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Your data matches 5 different statistics following compositions of up to 3 maps.
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Matching statistic: St000264
Mp00255: Decorated permutations —lower permutation⟶ Permutations
Mp00175: Permutations —inverse Foata bijection⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000264: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00175: Permutations —inverse Foata bijection⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000264: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[+,-,+,+] => [1,3,4,2] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> 4
[-,+,-,+] => [2,4,1,3] => [4,2,1,3] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 3
[-,3,2,+] => [2,4,1,3] => [4,2,1,3] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 3
[-,4,+,2] => [3,2,1,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> 3
[2,1,+,+] => [1,3,4,2] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> 4
[3,-,1,+] => [1,4,3,2] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 3
[4,-,1,3] => [1,3,4,2] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> 4
[+,-,+,+,+] => [1,3,4,5,2] => [3,4,5,1,2] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> 4
[+,+,-,+,+] => [1,2,4,5,3] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> 4
[-,-,+,+,+] => [3,4,5,1,2] => [3,4,1,5,2] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 4
[-,+,-,+,+] => [2,4,5,1,3] => [4,5,2,1,3] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> 3
[-,+,+,-,+] => [2,3,5,1,4] => [5,2,3,1,4] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[+,-,-,+,+] => [1,4,5,2,3] => [4,1,5,2,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 4
[+,-,+,-,+] => [1,3,5,2,4] => [5,3,1,2,4] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[+,-,+,+,-] => [1,3,4,2,5] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> 4
[-,-,+,-,+] => [3,5,1,2,4] => [1,5,3,2,4] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[-,+,-,+,-] => [2,4,1,3,5] => [4,2,1,3,5] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[+,-,+,5,4] => [1,3,4,2,5] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> 4
[-,+,-,5,4] => [2,4,1,3,5] => [4,2,1,3,5] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[-,+,4,3,+] => [2,3,5,1,4] => [5,2,3,1,4] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[+,-,4,3,+] => [1,3,5,2,4] => [5,3,1,2,4] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[-,-,4,3,+] => [3,5,1,2,4] => [1,5,3,2,4] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[+,-,5,3,4] => [1,3,4,2,5] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> 4
[-,+,5,+,3] => [2,4,3,1,5] => [4,2,3,1,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[+,-,5,+,3] => [1,4,3,2,5] => [4,3,1,2,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[-,-,5,+,3] => [4,3,1,2,5] => [1,4,3,2,5] => ([(2,3),(2,4),(3,4)],5)
=> 3
[+,-,5,-,3] => [1,3,2,5,4] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 4
[+,3,2,+,+] => [1,2,4,5,3] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> 4
[-,3,2,+,+] => [2,4,5,1,3] => [4,5,2,1,3] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> 3
[-,3,2,+,-] => [2,4,1,3,5] => [4,2,1,3,5] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[-,3,2,5,4] => [2,4,1,3,5] => [4,2,1,3,5] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[-,3,5,2,4] => [2,4,1,3,5] => [4,2,1,3,5] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[-,4,2,3,+] => [2,3,5,1,4] => [5,2,3,1,4] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[+,4,+,2,+] => [1,3,2,5,4] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 4
[-,4,+,2,+] => [3,2,5,1,4] => [3,5,2,1,4] => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> 3
[+,4,-,2,+] => [1,2,5,4,3] => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[-,4,-,2,+] => [2,5,1,4,3] => [2,5,4,1,3] => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> 3
[-,4,+,2,-] => [3,2,1,4,5] => [3,2,1,4,5] => ([(2,3),(2,4),(3,4)],5)
=> 3
[-,4,+,5,2] => [3,2,1,4,5] => [3,2,1,4,5] => ([(2,3),(2,4),(3,4)],5)
=> 3
[-,4,5,3,2] => [3,2,1,4,5] => [3,2,1,4,5] => ([(2,3),(2,4),(3,4)],5)
=> 3
[-,5,2,+,3] => [2,4,3,1,5] => [4,2,3,1,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[-,5,+,2,4] => [3,2,4,1,5] => [3,2,4,1,5] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[+,5,-,2,4] => [1,2,4,5,3] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> 4
[-,5,-,2,4] => [2,4,1,5,3] => [4,2,5,1,3] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> 3
[+,5,+,+,2] => [1,3,4,2,5] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> 4
[-,5,+,+,2] => [3,4,2,1,5] => [3,4,2,1,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[+,5,-,+,2] => [1,4,2,5,3] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> 4
[+,5,+,-,2] => [1,3,2,5,4] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 4
[-,5,+,-,2] => [3,2,1,5,4] => [3,2,5,1,4] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> 3
[-,5,-,-,2] => [2,1,5,3,4] => [5,2,1,3,4] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
Description
The girth of a graph, which is not a tree.
