3,5,1,2] => [5,1,3,2,4] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[4,5,1,2,3] => [4,5,1,3,2] => [4,1,5,2,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 3
[4,5,1,3,2] => [4,5,1,3,2] => [4,1,5,2,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 3
[4,5,2,1,3] => [4,5,2,1,3] => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[4,5,3,1,2] => [4,5,3,1,2] => [5,1,4,2,3] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[5,1,2,3,4] => [5,1,4,3,2] => [3,1,5,4,2] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> 3
[5,1,2,4,3] => [5,1,4,3,2] => [3,1,5,4,2] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> 3
Description
The diameter of a connected graph.
This is the greatest distance between any pair of vertices.
Matching statistic: St000454
Mp00068: Permutations —Simion-Schmidt map⟶ Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
Mp00011: Binary trees —to graph⟶ Graphs
St000454: Graphs ⟶ ℤResult quality: 4% ●values known / values provided: 4%●distinct values known / distinct values provided: 60%
Mp00061: Permutations —to increasing tree⟶ Binary trees
Mp00011: Binary trees —to graph⟶ Graphs
St000454: Graphs ⟶ ℤResult quality: 4% ●values known / values provided: 4%●distinct values known / distinct values provided: 60%
Values
[1] => [1] => [.,.]
=> ([],1)
=> 0
[1,2] => [1,2] => [.,[.,.]]
=> ([(0,1)],2)
=> 1
[2,1,3] => [2,1,3] => [[.,.],[.,.]]
=> ([(0,2),(1,2)],3)
=> ? = 1
[3,1,2] => [3,1,2] => [[.,.],[.,.]]
=> ([(0,2),(1,2)],3)
=> ? = 2
[2,3,1,4] => [2,4,1,3] => [[.,[.,.]],[.,.]]
=> ([(0,3),(1,2),(2,3)],4)
=> ? = 2
[2,4,1,3] => [2,4,1,3] => [[.,[.,.]],[.,.]]
=> ([(0,3),(1,2),(2,3)],4)
=> ? = 2
[3,2,1,4] => [3,2,1,4] => [[[.,.],.],[.,.]]
=> ([(0,3),(1,2),(2,3)],4)
=> ? = 1
[3,4,1,2] => [3,4,1,2] => [[.,[.,.]],[.,.]]
=> ([(0,3),(1,2),(2,3)],4)
=> ? = 2
[4,1,2,3] => [4,1,3,2] => [[.,.],[[.,.],.]]
=> ([(0,3),(1,2),(2,3)],4)
=> ? = 3
[4,1,3,2] => [4,1,3,2] => [[.,.],[[.,.],.]]
=> ([(0,3),(1,2),(2,3)],4)
=> ? = 3
[4,2,1,3] => [4,2,1,3] => [[[.,.],.],[.,.]]
=> ([(0,3),(1,2),(2,3)],4)
=> ? = 2
[4,3,1,2] => [4,3,1,2] => [[[.,.],.],[.,.]]
=> ([(0,3),(1,2),(2,3)],4)
=> ? = 2
[2,3,1,4,5] => [2,5,1,4,3] => [[.,[.,.]],[[.,.],.]]
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ? = 3
[2,3,1,5,4] => [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)
=> ? = 2
[2,3,5,1,4] => [2,5,4,1,3] => [[.,[[.,.],.]],[.,.]]
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ? = 2
[2,4,1,3,5] => [2,5,1,4,3] => [[.,[.,.]],[[.,.],.]]
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ? = 3
[2,4,1,5,3] => [2,5,1,4,3] => [[.,[.,.]],[[.,.],.]]
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ? = 3
[2,4,3,1,5] => [2,5,4,1,3] => [[.,[[.,.],.]],[.,.]]
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ? = 2
[2,4,5,1,3] => [2,5,4,1,3] => [[.,[[.,.],.]],[.,.]]
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ? = 2
[2,5,1,3,4] => [2,5,1,4,3] => [[.,[.,.]],[[.,.],.]]
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ? = 3
[2,5,1,4,3] => [2,5,1,4,3] => [[.,[.,.]],[[.,.],.]]
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ? = 3
[2,5,3,1,4] => [2,5,4,1,3] => [[.,[[.,.],.]],[.,.]]
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ? = 2
[2,5,4,1,3] => [2,5,4,1,3] => [[.,[[.,.],.]],[.,.]]
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ? = 2
[3,2,4,1,5] => [3,2,5,1,4] => [[[.,.],[.,.]],[.,.]]
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ? = 2
[3,2,5,1,4] => [3,2,5,1,4] => [[[.,.],[.,.]],[.,.]]
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ? = 2
[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)
=> ? = 2
[3,4,5,1,2] => [3,5,4,1,2] => [[.,[[.,.],.]],[.,.]]
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ? = 2
[3,5,1,2,4] => [3,5,1,4,2] => [[.,[.,.]],[[.,.],.]]
