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Your data matches 35 different statistics following compositions of up to 3 maps.
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Matching statistic: St001875
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Mp00324: Graphs —chromatic difference sequence⟶ Integer compositions
Mp00180: Integer compositions —to ribbon⟶ Skew partitions
Mp00192: Skew partitions —dominating sublattice⟶ Lattices
St001875: Lattices ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00180: Integer compositions —to ribbon⟶ Skew partitions
Mp00192: Skew partitions —dominating sublattice⟶ Lattices
St001875: Lattices ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([(0,1),(2,3),(2,4),(3,4)],5)
=> [2,2,1] => [[3,3,2],[2,1]]
=> ([(0,2),(2,1)],3)
=> 3
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> [2,2,1] => [[3,3,2],[2,1]]
=> ([(0,2),(2,1)],3)
=> 3
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> [2,2,1] => [[3,3,2],[2,1]]
=> ([(0,2),(2,1)],3)
=> 3
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> [2,2,1] => [[3,3,2],[2,1]]
=> ([(0,2),(2,1)],3)
=> 3
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [2,2,1] => [[3,3,2],[2,1]]
=> ([(0,2),(2,1)],3)
=> 3
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> [2,2,1] => [[3,3,2],[2,1]]
=> ([(0,2),(2,1)],3)
=> 3
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> [2,2,1] => [[3,3,2],[2,1]]
=> ([(0,2),(2,1)],3)
=> 3
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2,1] => [[3,3,2],[2,1]]
=> ([(0,2),(2,1)],3)
=> 3
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> [2,2,1] => [[3,3,2],[2,1]]
=> ([(0,2),(2,1)],3)
=> 3
([(0,5),(1,4),(2,3)],6)
=> [3,3] => [[5,3],[2]]
=> ([(0,2),(2,1)],3)
=> 3
([(0,1),(2,5),(3,4),(4,5)],6)
=> [3,3] => [[5,3],[2]]
=> ([(0,2),(2,1)],3)
=> 3
([(1,2),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 3
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> [3,3] => [[5,3],[2]]
=> ([(0,2),(2,1)],3)
=> 3
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 3
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 3
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 3
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 3
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 3
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 3
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> [3,3] => [[5,3],[2]]
=> ([(0,2),(2,1)],3)
=> 3
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 3
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 3
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 3
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 3
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 3
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 3
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 3
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 3
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> [3,3] => [[5,3],[2]]
=> ([(0,2),(2,1)],3)
=> 3
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,3] => [[5,3],[2]]
=> ([(0,2),(2,1)],3)
=> 3
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 3
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
=> [3,3] => [[5,3],[2]]
=> ([(0,2),(2,1)],3)
=> 3
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 3
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 3
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 3
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 3
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 3
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 3
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 3
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 3
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 3
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 3
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 3
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 3
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 3
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 3
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 3
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 3
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 3
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> [3,3] => [[5,3],[2]]
=> ([(0,2),(2,1)],3)
=> 3
Description
The number of simple modules with projective dimension at most 1.
Matching statistic: St001622
Mp00324: Graphs —chromatic difference sequence⟶ Integer compositions
Mp00180: Integer compositions —to ribbon⟶ Skew partitions
Mp00192: Skew partitions —dominating sublattice⟶ Lattices
St001622: Lattices ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00180: Integer compositions —to ribbon⟶ Skew partitions
Mp00192: Skew partitions —dominating sublattice⟶ Lattices
St001622: Lattices ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([(0,1),(2,3),(2,4),(3,4)],5)
=> [2,2,1] => [[3,3,2],[2,1]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> [2,2,1] => [[3,3,2],[2,1]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> [2,2,1] => [[3,3,2],[2,1]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> [2,2,1] => [[3,3,2],[2,1]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [2,2,1] => [[3,3,2],[2,1]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> [2,2,1] => [[3,3,2],[2,1]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> [2,2,1] => [[3,3,2],[2,1]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2,1] => [[3,3,2],[2,1]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> [2,2,1] => [[3,3,2],[2,1]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
([(0,5),(1,4),(2,3)],6)
=> [3,3] => [[5,3],[2]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
([(0,1),(2,5),(3,4),(4,5)],6)
=> [3,3] => [[5,3],[2]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
([(1,2),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> [3,3] => [[5,3],[2]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> [3,3] => [[5,3],[2]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> [3,3] => [[5,3],[2]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,3] => [[5,3],[2]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
=> [3,3] => [[5,3],[2]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1] => [[4,4,3],[3,2]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> [3,3] => [[5,3],[2]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
Description
The number of join-irreducible elements of a lattice.