This is the length of the shortest cycle in the graph.
Matching statistic: St000777
Mp00256: Decorated permutations —upper permutation⟶ Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000777: Graphs ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 50%
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000777: Graphs ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 50%
Values
[+,-,+,+] => [1,3,4,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 3 = 4 - 1
[-,+,-,+] => [2,4,1,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3 - 1
[-,3,2,+] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3 - 1
[-,4,+,2] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3 - 1
[2,1,+,+] => [2,3,4,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 3 = 4 - 1
[3,-,1,+] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3 - 1
[4,-,1,3] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 4 - 1
[+,-,+,+,+] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3 = 4 - 1
[+,+,-,+,+] => [1,2,4,5,3] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3 = 4 - 1
[-,-,+,+,+] => [3,4,5,1,2] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 4 - 1
[-,+,-,+,+] => [2,4,5,1,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 1
[-,+,+,-,+] => [2,3,5,1,4] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 1
[+,-,-,+,+] => [1,4,5,2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 4 - 1
[+,-,+,-,+] => [1,3,5,2,4] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 1
[+,-,+,+,-] => [1,3,4,2,5] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 4 - 1
[-,-,+,-,+] => [3,5,1,2,4] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 1
[-,+,-,+,-] => [2,4,1,3,5] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 1
[+,-,+,5,4] => [1,3,5,2,4] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 4 - 1
[-,+,-,5,4] => [2,5,1,3,4] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 1
[-,+,4,3,+] => [2,4,5,1,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 1
[+,-,4,3,+] => [1,4,5,2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 1
[-,-,4,3,+] => [4,5,1,2,3] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 1
[+,-,5,3,4] => [1,4,5,2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 4 - 1
[-,+,5,+,3] => [2,4,5,1,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 1
[+,-,5,+,3] => [1,4,5,2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 1
[-,-,5,+,3] => [4,5,1,2,3] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 1
[+,-,5,-,3] => [1,5,2,3,4] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 4 - 1
[+,3,2,+,+] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3 = 4 - 1
[-,3,2,+,+] => [3,4,5,1,2] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 1
[-,3,2,+,-] => [3,4,1,2,5] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 1
[-,3,2,5,4] => [3,5,1,2,4] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 1
[-,3,5,2,4] => [4,5,1,2,3] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 1
[-,4,2,3,+] => [3,4,5,1,2] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 1
[+,4,+,2,+] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3 = 4 - 1
[-,4,+,2,+] => [3,4,5,1,2] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 1
[+,4,-,2,+] => [1,4,5,2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 1
[-,4,-,2,+] => [4,5,1,2,3] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 1
[-,4,+,2,-] => [3,4,1,2,5] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 1
[-,4,+,5,2] => [3,5,1,2,4] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 1
[-,4,5,3,2] => [4,5,1,2,3] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 1
[-,5,2,+,3] => [3,4,5,1,2] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 1
[-,5,+,2,4] => [3,4,5,1,2] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 1
[+,5,-,2,4] => [1,4,5,2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 4 - 1
[-,5,-,2,4] => [4,5,1,2,3] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 1
[+,5,+,+,2] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3 = 4 - 1
[-,5,+,+,2] => [3,4,5,1,2] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 1
[+,5,-,+,2] => [1,4,5,2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 4 - 1
[+,5,+,-,2] => [1,3,5,2,4] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 4 - 1
[-,5,+,-,2] => [3,5,1,2,4] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 1
[-,5,-,-,2] => [5,1,2,3,4] => [1,4] => ([(3,4)],5)
=> ? = 3 - 1
[+,5,4,3,2] => [1,4,5,2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 4 - 1
[-,5,4,3,2] => [4,5,1,2,3] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 1
[2,1,+,+,+] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3 = 4 - 1
[2,1,-,+,+] => [2,4,5,1,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 4 - 1
[2,1,+,-,+] => [2,3,5,1,4] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 1
[2,1,+,+,-] => [2,3,4,1,5] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 4 - 1
[2,1,+,5,4] => [2,3,5,1,4] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 4 - 1
[2,1,4,3,+] => [2,4,5,1,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 1
[3,1,2,+,+] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3 = 4 - 1
[3,+,1,+,+] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3 = 4 - 1
