Your data matches 105 different statistics following compositions of up to 3 maps.
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Mp00203: Graphs coneGraphs
St001577: Graphs ⟶ ℤResult quality: 100% values known / values provided: 100%distinct values known / distinct values provided: 100%
Values
([],1)
=> ([(0,1)],2)
=> 0
([],2)
=> ([(0,2),(1,2)],3)
=> 0
([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 0
([],3)
=> ([(0,3),(1,3),(2,3)],4)
=> 0
([(1,2)],3)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> 0
([(0,2),(1,2)],3)
=> ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 0
([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 0
([],4)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> 0
([(2,3)],4)
=> ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 0
([(1,3),(2,3)],4)
=> ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 0
([(0,3),(1,3),(2,3)],4)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 0
([(0,3),(1,2)],4)
=> ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> 0
([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
([(1,2),(1,3),(2,3)],4)
=> ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 0
([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 0
([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> 0
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 0
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 0
([],5)
=> ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 0
([(3,4)],5)
=> ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> 0
([(2,4),(3,4)],5)
=> ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0
([(1,4),(2,4),(3,4)],5)
=> ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0
([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0
([(1,4),(2,3)],5)
=> ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> 0
([(1,4),(2,3),(3,4)],5)
=> ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> 1
([(0,1),(2,4),(3,4)],5)
=> ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0
([(2,3),(2,4),(3,4)],5)
=> ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0
([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> 1
([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0
([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> 0
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> 0
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0
([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> 1
([(0,1),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> 2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(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)
=> 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(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)
=> 0
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(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)
=> 0
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(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)
=> 0
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> ([(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)
=> 0
Description
The minimal number of edges to add or remove to make a graph a cograph. A cograph is a graph that can be obtained from the one vertex graph by complementation and disjoint union.
Matching statistic: St001353
Mp00203: Graphs coneGraphs
Mp00203: Graphs coneGraphs
St001353: Graphs ⟶ ℤResult quality: 67% values known / values provided: 77%distinct values known / distinct values provided: 67%
Values
([],1)
=> ([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 0
([],2)
=> ([(0,2),(1,2)],3)
=> ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 0
([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 0
([],3)
=> ([(0,3),(1,3),(2,3)],4)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 0
([(1,2)],3)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 0
([(0,2),(1,2)],3)
=> ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 0
([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 0
([],4)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0
([(2,3)],4)
=> ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0
([(1,3),(2,3)],4)
=> ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0
([(0,3),(1,3),(2,3)],4)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0
([(0,3),(1,2)],4)
=> ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 0
([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(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)
=> 1
([(1,2),(1,3),(2,3)],4)
=> ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(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)
=> 0
([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(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)
=> 0
([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> ([(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)
=> 0
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(0,3),(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)
=> 0
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(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)
=> 0
([],5)
=> ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 0
([(3,4)],5)
=> ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 0
([(2,4),(3,4)],5)
=> ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 0
([(1,4),(2,4),(3,4)],5)
=> ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 0
([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 0
([(1,4),(2,3)],5)
=> ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(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)
=> 0
([(1,4),(2,3),(3,4)],5)
=> ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1
([(0,1),(2,4),(3,4)],5)
=> ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 0
([(2,3),(2,4),(3,4)],5)
=> ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(0,6),(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)
=> 0
([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1
([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(0,6),(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)
=> 0
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(0,6),(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)
=> 0
([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 0
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(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)
=> 0
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(0,6),(1,3),(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)
=> 1
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(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)
=> 0
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 0
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(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)
=> 0
([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1
([(0,1),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,5),(0,6),(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)
=> 0
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 0
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,4),(0,5),(0,6),(1,3),(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)
=> ? = 1
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(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)
=> ([(0,3),(0,4),(0,5),(0,6),(1,2),(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)
=> ? = 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(0,6),(1,2),(1,3),(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)
=> ? = 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(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)
=> ? = 0
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(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)
=> ([(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)
=> ? = 0
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(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)
=> ([(0,3),(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)
=> ? = 0
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(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)
=> ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 0
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> ([(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)
=> ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 0
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(0,3),(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)
=> ([(0,2),(0,3),(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)
=> ? = 0
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(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)
=> ([(0,1),(0,2),(0,3),(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)
=> ? = 0
([],0)
=> ([],1)
=> ([(0,1)],2)
=> 0
Description
The number of prime nodes in the modular decomposition of a graph.