An element $j$ of a lattice $L$ is '''join irreducible''' if it is not the least element and if $j=x\vee y$, then $j\in\{x,y\}$ for all $x,y\in L$.
Matching statistic: St000264
Mp00324: Graphs —chromatic difference sequence⟶ Integer compositions
Mp00133: Integer compositions —delta morphism⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000264: Graphs ⟶ ℤResult quality: 25% ●values known / values provided: 47%●distinct values known / distinct values provided: 25%
Mp00133: Integer compositions —delta morphism⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000264: Graphs ⟶ ℤResult quality: 25% ●values known / values provided: 47%●distinct values known / distinct values provided: 25%
Values
([(0,1),(2,3),(2,4),(3,4)],5)
=> [2,2,1] => [2,1] => ([(0,2),(1,2)],3)
=> ? = 3
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> [2,2,1] => [2,1] => ([(0,2),(1,2)],3)
=> ? = 3
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> [2,2,1] => [2,1] => ([(0,2),(1,2)],3)
=> ? = 3
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> [2,2,1] => [2,1] => ([(0,2),(1,2)],3)
=> ? = 3
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [2,2,1] => [2,1] => ([(0,2),(1,2)],3)
=> ? = 3
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> [2,2,1] => [2,1] => ([(0,2),(1,2)],3)
=> ? = 3
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> [2,2,1] => [2,1] => ([(0,2),(1,2)],3)
=> ? = 3
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2,1] => [2,1] => ([(0,2),(1,2)],3)
=> ? = 3
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> [2,2,1] => [2,1] => ([(0,2),(1,2)],3)
=> ? = 3
([(0,5),(1,4),(2,3)],6)
=> [3,3] => [2] => ([],2)
=> ? = 3
([(0,1),(2,5),(3,4),(4,5)],6)
=> [3,3] => [2] => ([],2)
=> ? = 3
([(1,2),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> [3,3] => [2] => ([],2)
=> ? = 3
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
=> [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> [3,3] => [2] => ([],2)
=> ? = 3
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
=> [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> [3,3] => [2] => ([],2)
=> ? = 3
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,3] => [2] => ([],2)
=> ? = 3
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
=> [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
=> [3,3] => [2] => ([],2)
=> ? = 3
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
=> [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)
=> [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> [3,3] => [2] => ([],2)
=> ? = 3
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
=> [3,3] => [2] => ([],2)
=> ? = 3
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> [3,3] => [2] => ([],2)
=> ? = 3
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,3] => [2] => ([],2)
=> ? = 3
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> [3,3] => [2] => ([],2)
=> ? = 3
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
=> [2,2,2] => [3] => ([],3)
=> ? = 4
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
=> [2,2,2] => [3] => ([],3)
=> ? = 4
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> [2,2,2] => [3] => ([],3)
=> ? = 4
([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3
([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)
=> [2,2,2] => [3] => ([],3)
=> ? = 4
([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> [2,2,2] => [3] => ([],3)
=> ? = 4
([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3
([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,2] => [3] => ([],3)
=> ? = 4
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3
([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [2,2,2] => [3] => ([],3)
=> ? = 4
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [2,2,2] => [3] => ([],3)
=> ? = 4
([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [2,2,2] => [3] => ([],3)
=> ? = 4
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [2,2,1,1] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
=> [2,2,2] => [3] => ([],3)
=> ? = 4
([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,2] => [3] => ([],3)
=> ? = 4
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> [2,2,2] => [3] => ([],3)
=> ? = 4
([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3
([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [2,2,2] => [3] => ([],3)
=> ? = 4
([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 3
([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 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: St001645
(load all 3 compositions to match this statistic)
(load all 3 compositions to match this statistic)
Mp00324: Graphs —chromatic difference sequence⟶ Integer compositions
Mp00041: Integer compositions —conjugate⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St001645: Graphs ⟶ ℤResult quality: 25% ●values known / values provided: 26%●distinct values known / distinct values provided: 25%
Mp00041: Integer compositions —conjugate⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St001645: Graphs ⟶ ℤResult quality: 25% ●values known / values provided: 26%●distinct values known / distinct values provided: 25%
Values
([(0,1),(2,3),(2,4),(3,4)],5)
=> [2,2,1] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 + 4
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> [2,2,1] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 + 4
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> [2,2,1] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 + 4
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> [2,2,1] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 + 4
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [2,2,1] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 + 4
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> [2,2,1] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 + 4
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> [2,2,1] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 + 4
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2,1] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 + 4
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> [2,2,1] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 + 4
([(0,5),(1,4),(2,3)],6)
=> [3,3] => [1,1,2,1,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 4
([(0,1),(2,5),(3,4),(4,5)],6)
=> [3,3] => [1,1,2,1,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 4
([(1,2),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 4
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> [3,3] => [1,1,2,1,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 4
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 4
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 4
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 4
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 4
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 4
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