[4,1,+,2,+] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3 = 4 - 1
[5,1,+,+,2] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3 = 4 - 1
[+,-,+,+,+,+] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 4 - 1
[+,+,-,+,+,+] => [1,2,4,5,6,3] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 4 - 1
[+,+,+,-,+,+] => [1,2,3,5,6,4] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 4 - 1
[+,+,4,3,+,+] => [1,2,4,5,6,3] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 4 - 1
[+,+,5,+,3,+] => [1,2,4,5,6,3] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 4 - 1
[+,+,6,+,+,3] => [1,2,4,5,6,3] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 4 - 1
[+,3,2,+,+,+] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 4 - 1
[+,4,2,3,+,+] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 4 - 1
[+,4,+,2,+,+] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 4 - 1
[+,5,2,+,3,+] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 4 - 1
[+,5,+,2,4,+] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 4 - 1
[+,5,+,+,2,+] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 4 - 1
[+,6,2,+,+,3] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 4 - 1
[+,6,+,2,+,4] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 4 - 1
[+,6,+,+,2,5] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 4 - 1
[+,6,+,+,+,2] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 4 - 1
[2,1,+,+,+,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 4 - 1
[3,1,2,+,+,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 4 - 1
[3,+,1,+,+,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 4 - 1
[4,1,2,3,+,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 4 - 1
[4,1,+,2,+,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 4 - 1
[4,+,1,3,+,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 4 - 1
[4,+,+,1,+,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 4 - 1
[5,1,2,+,3,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 4 - 1
[5,1,+,2,4,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 4 - 1
[5,1,+,+,2,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 4 - 1
[5,+,1,+,3,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 4 - 1
[6,1,2,+,+,3] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 4 - 1
[6,1,+,2,+,4] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 4 - 1
[6,1,+,+,2,5] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 4 - 1
[6,1,+,+,+,2] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 4 - 1
[6,+,1,+,+,3] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 3 = 4 - 1
Description
The number of distinct eigenvalues of the distance Laplacian of a connected graph.
Matching statistic: St000259
Mp00256: Decorated permutations —upper permutation⟶ Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000259: Graphs ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 50%
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000259: Graphs ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 50%
Values
[+,-,+,+] => [1,3,4,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 4 - 2
[-,+,-,+] => [2,4,1,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3 - 2
[-,3,2,+] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3 - 2
[-,4,+,2] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3 - 2
[2,1,+,+] => [2,3,4,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 4 - 2
[3,-,1,+] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3 - 2
[4,-,1,3] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 4 - 2
[+,-,+,+,+] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 4 - 2
[+,+,-,+,+] => [1,2,4,5,3] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 4 - 2
[-,-,+,+,+] => [3,4,5,1,2] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 4 - 2
[-,+,-,+,+] => [2,4,5,1,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 2
[-,+,+,-,+] => [2,3,5,1,4] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 2
[+,-,-,+,+] => [1,4,5,2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 4 - 2
[+,-,+,-,+] => [1,3,5,2,4] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 2
[+,-,+,+,-] => [1,3,4,2,5] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 4 - 2
[-,-,+,-,+] => [3,5,1,2,4] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 2
[-,+,-,+,-] => [2,4,1,3,5] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 2
[+,-,+,5,4] => [1,3,5,2,4] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 4 - 2
[-,+,-,5,4] => [2,5,1,3,4] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 2
[-,+,4,3,+] => [2,4,5,1,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 2
[+,-,4,3,+] => [1,4,5,2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 2
[-,-,4,3,+] => [4,5,1,2,3] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 2
[+,-,5,3,4] => [1,4,5,2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 4 - 2
[-,+,5,+,3] => [2,4,5,1,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 2
[+,-,5,+,3] => [1,4,5,2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 2
[-,-,5,+,3] => [4,5,1,2,3] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 2
[+,-,5,-,3] => [1,5,2,3,4] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 4 - 2
