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Matching statistic: St001542
St001542: Decorated permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[+,+] => 0
[-,+] => 1
[+,-] => 1
[-,-] => 2
[2,1] => 1
[+,+,+] => 0
[-,+,+] => 1
[+,-,+] => 1
[+,+,-] => 1
[-,-,+] => 2
[-,+,-] => 2
[+,-,-] => 2
[-,-,-] => 3
[+,3,2] => 1
[-,3,2] => 2
[2,1,+] => 1
[2,1,-] => 2
[2,3,1] => 2
[3,1,2] => 1
[3,+,1] => 1
[3,-,1] => 2
[+,+,+,+] => 0
[-,+,+,+] => 1
[+,-,+,+] => 1
[+,+,-,+] => 1
[+,+,+,-] => 1
[-,-,+,+] => 2
[-,+,-,+] => 2
[-,+,+,-] => 2
[+,-,-,+] => 2
[+,-,+,-] => 2
[+,+,-,-] => 2
[-,-,-,+] => 3
[-,-,+,-] => 3
[-,+,-,-] => 3
[+,-,-,-] => 3
[-,-,-,-] => 4
[+,+,4,3] => 1
[-,+,4,3] => 2
[+,-,4,3] => 2
[-,-,4,3] => 3
[+,3,2,+] => 1
[-,3,2,+] => 2
[+,3,2,-] => 2
[-,3,2,-] => 3
[+,3,4,2] => 2
[-,3,4,2] => 3
[+,4,2,3] => 1
[-,4,2,3] => 2
[+,4,+,2] => 1
Description
The dimension of the subspace of the complex vector space for the associated Grassmannian.
Given an affine permutation, this is $$\frac{1}{n} \sum^n_{i=1} (f(i)-i)$$
This value is seen as $k$ in the notation Gr($k,n$), ($k,n$)-bounded affine permutations, ($k,n$)-Grassmann necklaces, and ($k,n$)-Le diagrams.
Matching statistic: St000260
Mp00256: Decorated permutations —upper permutation⟶ Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000260: Graphs ⟶ ℤResult quality: 13% ●values known / values provided: 13%●distinct values known / distinct values provided: 17%
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000260: Graphs ⟶ ℤResult quality: 13% ●values known / values provided: 13%●distinct values known / distinct values provided: 17%
Values
[+,+] => [1,2] => [2] => ([],2)
=> ? = 0
[-,+] => [2,1] => [1,1] => ([(0,1)],2)
=> 1
[+,-] => [1,2] => [2] => ([],2)
=> ? = 1
[-,-] => [1,2] => [2] => ([],2)
=> ? = 2
[2,1] => [2,1] => [1,1] => ([(0,1)],2)
=> 1
[+,+,+] => [1,2,3] => [3] => ([],3)
=> ? = 0
[-,+,+] => [2,3,1] => [2,1] => ([(0,2),(1,2)],3)
=> 1
[+,-,+] => [1,3,2] => [2,1] => ([(0,2),(1,2)],3)
=> 1
[+,+,-] => [1,2,3] => [3] => ([],3)
=> ? = 1
[-,-,+] => [3,1,2] => [1,2] => ([(1,2)],3)
=> ? = 2
[-,+,-] => [2,1,3] => [1,2] => ([(1,2)],3)
=> ? = 2
[+,-,-] => [1,2,3] => [3] => ([],3)
=> ? = 2
[-,-,-] => [1,2,3] => [3] => ([],3)
=> ? = 3
[+,3,2] => [1,3,2] => [2,1] => ([(0,2),(1,2)],3)
=> 1
[-,3,2] => [3,1,2] => [1,2] => ([(1,2)],3)
=> ? = 2
[2,1,+] => [2,3,1] => [2,1] => ([(0,2),(1,2)],3)
=> 1
[2,1,-] => [2,1,3] => [1,2] => ([(1,2)],3)
=> ? = 2
[2,3,1] => [3,1,2] => [1,2] => ([(1,2)],3)
=> ? = 2
[3,1,2] => [2,3,1] => [2,1] => ([(0,2),(1,2)],3)
=> 1
[3,+,1] => [2,3,1] => [2,1] => ([(0,2),(1,2)],3)
=> 1
[3,-,1] => [3,1,2] => [1,2] => ([(1,2)],3)
=> ? = 2
[+,+,+,+] => [1,2,3,4] => [4] => ([],4)
=> ? = 0
[-,+,+,+] => [2,3,4,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1
[+,-,+,+] => [1,3,4,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1
[+,+,-,+] => [1,2,4,3] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1
[+,+,+,-] => [1,2,3,4] => [4] => ([],4)
=> ? = 1
[-,-,+,+] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 2
[-,+,-,+] => [2,4,1,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 2
[-,+,+,-] => [2,3,1,4] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 2
[+,-,-,+] => [1,4,2,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 2
[+,-,+,-] => [1,3,2,4] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 2
[+,+,-,-] => [1,2,3,4] => [4] => ([],4)
=> ? = 2
[-,-,-,+] => [4,1,2,3] => [1,3] => ([(2,3)],4)
=> ? = 3
[-,-,+,-] => [3,1,2,4] => [1,3] => ([(2,3)],4)
=> ? = 3
[-,+,-,-] => [2,1,3,4] => [1,3] => ([(2,3)],4)
=> ? = 3
[+,-,-,-] => [1,2,3,4] => [4] => ([],4)
=> ? = 3
[-,-,-,-] => [1,2,3,4] => [4] => ([],4)
=> ? = 4
[+,+,4,3] => [1,2,4,3] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1
[-,+,4,3] => [2,4,1,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 2
[+,-,4,3] => [1,4,2,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 2
[-,-,4,3] => [4,1,2,3] => [1,3] => ([(2,3)],4)
=> ? = 3
[+,3,2,+] => [1,3,4,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1