=> [3,2,1] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 4
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> [3,3] => [1,1,2,1,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 4
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 4
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
=> [3,2,1] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 4
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 4
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 4
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 4
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 4
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 4
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 4
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> [3,3] => [1,1,2,1,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 4
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,3] => [1,1,2,1,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 4
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
=> [3,2,1] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 4
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
=> [3,3] => [1,1,2,1,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 4
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
=> [3,2,1] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 4
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 4
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 4
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 4
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 4
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 4
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 4
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 4
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 4
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 4
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)
=> [3,2,1] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 4
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 4
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 4
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 4
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 4
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 4
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 4
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> [3,3] => [1,1,2,1,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 4
([(1,6),(2,5),(3,4)],7)
=> [4,3] => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
([(1,2),(3,6),(4,5),(5,6)],7)
=> [4,3] => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
([(0,3),(1,2),(4,6),(5,6)],7)
=> [4,3] => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
([(2,3),(4,5),(4,6),(5,6)],7)
=> [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
([(1,6),(2,5),(3,4),(4,6),(5,6)],7)
=> [4,3] => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)
=> [4,3] => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
([(2,5),(3,4),(3,6),(4,6),(5,6)],7)
=> [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
=> [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
=> [4,3] => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
([(1,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
=> [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
([(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
=> [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
([(0,6),(1,6),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
=> [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
=> [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
=> [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
([(2,5),(2,6),(3,4),(3,6),(4,5)],7)
=> [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
([(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
=> [4,3] => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
=> [4,3] => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
([(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
=> [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
([(1,6),(2,3),(2,5),(3,4),(4,6),(5,6)],7)
=> [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
([(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
=> [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
([(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
=> [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
([(0,6),(1,6),(2,5),(3,4),(3,6),(4,5),(5,6)],7)
=> [4,3] => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
([(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
=> [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6),(5,6)],7)
=> [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
([(0,6),(1,6),(2,3),(2,5),(3,4),(4,6),(5,6)],7)
=> [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
([(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
([(0,6),(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)
=> [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
([(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
=> [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
([(0,6),(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
=> [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
([(0,6),(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
([(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
=> [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
=> [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
([(1,6),(2,5),(3,4),(3,5),(4,6)],7)
=> [4,3] => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
([(1,2),(3,5),(3,6),(4,5),(4,6)],7)
=> [4,3] => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
([(0,6),(1,5),(2,4),(3,4),(5,6)],7)
=> [4,3] => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
([(1,6),(2,6),(3,4),(3,5),(4,5)],7)
=> [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7)
=> [4,3] => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
=> [4,3] => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [4,3] => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6)],7)
=> [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
=> [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
([(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
=> [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
=> [4,3] => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
([(0,1),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
=> [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
([(1,5),(2,5),(3,4),(3,6),(4,6),(5,6)],7)
=> [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
([(0,5),(1,6),(2,3),(2,4),(3,6),(4,6),(5,6)],7)
=> [4,3] => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
([(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
=> [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
([(0,5),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6)],7)
=> [4,2,1] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
Description
The pebbling number of a connected graph.