[+,3,2,+,+] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 4 - 2
[-,3,2,+,+] => [3,4,5,1,2] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 2
[-,3,2,+,-] => [3,4,1,2,5] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 2
[-,3,2,5,4] => [3,5,1,2,4] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 2
[-,3,5,2,4] => [4,5,1,2,3] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 2
[-,4,2,3,+] => [3,4,5,1,2] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 2
[+,4,+,2,+] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 4 - 2
[-,4,+,2,+] => [3,4,5,1,2] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 2
[+,4,-,2,+] => [1,4,5,2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 2
[-,4,-,2,+] => [4,5,1,2,3] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 2
[-,4,+,2,-] => [3,4,1,2,5] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 2
[-,4,+,5,2] => [3,5,1,2,4] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 2
[-,4,5,3,2] => [4,5,1,2,3] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 2
[-,5,2,+,3] => [3,4,5,1,2] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 2
[-,5,+,2,4] => [3,4,5,1,2] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 2
[+,5,-,2,4] => [1,4,5,2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 4 - 2
[-,5,-,2,4] => [4,5,1,2,3] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 2
[+,5,+,+,2] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 4 - 2
[-,5,+,+,2] => [3,4,5,1,2] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 2
[+,5,-,+,2] => [1,4,5,2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 4 - 2
[+,5,+,-,2] => [1,3,5,2,4] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 4 - 2
[-,5,+,-,2] => [3,5,1,2,4] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 2
[-,5,-,-,2] => [5,1,2,3,4] => [1,4] => ([(3,4)],5)
=> ? = 3 - 2
[+,5,4,3,2] => [1,4,5,2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 4 - 2
[-,5,4,3,2] => [4,5,1,2,3] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 2
[2,1,+,+,+] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 4 - 2
[2,1,-,+,+] => [2,4,5,1,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 4 - 2
[2,1,+,-,+] => [2,3,5,1,4] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 2
[2,1,+,+,-] => [2,3,4,1,5] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 4 - 2
[2,1,+,5,4] => [2,3,5,1,4] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 4 - 2
[2,1,4,3,+] => [2,4,5,1,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 2
[3,1,2,+,+] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 4 - 2
[3,+,1,+,+] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 4 - 2
[4,1,+,2,+] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 4 - 2
[5,1,+,+,2] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 4 - 2
[+,-,+,+,+,+] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 4 - 2
[+,+,-,+,+,+] => [1,2,4,5,6,3] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 4 - 2
[+,+,+,-,+,+] => [1,2,3,5,6,4] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 4 - 2
[+,+,4,3,+,+] => [1,2,4,5,6,3] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 4 - 2
[+,+,5,+,3,+] => [1,2,4,5,6,3] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 4 - 2
[+,+,6,+,+,3] => [1,2,4,5,6,3] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 4 - 2
[+,3,2,+,+,+] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 4 - 2
[+,4,2,3,+,+] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 4 - 2
[+,4,+,2,+,+] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 4 - 2
[+,5,2,+,3,+] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 4 - 2
[+,5,+,2,4,+] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 4 - 2
[+,5,+,+,2,+] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 4 - 2
[+,6,2,+,+,3] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 4 - 2
[+,6,+,2,+,4] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 4 - 2
[+,6,+,+,2,5] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 4 - 2
[+,6,+,+,+,2] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 4 - 2
[2,1,+,+,+,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 4 - 2
[3,1,2,+,+,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 4 - 2
[3,+,1,+,+,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 4 - 2
[4,1,2,3,+,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 4 - 2
[4,1,+,2,+,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 4 - 2
[4,+,1,3,+,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 4 - 2
[4,+,+,1,+,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 4 - 2
[5,1,2,+,3,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 4 - 2
[5,1,+,2,4,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 4 - 2
[5,1,+,+,2,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 4 - 2
[5,+,1,+,3,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 4 - 2
[6,1,2,+,+,3] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 4 - 2
[6,1,+,2,+,4] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 4 - 2
[6,1,+,+,2,5] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 4 - 2
[6,1,+,+,+,2] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 4 - 2
[6,+,1,+,+,3] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 4 - 2
Description
The diameter of a connected graph.