[-,3,2,+] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 2
[+,3,2,-] => [1,3,2,4] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 2
[-,3,2,-] => [3,1,2,4] => [1,3] => ([(2,3)],4)
=> ? = 3
[+,3,4,2] => [1,4,2,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 2
[-,3,4,2] => [4,1,2,3] => [1,3] => ([(2,3)],4)
=> ? = 3
[+,4,2,3] => [1,3,4,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1
[-,4,2,3] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 2
[+,4,+,2] => [1,3,4,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1
[-,4,+,2] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 2
[+,4,-,2] => [1,4,2,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 2
[-,4,-,2] => [4,1,2,3] => [1,3] => ([(2,3)],4)
=> ? = 3
[2,1,+,+] => [2,3,4,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1
[2,1,-,+] => [2,4,1,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 2
[2,1,+,-] => [2,3,1,4] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 2
[2,1,-,-] => [2,1,3,4] => [1,3] => ([(2,3)],4)
=> ? = 3
[2,1,4,3] => [2,4,1,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 2
[2,3,1,+] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 2
[2,3,1,-] => [3,1,2,4] => [1,3] => ([(2,3)],4)
=> ? = 3
[2,3,4,1] => [4,1,2,3] => [1,3] => ([(2,3)],4)
=> ? = 3
[2,4,1,3] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 2
[2,4,+,1] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 2
[2,4,-,1] => [4,1,2,3] => [1,3] => ([(2,3)],4)
=> ? = 3
[3,1,2,+] => [2,3,4,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1
[3,1,2,-] => [2,3,1,4] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 2
[3,1,4,2] => [2,4,1,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 2
[3,+,1,+] => [2,3,4,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1
[4,1,2,3] => [2,3,4,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1
[4,1,+,2] => [2,3,4,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1
[4,+,1,3] => [2,3,4,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1
[4,+,+,1] => [2,3,4,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1
[-,+,+,+,+] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[+,-,+,+,+] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[+,+,-,+,+] => [1,2,4,5,3] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[+,+,+,-,+] => [1,2,3,5,4] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[+,+,+,5,4] => [1,2,3,5,4] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[+,+,4,3,+] => [1,2,4,5,3] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[+,+,5,3,4] => [1,2,4,5,3] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[+,+,5,+,3] => [1,2,4,5,3] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[+,3,2,+,+] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[+,4,2,3,+] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[+,4,+,2,+] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[+,5,2,3,4] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[+,5,2,+,3] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[+,5,+,2,4] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[+,5,+,+,2] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[2,1,+,+,+] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[3,1,2,+,+] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[3,+,1,+,+] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[4,1,2,3,+] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[4,1,+,2,+] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[4,+,1,3,+] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[4,+,+,1,+] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[5,1,2,3,4] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[5,1,2,+,3] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[5,1,+,2,4] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[5,1,+,+,2] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[5,+,1,3,4] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[5,+,1,+,3] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
Description
The radius of a connected graph.