Matching statistic: St000259
Mp00324: Graphs —chromatic difference sequence⟶ Integer compositions
Mp00172: Integer compositions —rotate back to front⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000259: Graphs ⟶ ℤResult quality: 25% ●values known / values provided: 25%●distinct values known / distinct values provided: 25%
Mp00172: Integer compositions —rotate back to front⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000259: Graphs ⟶ ℤResult quality: 25% ●values known / values provided: 25%●distinct values known / distinct values provided: 25%
Values
([(0,1),(2,3),(2,4),(3,4)],5)
=> [2,2,1] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 - 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> [2,2,1] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 - 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> [2,2,1] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 - 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> [2,2,1] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 - 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [2,2,1] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 - 1
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> [2,2,1] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 - 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> [2,2,1] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 - 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2,1] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 - 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> [2,2,1] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 - 1
([(0,5),(1,4),(2,3)],6)
=> [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,1),(2,5),(3,4),(4,5)],6)
=> [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? = 3 - 1
([(1,2),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? = 3 - 1
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? = 3 - 1
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
=> [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 2 = 3 - 1
([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 2 = 3 - 1
([(1,2),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 2 = 3 - 1
([(0,1),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 2 = 3 - 1
([(0,6),(1,2),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 2 = 3 - 1
([(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 2 = 3 - 1
([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 2 = 3 - 1
([(1,4),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 2 = 3 - 1
([(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 2 = 3 - 1
([(0,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 2 = 3 - 1
([(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 2 = 3 - 1
([(0,6),(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 2 = 3 - 1
([(0,6),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 2 = 3 - 1
([(0,5),(1,2),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 2 = 3 - 1
([(0,1),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 2 = 3 - 1
([(0,2),(1,5),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 2 = 3 - 1
([(0,5),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 2 = 3 - 1
([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 2 = 3 - 1
([(0,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 2 = 3 - 1
([(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 2 = 3 - 1
([(0,1),(0,6),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 2 = 3 - 1
([(0,4),(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 2 = 3 - 1
([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 2 = 3 - 1
([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 2 = 3 - 1
([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 2 = 3 - 1
([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 2 = 3 - 1
([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 2 = 3 - 1
([(0,6),(1,3),(1,5),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 2 = 3 - 1
([(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 2 = 3 - 1
([(0,6),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 2 = 3 - 1
([(0,5),(1,2),(1,4),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 2 = 3 - 1
([(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 2 = 3 - 1
([(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 2 = 3 - 1
Description
The diameter of a connected graph.
This is the greatest distance between any pair of vertices.
Matching statistic: St000260
Mp00324: Graphs —chromatic difference sequence⟶ Integer compositions
Mp00172: Integer compositions —rotate back to front⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000260: Graphs ⟶ ℤResult quality: 25% ●values known / values provided: 25%●distinct values known / distinct values provided: 25%
Mp00172: Integer compositions —rotate back to front⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000260: Graphs ⟶ ℤResult quality: 25% ●values known / values provided: 25%●distinct values known / distinct values provided: 25%
Values
([(0,1),(2,3),(2,4),(3,4)],5)
=> [2,2,1] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 - 2
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> [2,2,1] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 - 2
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> [2,2,1] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 - 2
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> [2,2,1] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 - 2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [2,2,1] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 - 2
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> [2,2,1] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 - 2
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> [2,2,1] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 - 2
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2,1] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 - 2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> [2,2,1] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 - 2
([(0,5),(1,4),(2,3)],6)
=> [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,1),(2,5),(3,4),(4,5)],6)
=> [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? = 3 - 2
([(1,2),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? = 3 - 2
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 2
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 2
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? = 3 - 2
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 2
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 2
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
=> [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1 = 3 - 2
([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1 = 3 - 2
([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1 = 3 - 2
([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1 = 3 - 2
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1 = 3 - 2
([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1 = 3 - 2
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1 = 3 - 2
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1 = 3 - 2
([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1 = 3 - 2
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1 = 3 - 2
([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1 = 3 - 2
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1 = 3 - 2
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1 = 3 - 2
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1 = 3 - 2
([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1 = 3 - 2
([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1 = 3 - 2
([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1 = 3 - 2
([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1 = 3 - 2
([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1 = 3 - 2
([(1,2),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1 = 3 - 2
([(0,1),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1 = 3 - 2
([(0,6),(1,2),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1 = 3 - 2
([(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1 = 3 - 2
([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1 = 3 - 2
([(1,4),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1 = 3 - 2
([(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1 = 3 - 2
([(0,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1 = 3 - 2
([(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1 = 3 - 2
([(0,6),(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1 = 3 - 2
([(0,6),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1 = 3 - 2
([(0,5),(1,2),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1 = 3 - 2
([(0,1),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1 = 3 - 2
([(0,2),(1,5),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1 = 3 - 2
([(0,5),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1 = 3 - 2
([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1 = 3 - 2
([(0,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1 = 3 - 2
([(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1 = 3 - 2
([(0,1),(0,6),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1 = 3 - 2
([(0,4),(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1 = 3 - 2
([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1 = 3 - 2
([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1 = 3 - 2
([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1 = 3 - 2
([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1 = 3 - 2
([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1 = 3 - 2
([(0,6),(1,3),(1,5),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1 = 3 - 2
([(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1 = 3 - 2
([(0,6),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1 = 3 - 2
([(0,5),(1,2),(1,4),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1 = 3 - 2
([(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1 = 3 - 2
([(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1 = 3 - 2
Description
The radius of a connected graph.
This is the minimum eccentricity of any vertex.