This is the greatest distance between any pair of vertices.
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: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 50%
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000260: Graphs ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 50%
Values
[+,-,+,+] => [1,3,4,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1 = 4 - 3
[-,+,-,+] => [2,4,1,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3 - 3
[-,3,2,+] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3 - 3
[-,4,+,2] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3 - 3
[2,1,+,+] => [2,3,4,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1 = 4 - 3
[3,-,1,+] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3 - 3
[4,-,1,3] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 4 - 3
[+,-,+,+,+] => [1,3,4,5,2] => [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 = 4 - 3
[-,-,+,+,+] => [3,4,5,1,2] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 4 - 3
[-,+,-,+,+] => [2,4,5,1,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 3
[-,+,+,-,+] => [2,3,5,1,4] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 3
[+,-,-,+,+] => [1,4,5,2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 4 - 3
[+,-,+,-,+] => [1,3,5,2,4] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 3
[+,-,+,+,-] => [1,3,4,2,5] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 4 - 3
[-,-,+,-,+] => [3,5,1,2,4] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 3
[-,+,-,+,-] => [2,4,1,3,5] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 3
[+,-,+,5,4] => [1,3,5,2,4] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 4 - 3
[-,+,-,5,4] => [2,5,1,3,4] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 3
[-,+,4,3,+] => [2,4,5,1,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 3
[+,-,4,3,+] => [1,4,5,2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 3
[-,-,4,3,+] => [4,5,1,2,3] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 3
[+,-,5,3,4] => [1,4,5,2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 4 - 3
[-,+,5,+,3] => [2,4,5,1,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 3
[+,-,5,+,3] => [1,4,5,2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 3
[-,-,5,+,3] => [4,5,1,2,3] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 3
[+,-,5,-,3] => [1,5,2,3,4] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 4 - 3
[+,3,2,+,+] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 4 - 3
[-,3,2,+,+] => [3,4,5,1,2] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 3
[-,3,2,+,-] => [3,4,1,2,5] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 3
[-,3,2,5,4] => [3,5,1,2,4] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 3
[-,3,5,2,4] => [4,5,1,2,3] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 3
[-,4,2,3,+] => [3,4,5,1,2] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 3
[+,4,+,2,+] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 4 - 3
[-,4,+,2,+] => [3,4,5,1,2] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 3
[+,4,-,2,+] => [1,4,5,2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 3
[-,4,-,2,+] => [4,5,1,2,3] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 3
[-,4,+,2,-] => [3,4,1,2,5] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 3
[-,4,+,5,2] => [3,5,1,2,4] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 3
[-,4,5,3,2] => [4,5,1,2,3] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 3
[-,5,2,+,3] => [3,4,5,1,2] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 3
[-,5,+,2,4] => [3,4,5,1,2] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 3
[+,5,-,2,4] => [1,4,5,2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 4 - 3
[-,5,-,2,4] => [4,5,1,2,3] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 3
[+,5,+,+,2] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 4 - 3
[-,5,+,+,2] => [3,4,5,1,2] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 3
[+,5,-,+,2] => [1,4,5,2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 4 - 3
[+,5,+,-,2] => [1,3,5,2,4] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 4 - 3
[-,5,+,-,2] => [3,5,1,2,4] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 3
[-,5,-,-,2] => [5,1,2,3,4] => [1,4] => ([(3,4)],5)
=> ? = 3 - 3
[+,5,4,3,2] => [1,4,5,2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 4 - 3
[-,5,4,3,2] => [4,5,1,2,3] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 3
[2,1,+,+,+] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 4 - 3
[2,1,-,+,+] => [2,4,5,1,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 4 - 3
[2,1,+,-,+] => [2,3,5,1,4] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 3
[2,1,+,+,-] => [2,3,4,1,5] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 4 - 3
[2,1,+,5,4] => [2,3,5,1,4] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 4 - 3
[2,1,4,3,+] => [2,4,5,1,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 3
[3,1,2,+,+] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 4 - 3
[3,+,1,+,+] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 4 - 3
[4,1,+,2,+] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 4 - 3