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ? = 3
[3,5,1,4,2] => [3,5,1,4,2] => [[.,[.,.]],[[.,.],.]]
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ? = 3
[3,5,2,1,4] => [3,5,2,1,4] => [[[.,[.,.]],.],[.,.]]
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ? = 2
[3,5,4,1,2] => [3,5,4,1,2] => [[.,[[.,.],.]],[.,.]]
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ? = 2
[4,1,2,3,5] => [4,1,5,3,2] => [[.,.],[[[.,.],.],.]]
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ? = 4
[4,1,2,5,3] => [4,1,5,3,2] => [[.,.],[[[.,.],.],.]]
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ? = 4
[4,1,3,2,5] => [4,1,5,3,2] => [[.,.],[[[.,.],.],.]]
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ? = 4
[4,1,3,5,2] => [4,1,5,3,2] => [[.,.],[[[.,.],.],.]]
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ? = 4
[4,1,5,2,3] => [4,1,5,3,2] => [[.,.],[[[.,.],.],.]]
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ? = 4
[4,1,5,3,2] => [4,1,5,3,2] => [[.,.],[[[.,.],.],.]]
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ? = 4
[4,2,3,1,5] => [4,2,5,1,3] => [[[.,.],[.,.]],[.,.]]
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ? = 2
[4,2,5,1,3] => [4,2,5,1,3] => [[[.,.],[.,.]],[.,.]]
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ? = 2
[4,3,2,1,5] => [4,3,2,1,5] => [[[[.,.],.],.],[.,.]]
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ? = 1
[4,3,5,1,2] => [4,3,5,1,2] => [[[.,.],[.,.]],[.,.]]
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ? = 2
[4,5,1,2,3] => [4,5,1,3,2] => [[.,[.,.]],[[.,.],.]]
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ? = 3
[4,5,1,3,2] => [4,5,1,3,2] => [[.,[.,.]],[[.,.],.]]
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ? = 3
[4,5,2,1,3] => [4,5,2,1,3] => [[[.,[.,.]],.],[.,.]]
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ? = 2
[4,5,3,1,2] => [4,5,3,1,2] => [[[.,[.,.]],.],[.,.]]
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ? = 2
[5,1,2,3,4] => [5,1,4,3,2] => [[.,.],[[[.,.],.],.]]
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ? = 3
[5,1,2,4,3] => [5,1,4,3,2] => [[.,.],[[[.,.],.],.]]
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ? = 3
[5,1,3,2,4] => [5,1,4,3,2] => [[.,.],[[[.,.],.],.]]
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ? = 3
[5,1,3,4,2] => [5,1,4,3,2] => [[.,.],[[[.,.],.],.]]
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ? = 3
[3,4,2,5,6,1,7] => [3,7,2,6,5,1,4] => [[[.,[.,.]],[[.,.],.]],[.,.]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 2
[3,4,2,5,7,1,6] => [3,7,2,6,5,1,4] => [[[.,[.,.]],[[.,.],.]],[.,.]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 2
[3,4,2,6,5,1,7] => [3,7,2,6,5,1,4] => [[[.,[.,.]],[[.,.],.]],[.,.]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 2
[3,4,2,6,7,1,5] => [3,7,2,6,5,1,4] => [[[.,[.,.]],[[.,.],.]],[.,.]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 2
[3,4,2,7,5,1,6] => [3,7,2,6,5,1,4] => [[[.,[.,.]],[[.,.],.]],[.,.]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 2
[3,4,2,7,6,1,5] => [3,7,2,6,5,1,4] => [[[.,[.,.]],[[.,.],.]],[.,.]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 2
[3,5,2,4,6,1,7] => [3,7,2,6,5,1,4] => [[[.,[.,.]],[[.,.],.]],[.,.]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 2
[3,5,2,4,7,1,6] => [3,7,2,6,5,1,4] => [[[.,[.,.]],[[.,.],.]],[.,.]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 2
[3,5,2,6,4,1,7] => [3,7,2,6,5,1,4] => [[[.,[.,.]],[[.,.],.]],[.,.]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 2
[3,5,2,6,7,1,4] => [3,7,2,6,5,1,4] => [[[.,[.,.]],[[.,.],.]],[.,.]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 2
[3,5,2,7,4,1,6] => [3,7,2,6,5,1,4] => [[[.,[.,.]],[[.,.],.]],[.,.]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 2
[3,5,2,7,6,1,4] => [3,7,2,6,5,1,4] => [[[.,[.,.]],[[.,.],.]],[.,.]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 2
[3,6,2,4,5,1,7] => [3,7,2,6,5,1,4] => [[[.,[.,.]],[[.,.],.]],[.,.]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 2
[3,6,2,4,7,1,5] => [3,7,2,6,5,1,4] => [[[.,[.,.]],[[.,.],.]],[.,.]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 2