This is the minimum eccentricity of any vertex.
Matching statistic: St000456
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00256: Decorated permutations —upper permutation⟶ Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000456: Graphs ⟶ ℤResult quality: 13% ●values known / values provided: 13%●distinct values known / distinct values provided: 17%
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000456: Graphs ⟶ ℤResult quality: 13% ●values known / values provided: 13%●distinct values known / distinct values provided: 17%
Values
[+,+] => [1,2] => [2] => ([],2)
=> ? = 0
[-,+] => [2,1] => [1,1] => ([(0,1)],2)
=> 1
[+,-] => [1,2] => [2] => ([],2)
=> ? = 1
[-,-] => [1,2] => [2] => ([],2)
=> ? = 2
[2,1] => [2,1] => [1,1] => ([(0,1)],2)
=> 1
[+,+,+] => [1,2,3] => [3] => ([],3)
=> ? = 0
[-,+,+] => [2,3,1] => [2,1] => ([(0,2),(1,2)],3)
=> 1
[+,-,+] => [1,3,2] => [2,1] => ([(0,2),(1,2)],3)
=> 1
[+,+,-] => [1,2,3] => [3] => ([],3)
=> ? = 1
[-,-,+] => [3,1,2] => [1,2] => ([(1,2)],3)
=> ? = 2
[-,+,-] => [2,1,3] => [1,2] => ([(1,2)],3)
=> ? = 2
[+,-,-] => [1,2,3] => [3] => ([],3)
=> ? = 2
[-,-,-] => [1,2,3] => [3] => ([],3)
=> ? = 3
[+,3,2] => [1,3,2] => [2,1] => ([(0,2),(1,2)],3)
=> 1
[-,3,2] => [3,1,2] => [1,2] => ([(1,2)],3)
=> ? = 2
[2,1,+] => [2,3,1] => [2,1] => ([(0,2),(1,2)],3)
=> 1
[2,1,-] => [2,1,3] => [1,2] => ([(1,2)],3)
=> ? = 2
[2,3,1] => [3,1,2] => [1,2] => ([(1,2)],3)
=> ? = 2
[3,1,2] => [2,3,1] => [2,1] => ([(0,2),(1,2)],3)
=> 1
[3,+,1] => [2,3,1] => [2,1] => ([(0,2),(1,2)],3)
=> 1
[3,-,1] => [3,1,2] => [1,2] => ([(1,2)],3)
=> ? = 2
[+,+,+,+] => [1,2,3,4] => [4] => ([],4)
=> ? = 0
[-,+,+,+] => [2,3,4,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1
[+,-,+,+] => [1,3,4,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1
[+,+,-,+] => [1,2,4,3] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1
[+,+,+,-] => [1,2,3,4] => [4] => ([],4)
=> ? = 1
[-,-,+,+] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 2
[-,+,-,+] => [2,4,1,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 2
[-,+,+,-] => [2,3,1,4] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 2
[+,-,-,+] => [1,4,2,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 2
[+,-,+,-] => [1,3,2,4] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 2
[+,+,-,-] => [1,2,3,4] => [4] => ([],4)
=> ? = 2
[-,-,-,+] => [4,1,2,3] => [1,3] => ([(2,3)],4)
=> ? = 3
[-,-,+,-] => [3,1,2,4] => [1,3] => ([(2,3)],4)
=> ? = 3
[-,+,-,-] => [2,1,3,4] => [1,3] => ([(2,3)],4)
=> ? = 3
[+,-,-,-] => [1,2,3,4] => [4] => ([],4)
=> ? = 3
[-,-,-,-] => [1,2,3,4] => [4] => ([],4)
=> ? = 4
[+,+,4,3] => [1,2,4,3] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1
[-,+,4,3] => [2,4,1,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 2
[+,-,4,3] => [1,4,2,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 2
[-,-,4,3] => [4,1,2,3] => [1,3] => ([(2,3)],4)
=> ? = 3
[+,3,2,+] => [1,3,4,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1
[-,3,2,+] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 2
[+,3,2,-] => [1,3,2,4] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 2
[-,3,2,-] => [3,1,2,4] => [1,3] => ([(2,3)],4)
=> ? = 3
[+,3,4,2] => [1,4,2,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 2
[-,3,4,2] => [4,1,2,3] => [1,3] => ([(2,3)],4)
=> ? = 3
[+,4,2,3] => [1,3,4,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1
[-,4,2,3] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 2
[+,4,+,2] => [1,3,4,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1
[-,4,+,2] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 2
[+,4,-,2] => [1,4,2,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 2