Matching statistic: St000772
Mp00324: Graphs —chromatic difference sequence⟶ Integer compositions
Mp00172: Integer compositions —rotate back to front⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000772: Graphs ⟶ ℤResult quality: 25% ●values known / values provided: 25%●distinct values known / distinct values provided: 25%
Mp00172: Integer compositions —rotate back to front⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000772: Graphs ⟶ ℤResult quality: 25% ●values known / values provided: 25%●distinct values known / distinct values provided: 25%
Values
([(0,1),(2,3),(2,4),(3,4)],5)
=> [2,2,1] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 - 2
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> [2,2,1] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 - 2
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> [2,2,1] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 - 2
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> [2,2,1] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 - 2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [2,2,1] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 - 2
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> [2,2,1] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 - 2
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> [2,2,1] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 - 2
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2,1] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 - 2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> [2,2,1] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 - 2
([(0,5),(1,4),(2,3)],6)
=> [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,1),(2,5),(3,4),(4,5)],6)
=> [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? = 3 - 2
([(1,2),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? = 3 - 2
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 2
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 2
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? = 3 - 2
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 2
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 2
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
=> [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? = 3 - 2
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1 = 3 - 2
([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1 = 3 - 2
([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1 = 3 - 2
([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1 = 3 - 2
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1 = 3 - 2
([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1 = 3 - 2
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1 = 3 - 2
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1 = 3 - 2
([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1 = 3 - 2
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1 = 3 - 2
([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1 = 3 - 2
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1 = 3 - 2
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1 = 3 - 2
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1 = 3 - 2
([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1 = 3 - 2
([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1 = 3 - 2
([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1 = 3 - 2
([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1 = 3 - 2
([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1 = 3 - 2
([(1,2),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1 = 3 - 2
([(0,1),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1 = 3 - 2
([(0,6),(1,2),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1 = 3 - 2
([(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1 = 3 - 2
([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1 = 3 - 2
([(1,4),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1 = 3 - 2
([(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1 = 3 - 2
([(0,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1 = 3 - 2
([(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1 = 3 - 2
([(0,6),(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1 = 3 - 2
([(0,6),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1 = 3 - 2
([(0,5),(1,2),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1 = 3 - 2
([(0,1),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1 = 3 - 2
([(0,2),(1,5),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1 = 3 - 2
([(0,5),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1 = 3 - 2
([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1 = 3 - 2
([(0,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1 = 3 - 2
([(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1 = 3 - 2
([(0,1),(0,6),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1 = 3 - 2
([(0,4),(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1 = 3 - 2
([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1 = 3 - 2
([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1 = 3 - 2
([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1 = 3 - 2
([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1 = 3 - 2
([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1 = 3 - 2
([(0,6),(1,3),(1,5),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1 = 3 - 2
([(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1 = 3 - 2
([(0,6),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1 = 3 - 2
([(0,5),(1,2),(1,4),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1 = 3 - 2
([(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1 = 3 - 2
([(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1 = 3 - 2
Description
The multiplicity of the largest distance Laplacian eigenvalue in a connected graph.
The distance Laplacian of a graph is the (symmetric) matrix with row and column sums $0$, which has the negative distances between two vertices as its off-diagonal entries. This statistic is the largest multiplicity of an eigenvalue.
For example, the cycle on four vertices has distance Laplacian
$$
\left(\begin{array}{rrrr}
4 & -1 & -2 & -1 \\
-1 & 4 & -1 & -2 \\
-2 & -1 & 4 & -1 \\
-1 & -2 & -1 & 4
\end{array}\right).
$$
Its eigenvalues are $0,4,4,6$, so the statistic is $1$.
The path on four vertices has eigenvalues $0, 4.7\dots, 6, 9.2\dots$ and therefore also statistic $1$.
The graphs with statistic $n-1$, $n-2$ and $n-3$ have been characterised, see [1].