[5,1,+,+,2] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 4 - 3
[+,-,+,+,+,+] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 4 - 3
[+,+,-,+,+,+] => [1,2,4,5,6,3] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 4 - 3
[+,+,+,-,+,+] => [1,2,3,5,6,4] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 4 - 3
[+,+,4,3,+,+] => [1,2,4,5,6,3] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 4 - 3
[+,+,5,+,3,+] => [1,2,4,5,6,3] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 4 - 3
[+,+,6,+,+,3] => [1,2,4,5,6,3] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 4 - 3
[+,3,2,+,+,+] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 4 - 3
[+,4,2,3,+,+] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 4 - 3
[+,4,+,2,+,+] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 4 - 3
[+,5,2,+,3,+] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 4 - 3
[+,5,+,2,4,+] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 4 - 3
[+,5,+,+,2,+] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 4 - 3
[+,6,2,+,+,3] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 4 - 3
[+,6,+,2,+,4] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 4 - 3
[+,6,+,+,2,5] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 4 - 3
[+,6,+,+,+,2] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 4 - 3
[2,1,+,+,+,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 4 - 3
[3,1,2,+,+,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 4 - 3
[3,+,1,+,+,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 4 - 3
[4,1,2,3,+,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 4 - 3
[4,1,+,2,+,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 4 - 3
[4,+,1,3,+,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 4 - 3
[4,+,+,1,+,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 4 - 3
[5,1,2,+,3,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 4 - 3
[5,1,+,2,4,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 4 - 3
[5,1,+,+,2,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 4 - 3
[5,+,1,+,3,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 4 - 3
[6,1,2,+,+,3] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 4 - 3
[6,1,+,2,+,4] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 4 - 3
[6,1,+,+,2,5] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 4 - 3
[6,1,+,+,+,2] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 4 - 3
[6,+,1,+,+,3] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 4 - 3
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: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 50%
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000456: Graphs ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 50%
Values
[+,-,+,+] => [1,3,4,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1 = 4 - 3
[-,+,-,+] => [2,4,1,3] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3 - 3
[-,3,2,+] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3 - 3
[-,4,+,2] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3 - 3
[2,1,+,+] => [2,3,4,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 1 = 4 - 3
[3,-,1,+] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3 - 3
[4,-,1,3] => [3,4,1,2] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 4 - 3
[+,-,+,+,+] => [1,3,4,5,2] => [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 = 4 - 3
[-,-,+,+,+] => [3,4,5,1,2] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 4 - 3
[-,+,-,+,+] => [2,4,5,1,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 3
[-,+,+,-,+] => [2,3,5,1,4] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 3
[+,-,-,+,+] => [1,4,5,2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 4 - 3
[+,-,+,-,+] => [1,3,5,2,4] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 3
[+,-,+,+,-] => [1,3,4,2,5] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 4 - 3
[-,-,+,-,+] => [3,5,1,2,4] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 3
[-,+,-,+,-] => [2,4,1,3,5] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 3
[+,-,+,5,4] => [1,3,5,2,4] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 4 - 3
[-,+,-,5,4] => [2,5,1,3,4] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 3
[-,+,4,3,+] => [2,4,5,1,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 3
[+,-,4,3,+] => [1,4,5,2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 3
[-,-,4,3,+] => [4,5,1,2,3] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 3
[+,-,5,3,4] => [1,4,5,2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 4 - 3
[-,+,5,+,3] => [2,4,5,1,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 3
[+,-,5,+,3] => [1,4,5,2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 3
[-,-,5,+,3] => [4,5,1,2,3] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 3
[+,-,5,-,3] => [1,5,2,3,4] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 4 - 3
[+,3,2,+,+] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 4 - 3
[-,3,2,+,+] => [3,4,5,1,2] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 3
[-,3,2,+,-] => [3,4,1,2,5] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 3