[3,6,2,5,4,1,7] => [3,7,2,6,5,1,4] => [[[.,[.,.]],[[.,.],.]],[.,.]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 2
[3,6,2,5,7,1,4] => [3,7,2,6,5,1,4] => [[[.,[.,.]],[[.,.],.]],[.,.]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 2
[3,6,2,7,4,1,5] => [3,7,2,6,5,1,4] => [[[.,[.,.]],[[.,.],.]],[.,.]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 2
[3,6,2,7,5,1,4] => [3,7,2,6,5,1,4] => [[[.,[.,.]],[[.,.],.]],[.,.]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 2
[3,7,2,4,5,1,6] => [3,7,2,6,5,1,4] => [[[.,[.,.]],[[.,.],.]],[.,.]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 2
[3,7,2,4,6,1,5] => [3,7,2,6,5,1,4] => [[[.,[.,.]],[[.,.],.]],[.,.]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 2
[3,7,2,5,4,1,6] => [3,7,2,6,5,1,4] => [[[.,[.,.]],[[.,.],.]],[.,.]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 2
[3,7,2,5,6,1,4] => [3,7,2,6,5,1,4] => [[[.,[.,.]],[[.,.],.]],[.,.]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 2
[3,7,2,6,4,1,5] => [3,7,2,6,5,1,4] => [[[.,[.,.]],[[.,.],.]],[.,.]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 2
[3,7,2,6,5,1,4] => [3,7,2,6,5,1,4] => [[[.,[.,.]],[[.,.],.]],[.,.]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 2
[4,3,2,5,6,1,7] => [4,3,2,7,6,1,5] => [[[[.,.],.],[[.,.],.]],[.,.]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 2
[4,3,2,5,7,1,6] => [4,3,2,7,6,1,5] => [[[[.,.],.],[[.,.],.]],[.,.]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 2
[4,3,2,6,5,1,7] => [4,3,2,7,6,1,5] => [[[[.,.],.],[[.,.],.]],[.,.]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 2
[4,3,2,6,7,1,5] => [4,3,2,7,6,1,5] => [[[[.,.],.],[[.,.],.]],[.,.]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 2
[4,3,2,7,5,1,6] => [4,3,2,7,6,1,5] => [[[[.,.],.],[[.,.],.]],[.,.]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 2
[4,3,2,7,6,1,5] => [4,3,2,7,6,1,5] => [[[[.,.],.],[[.,.],.]],[.,.]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 2
[4,5,2,3,6,1,7] => [4,7,2,6,5,1,3] => [[[.,[.,.]],[[.,.],.]],[.,.]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 2
[4,5,2,3,7,1,6] => [4,7,2,6,5,1,3] => [[[.,[.,.]],[[.,.],.]],[.,.]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 2
[4,5,2,6,3,1,7] => [4,7,2,6,5,1,3] => [[[.,[.,.]],[[.,.],.]],[.,.]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 2
[4,5,2,6,7,1,3] => [4,7,2,6,5,1,3] => [[[.,[.,.]],[[.,.],.]],[.,.]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 2
[4,5,2,7,3,1,6] => [4,7,2,6,5,1,3] => [[[.,[.,.]],[[.,.],.]],[.,.]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 2
[4,5,2,7,6,1,3] => [4,7,2,6,5,1,3] => [[[.,[.,.]],[[.,.],.]],[.,.]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 2
[4,5,3,6,7,1,2] => [4,7,3,6,5,1,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 2
[4,5,3,7,6,1,2] => [4,7,3,6,5,1,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 2
[4,6,2,3,5,1,7] => [4,7,2,6,5,1,3] => [[[.,[.,.]],[[.,.],.]],[.,.]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 2
[4,6,2,3,7,1,5] => [4,7,2,6,5,1,3] => [[[.,[.,.]],[[.,.],.]],[.,.]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 2
[4,6,2,5,3,1,7] => [4,7,2,6,5,1,3] => [[[.,[.,.]],[[.,.],.]],[.,.]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 2
[4,6,2,5,7,1,3] => [4,7,2,6,5,1,3] => [[[.,[.,.]],[[.,.],.]],[.,.]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 2
[4,6,2,7,3,1,5] => [4,7,2,6,5,1,3] => [[[.,[.,.]],[[.,.],.]],[.,.]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 2
[4,6,2,7,5,1,3] => [4,7,2,6,5,1,3] => [[[.,[.,.]],[[.,.],.]],[.,.]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 2
[4,6,3,5,7,1,2] => [4,7,3,6,5,1,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 2
[4,6,3,7,5,1,2] => [4,7,3,6,5,1,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 2
[4,7,2,3,5,1,6] => [4,7,2,6,5,1,3] => [[[.,[.,.]],[[.,.],.]],[.,.]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> 2
[4,7,2,3,6,1,5] => [4,7,2,6,5,1,3] => [[[.,[.,.]],[[.,.],.]],[.,.]]
=> ([(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.
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!