[-,4,-,2] => [4,1,2,3] => [1,3] => ([(2,3)],4)
=> ? = 3
[2,1,+,+] => [2,3,4,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1
[2,1,-,+] => [2,4,1,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 2
[2,1,+,-] => [2,3,1,4] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 2
[2,1,-,-] => [2,1,3,4] => [1,3] => ([(2,3)],4)
=> ? = 3
[2,1,4,3] => [2,4,1,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 2
[2,3,1,+] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 2
[2,3,1,-] => [3,1,2,4] => [1,3] => ([(2,3)],4)
=> ? = 3
[2,3,4,1] => [4,1,2,3] => [1,3] => ([(2,3)],4)
=> ? = 3
[2,4,1,3] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 2
[2,4,+,1] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 2
[2,4,-,1] => [4,1,2,3] => [1,3] => ([(2,3)],4)
=> ? = 3
[3,1,2,+] => [2,3,4,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1
[3,1,2,-] => [2,3,1,4] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 2
[3,1,4,2] => [2,4,1,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 2
[3,+,1,+] => [2,3,4,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1
[4,1,2,3] => [2,3,4,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1
[4,1,+,2] => [2,3,4,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1
[4,+,1,3] => [2,3,4,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1
[4,+,+,1] => [2,3,4,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1
[-,+,+,+,+] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[+,-,+,+,+] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[+,+,-,+,+] => [1,2,4,5,3] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[+,+,+,-,+] => [1,2,3,5,4] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[+,+,+,5,4] => [1,2,3,5,4] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[+,+,4,3,+] => [1,2,4,5,3] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[+,+,5,3,4] => [1,2,4,5,3] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[+,+,5,+,3] => [1,2,4,5,3] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[+,3,2,+,+] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[+,4,2,3,+] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[+,4,+,2,+] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[+,5,2,3,4] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[+,5,2,+,3] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[+,5,+,2,4] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[+,5,+,+,2] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[2,1,+,+,+] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[3,1,2,+,+] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[3,+,1,+,+] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[4,1,2,3,+] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[4,1,+,2,+] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[4,+,1,3,+] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[4,+,+,1,+] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[5,1,2,3,4] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[5,1,2,+,3] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[5,1,+,2,4] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[5,1,+,+,2] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[5,+,1,3,4] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
[5,+,1,+,3] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
Description
The monochromatic index of a connected graph.
This is the maximal number of colours such that there is a colouring of the edges where any two vertices can be joined by a monochromatic path.
For example, a circle graph other than the triangle can be coloured with at most two colours: one edge blue, all the others red.
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