Matching statistic: St000777
Mp00324: Graphs —chromatic difference sequence⟶ Integer compositions
Mp00172: Integer compositions —rotate back to front⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000777: Graphs ⟶ ℤResult quality: 25% ●values known / values provided: 25%●distinct values known / distinct values provided: 25%
Mp00172: Integer compositions —rotate back to front⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000777: Graphs ⟶ ℤResult quality: 25% ●values known / values provided: 25%●distinct values known / distinct values provided: 25%
Values
([(0,1),(2,3),(2,4),(3,4)],5)
=> [2,2,1] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 + 3
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> [2,2,1] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 + 3
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> [2,2,1] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 + 3
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> [2,2,1] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 + 3
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [2,2,1] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 + 3
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> [2,2,1] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 + 3
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> [2,2,1] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 + 3
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2,1] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 + 3
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> [2,2,1] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 + 3
([(0,5),(1,4),(2,3)],6)
=> [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? = 3 + 3
([(0,1),(2,5),(3,4),(4,5)],6)
=> [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? = 3 + 3
([(1,2),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 3
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? = 3 + 3
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 3
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 3
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 3
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 3
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 3
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 3
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? = 3 + 3
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 3
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 3
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 3
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 3
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 3
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 3
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 3
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 3
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? = 3 + 3
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? = 3 + 3
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 3
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
=> [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? = 3 + 3
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 3
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 3
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 3
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 3
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 3
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 3
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 3
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 3
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 3
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 3
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 3
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 3
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 3
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 3
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 3
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 3
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 3
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? = 3 + 3
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 3 + 3
([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 3 + 3
([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 3 + 3
([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 3 + 3
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 3 + 3
([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 3 + 3
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 3 + 3
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 3 + 3
([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 3 + 3
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 3 + 3
([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 3 + 3
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 3 + 3
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 3 + 3
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 3 + 3
([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 3 + 3
([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 3 + 3
([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 3 + 3
([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,2,1,1] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 3 + 3
([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 3 + 3
([(1,2),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 3 + 3
([(0,1),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 3 + 3
([(0,6),(1,2),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 3 + 3
([(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 3 + 3
([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 3 + 3
([(1,4),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 3 + 3
([(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 3 + 3
([(0,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 3 + 3
([(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 3 + 3
([(0,6),(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 3 + 3
([(0,6),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 3 + 3
([(0,5),(1,2),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 3 + 3
([(0,1),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 3 + 3
([(0,2),(1,5),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 3 + 3
([(0,5),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 3 + 3
([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 3 + 3
([(0,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 3 + 3
([(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 3 + 3
([(0,1),(0,6),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 3 + 3
([(0,4),(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 3 + 3
([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 3 + 3
([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 3 + 3
([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 3 + 3
([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 3 + 3
([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 3 + 3
([(0,6),(1,3),(1,5),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 3 + 3
([(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 3 + 3
([(0,6),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 3 + 3
([(0,5),(1,2),(1,4),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 3 + 3
([(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 3 + 3
([(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,2,1,1] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 3 + 3
Description
The number of distinct eigenvalues of the distance Laplacian of a connected graph.
Matching statistic: St000454
(load all 4 compositions to match this statistic)
(load all 4 compositions to match this statistic)
Mp00324: Graphs —chromatic difference sequence⟶ Integer compositions
Mp00173: Integer compositions —rotate front to back⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000454: Graphs ⟶ ℤResult quality: 16% ●values known / values provided: 16%●distinct values known / distinct values provided: 25%
Mp00173: Integer compositions —rotate front to back⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000454: Graphs ⟶ ℤResult quality: 16% ●values known / values provided: 16%●distinct values known / distinct values provided: 25%
Values
([(0,1),(2,3),(2,4),(3,4)],5)