[-,3,2,5,4] => [3,5,1,2,4] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 3
[-,3,5,2,4] => [4,5,1,2,3] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 3
[-,4,2,3,+] => [3,4,5,1,2] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 3
[+,4,+,2,+] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 4 - 3
[-,4,+,2,+] => [3,4,5,1,2] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 3
[+,4,-,2,+] => [1,4,5,2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 3
[-,4,-,2,+] => [4,5,1,2,3] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 3
[-,4,+,2,-] => [3,4,1,2,5] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 3
[-,4,+,5,2] => [3,5,1,2,4] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 3
[-,4,5,3,2] => [4,5,1,2,3] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 3
[-,5,2,+,3] => [3,4,5,1,2] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 3
[-,5,+,2,4] => [3,4,5,1,2] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 3
[+,5,-,2,4] => [1,4,5,2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 4 - 3
[-,5,-,2,4] => [4,5,1,2,3] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 3
[+,5,+,+,2] => [1,3,4,5,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 4 - 3
[-,5,+,+,2] => [3,4,5,1,2] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 3
[+,5,-,+,2] => [1,4,5,2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 4 - 3
[+,5,+,-,2] => [1,3,5,2,4] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 4 - 3
[-,5,+,-,2] => [3,5,1,2,4] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 3
[-,5,-,-,2] => [5,1,2,3,4] => [1,4] => ([(3,4)],5)
=> ? = 3 - 3
[+,5,4,3,2] => [1,4,5,2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 4 - 3
[-,5,4,3,2] => [4,5,1,2,3] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 3
[2,1,+,+,+] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 4 - 3
[2,1,-,+,+] => [2,4,5,1,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 4 - 3
[2,1,+,-,+] => [2,3,5,1,4] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 3
[2,1,+,+,-] => [2,3,4,1,5] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 4 - 3
[2,1,+,5,4] => [2,3,5,1,4] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 4 - 3
[2,1,4,3,+] => [2,4,5,1,3] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 3
[3,1,2,+,+] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 4 - 3
[3,+,1,+,+] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 4 - 3
[4,1,+,2,+] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 4 - 3
[5,1,+,+,2] => [2,3,4,5,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 4 - 3
[+,-,+,+,+,+] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 4 - 3
[+,+,-,+,+,+] => [1,2,4,5,6,3] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 4 - 3
[+,+,+,-,+,+] => [1,2,3,5,6,4] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 4 - 3
[+,+,4,3,+,+] => [1,2,4,5,6,3] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 4 - 3
[+,+,5,+,3,+] => [1,2,4,5,6,3] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 4 - 3
[+,+,6,+,+,3] => [1,2,4,5,6,3] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 4 - 3
[+,3,2,+,+,+] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 4 - 3
[+,4,2,3,+,+] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 4 - 3
[+,4,+,2,+,+] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 4 - 3
[+,5,2,+,3,+] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 4 - 3
[+,5,+,2,4,+] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 4 - 3
[+,5,+,+,2,+] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 4 - 3
[+,6,2,+,+,3] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 4 - 3
[+,6,+,2,+,4] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 4 - 3
[+,6,+,+,2,5] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 4 - 3
[+,6,+,+,+,2] => [1,3,4,5,6,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 4 - 3
[2,1,+,+,+,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 4 - 3
[3,1,2,+,+,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 4 - 3
[3,+,1,+,+,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 4 - 3
[4,1,2,3,+,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 4 - 3
[4,1,+,2,+,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 4 - 3
[4,+,1,3,+,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 4 - 3
[4,+,+,1,+,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 4 - 3
[5,1,2,+,3,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 4 - 3
[5,1,+,2,4,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 4 - 3
[5,1,+,+,2,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 4 - 3
[5,+,1,+,3,+] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 4 - 3
[6,1,2,+,+,3] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 4 - 3
[6,1,+,2,+,4] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 4 - 3
[6,1,+,+,2,5] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 4 - 3
[6,1,+,+,+,2] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 4 - 3
[6,+,1,+,+,3] => [2,3,4,5,6,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 1 = 4 - 3
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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