=> [2,2,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 - 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> [2,2,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 - 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> [2,2,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 - 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> [2,2,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 - 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [2,2,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 - 1
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> [2,2,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 - 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> [2,2,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 - 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 - 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> [2,2,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 - 1
([(0,5),(1,4),(2,3)],6)
=> [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,1),(2,5),(3,4),(4,5)],6)
=> [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? = 3 - 1
([(1,2),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? = 3 - 1
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? = 3 - 1
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
=> [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? = 3 - 1
([(0,3),(1,2),(4,5),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 4 - 1
([(0,1),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 4 - 1
([(0,5),(1,4),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 4 - 1
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 4 - 1
([(0,5),(1,4),(1,6),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 4 - 1
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 4 - 1
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 4 - 1
([(0,6),(1,5),(2,3),(2,4),(3,4),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 4 - 1
([(0,4),(1,3),(2,5),(2,6),(3,5),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 4 - 1
([(0,1),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 4 - 1
([(0,5),(1,2),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 4 - 1
([(0,6),(1,4),(2,3),(2,5),(3,5),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 4 - 1
([(0,5),(1,4),(1,5),(2,3),(2,6),(3,6),(4,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 4 - 1
([(0,4),(1,2),(1,6),(2,5),(3,5),(3,6),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 4 - 1
([(0,5),(1,2),(1,6),(2,6),(3,4),(3,6),(4,5),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 4 - 1
([(0,4),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 4 - 1
([(0,1),(0,5),(1,4),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 4 - 1
([(0,4),(1,3),(2,5),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 4 - 1
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 4 - 1
([(0,5),(1,4),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 4 - 1
([(0,1),(0,6),(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 4 - 1
([(0,3),(1,5),(1,6),(2,4),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 4 - 1
([(0,5),(1,2),(1,6),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 4 - 1
([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 4 - 1
([(0,1),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 4 - 1
([(0,6),(1,2),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 4 - 1
([(0,3),(0,6),(1,2),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 4 - 1
([(0,5),(1,3),(1,6),(2,4),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 4 - 1
([(0,5),(1,4),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 4 - 1
([(0,1),(0,6),(1,4),(2,4),(2,6),(3,5),(3,6),(4,5),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 4 - 1
([(0,4),(1,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 4 - 1
([(0,5),(1,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 4 - 1
([(0,3),(1,5),(1,6),(2,4),(2,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 4 - 1
([(0,4),(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 4 - 1
([(0,6),(1,2),(1,6),(2,5),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 4 - 1
([(0,3),(0,6),(1,2),(1,6),(2,5),(3,5),(4,5),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 4 - 1
([(0,4),(0,6),(1,3),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 4 - 1
([(0,4),(1,5),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 4 - 1
([(0,5),(1,4),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 4 - 1
([(0,1),(0,6),(1,5),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 4 - 1
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 4 - 1
([(0,6),(1,5),(2,3),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 4 - 1
([(0,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,6),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 4 - 1
([(0,2),(1,5),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 4 - 1
([(0,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 4 - 1
([(0,5),(0,6),(1,2),(1,4),(2,3),(3,5),(4,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 4 - 1
([(0,3),(1,4),(1,5),(2,4),(2,6),(3,5),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 4 - 1
([(0,1),(0,3),(1,2),(2,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 4 - 1
([(0,3),(0,4),(1,2),(1,6),(2,5),(3,5),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 4 - 1
([(0,6),(1,2),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 4 - 1
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.
Matching statistic: St000422
(load all 4 compositions to match this statistic)
(load all 4 compositions to match this statistic)
Mp00324: Graphs —chromatic difference sequence⟶ Integer compositions
Mp00173: Integer compositions —rotate front to back⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000422: Graphs ⟶ ℤResult quality: 16% ●values known / values provided: 16%●distinct values known / distinct values provided: 25%
Mp00173: Integer compositions —rotate front to back⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000422: Graphs ⟶ ℤResult quality: 16% ●values known / values provided: 16%●distinct values known / distinct values provided: 25%
Values
([(0,1),(2,3),(2,4),(3,4)],5)
=> [2,2,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 + 2
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> [2,2,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 + 2
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> [2,2,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 + 2
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> [2,2,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 + 2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [2,2,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 + 2
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> [2,2,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 + 2
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> [2,2,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 + 2
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 + 2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> [2,2,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 + 2
([(0,5),(1,4),(2,3)],6)
=> [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? = 3 + 2
([(0,1),(2,5),(3,4),(4,5)],6)
=> [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? = 3 + 2
([(1,2),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 2
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? = 3 + 2
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 2
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 2
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 2
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 2
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 2
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 2
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? = 3 + 2
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 2
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 2
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 2
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 2
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 2
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 2
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 2
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 2
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? = 3 + 2
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? = 3 + 2
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 2
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
=> [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? = 3 + 2
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 2
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 2
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 2
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 2
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 2
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 2
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 2
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 2
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 2
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 2
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 2
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 2
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 2
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 2
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3 + 2
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6)
=> ? = 3 + 2
([(0,3),(1,2),(4,5),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 4 + 2
([(0,1),(2,3),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 4 + 2
([(0,5),(1,4),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 4 + 2
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 4 + 2
([(0,5),(1,4),(1,6),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 4 + 2
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 4 + 2
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 4 + 2
([(0,6),(1,5),(2,3),(2,4),(3,4),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 4 + 2
([(0,4),(1,3),(2,5),(2,6),(3,5),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 4 + 2
([(0,1),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 4 + 2
([(0,5),(1,2),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 4 + 2
([(0,6),(1,4),(2,3),(2,5),(3,5),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 4 + 2
([(0,5),(1,4),(1,5),(2,3),(2,6),(3,6),(4,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 4 + 2
([(0,4),(1,2),(1,6),(2,5),(3,5),(3,6),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 4 + 2
([(0,5),(1,2),(1,6),(2,6),(3,4),(3,6),(4,5),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 4 + 2
([(0,4),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 4 + 2
([(0,1),(0,5),(1,4),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 4 + 2
([(0,4),(1,3),(2,5),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 4 + 2
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 4 + 2
([(0,5),(1,4),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 4 + 2
([(0,1),(0,6),(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 4 + 2
([(0,3),(1,5),(1,6),(2,4),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 4 + 2
([(0,5),(1,2),(1,6),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 4 + 2
([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 4 + 2
([(0,1),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 4 + 2
([(0,6),(1,2),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 4 + 2
([(0,3),(0,6),(1,2),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 4 + 2
([(0,5),(1,3),(1,6),(2,4),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 4 + 2
([(0,5),(1,4),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 4 + 2
([(0,1),(0,6),(1,4),(2,4),(2,6),(3,5),(3,6),(4,5),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 4 + 2
([(0,4),(1,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 4 + 2
([(0,5),(1,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 4 + 2
([(0,3),(1,5),(1,6),(2,4),(2,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 4 + 2
([(0,4),(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 4 + 2
([(0,6),(1,2),(1,6),(2,5),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 4 + 2
([(0,3),(0,6),(1,2),(1,6),(2,5),(3,5),(4,5),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 4 + 2
([(0,4),(0,6),(1,3),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 4 + 2
([(0,4),(1,5),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 4 + 2
([(0,5),(1,4),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 4 + 2
([(0,1),(0,6),(1,5),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 4 + 2
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 4 + 2
([(0,6),(1,5),(2,3),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 4 + 2
([(0,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,6),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 4 + 2
([(0,2),(1,5),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 4 + 2
([(0,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 4 + 2
([(0,5),(0,6),(1,2),(1,4),(2,3),(3,5),(4,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 4 + 2
([(0,3),(1,4),(1,5),(2,4),(2,6),(3,5),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 4 + 2
([(0,1),(0,3),(1,2),(2,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 4 + 2
([(0,3),(0,4),(1,2),(1,6),(2,5),(3,5),(4,6),(5,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 4 + 2
([(0,6),(1,2),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
=> [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 6 = 4 + 2
Description
The energy of a graph, if it is integral.
The energy of a graph is the sum of the absolute values of its eigenvalues. This statistic is only defined for graphs with integral energy. It is known, that the energy is never an odd integer [2]. In fact, it is never the square root of an odd integer [3].
The energy of a graph is the sum of the energies of the connected components of a graph. The energy of the complete graph $K_n$ equals $2n-2$. For this reason, we do not define the energy of the empty graph.
The following 25 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St000329The number of evenly positioned ascents of the Dyck path, with the initial position equal to 1. St001508The degree of the standard monomial associated to a Dyck path relative to the diagonal boundary. St001591The number of graphs with the given composition of multiplicities of Laplacian eigenvalues. St001873For a Nakayama algebra corresponding to a Dyck path, we define the matrix C with entries the Hom-spaces between $e_i J$ and $e_j J$ (the radical of the indecomposable projective modules). St000299The number of nonisomorphic vertex-induced subtrees. St001165Number of simple modules with even projective dimension in the corresponding Nakayama algebra. St000965The sum of the dimension of Ext^i(D(A),A) for i=1,. St001188The number of simple modules $S$ with grade $\inf \{ i \geq 0 | Ext^i(S,A) \neq 0 \}$ at least two in the Nakayama algebra $A$ corresponding to the Dyck path. St001212The number of simple modules in the corresponding Nakayama algebra that have non-zero second Ext-group with the regular module. St001215Let X be the direct sum of all simple modules of the corresponding Nakayama algebra. St001222Number of simple modules in the corresponding LNakayama algebra that have a unique 2-extension with the regular module. St001244The number of simple modules of projective dimension one that are not 1-regular for the Nakayama algebra associated to a Dyck path. St001493The number of simple modules with maximal even projective dimension in the corresponding Nakayama algebra. St001507The sum of projective dimension of simple modules with even projective dimension divided by 2 in the LNakayama algebra corresponding to Dyck paths. St001140Number of indecomposable modules with projective and injective dimension at least two in the corresponding Nakayama algebra. St001578The minimal number of edges to add or remove to make a graph a line graph. St001964The interval resolution global dimension of a poset. St000741The Colin de Verdière graph invariant. St001630The global dimension of the incidence algebra of the lattice over the rational numbers. St001877Number of indecomposable injective modules with projective dimension 2. St001878The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L. St000455The second largest eigenvalue of a graph if it is integral. St001570The minimal number of edges to add to make a graph Hamiltonian. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St001711The number of permutations such that conjugation with a permutation of given cycle type yields the squared permutation.
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