Mp00247: Graphs de-duplicateGraphs
Mp00157: Graphs connected complementGraphs
Mp00111: Graphs complementGraphs
St000455: Graphs ⟶ ℤResult quality: 45% values known / values provided: 45%distinct values known / distinct values provided: 67%
Values
([],1)
=> ([],1)
=> ([],1)
=> ([],1)
=> ? = 0
([],2)
=> ([],1)
=> ([],1)
=> ([],1)
=> ? = 0
([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> ? = 0
([],3)
=> ([],1)
=> ([],1)
=> ([],1)
=> ? = 0
([(1,2)],3)
=> ([(1,2)],3)
=> ([(1,2)],3)
=> ([(0,2),(1,2)],3)
=> 0
([(0,2),(1,2)],3)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> ? = 0
([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? = 0
([],4)
=> ([],1)
=> ([],1)
=> ([],1)
=> ? = 0
([(2,3)],4)
=> ([(1,2)],3)
=> ([(1,2)],3)
=> ([(0,2),(1,2)],3)
=> 0
([(1,3),(2,3)],4)
=> ([(1,2)],3)
=> ([(1,2)],3)
=> ([(0,2),(1,2)],3)
=> 0
([(0,3),(1,3),(2,3)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> ? = 0
([(0,3),(1,2)],4)
=> ([(0,3),(1,2)],4)
=> ([(0,3),(1,2)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> 0
([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> ? = 1
([(1,2),(1,3),(2,3)],4)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,3),(1,3),(2,3)],4)
=> 0
([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(1,3),(2,3)],4)
=> 0
([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> ? = 0
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? = 0
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([],4)
=> ? = 0
([],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> ? = 0
([(3,4)],5)
=> ([(1,2)],3)
=> ([(1,2)],3)
=> ([(0,2),(1,2)],3)
=> 0
([(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ([(1,2)],3)
=> ([(0,2),(1,2)],3)
=> 0
([(1,4),(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ([(1,2)],3)
=> ([(0,2),(1,2)],3)
=> 0
([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> ? = 0
([(1,4),(2,3)],5)
=> ([(1,4),(2,3)],5)
=> ([(1,4),(2,3)],5)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> 0
([(1,4),(2,3),(3,4)],5)
=> ([(1,4),(2,3),(3,4)],5)
=> ([(1,4),(2,3),(3,4)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 1
([(0,1),(2,4),(3,4)],5)
=> ([(0,3),(1,2)],4)
=> ([(0,3),(1,2)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> 0
([(2,3),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,3),(1,3),(2,3)],4)
=> 0
([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> ? = 1
([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(1,3),(2,3)],4)
=> 0
([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(1,2)],3)
=> ([(1,2)],3)
=> ([(0,2),(1,2)],3)
=> 0
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> ? = 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,3),(1,3),(2,3)],4)
=> 0
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ? = 1
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(1,3),(2,3)],4)
=> 0
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> ? = 0
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? = 0
([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> 1
([(0,1),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> 0
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(1,3),(1,4),(2,3),(2,4)],5)
=> 0
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ? = 2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ? = 1
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,4),(2,3),(3,4)],5)
=> ? = 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> ? = 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> 0
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,4),(2,4),(3,4)],5)
=> 0
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(2,4),(3,4)],5)
=> 0
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(1,3),(2,3)],4)
=> 0
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? = 0
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([],4)
=> ? = 0
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],5)
=> ? = 0
([],0)
=> ([],0)
=> ([],0)
=> ([],0)
=> ? = 0
Description
The second largest eigenvalue of a graph if it is integral. This statistic is undefined if the second largest eigenvalue of the graph is not integral. Chapter 4 of [1] provides lots of context.
Mp00251: Graphs clique sizesInteger partitions
Mp00179: Integer partitions to skew partitionSkew partitions
St001435: Skew partitions ⟶ ℤResult quality: 33% values known / values provided: 40%distinct values known / distinct values provided: 33%
Values
([],1)
=> [1]
=> [[1],[]]
=> 0
([],2)
=> [1,1]
=> [[1,1],[]]
=> 0
([(0,1)],2)
=> [2]
=> [[2],[]]
=> 0
([],3)
=> [1,1,1]
=> [[1,1,1],[]]
=> 0
([(1,2)],3)
=> [2,1]
=> [[2,1],[]]
=> 0
([(0,2),(1,2)],3)
=> [2,2]
=> [[2,2],[]]
=> 0
([(0,1),(0,2),(1,2)],3)
=> [3]
=> [[3],[]]
=> 0
([],4)
=> [1,1,1,1]
=> [[1,1,1,1],[]]
=> 0
([(2,3)],4)
=> [2,1,1]
=> [[2,1,1],[]]
=> 0
([(1,3),(2,3)],4)
=> [2,2,1]
=> [[2,2,1],[]]
=> 0
([(0,3),(1,3),(2,3)],4)
=> [2,2,2]
=> [[2,2,2],[]]
=> ? = 0
([(0,3),(1,2)],4)
=> [2,2]
=> [[2,2],[]]
=> 0
([(0,3),(1,2),(2,3)],4)
=> [2,2,2]
=> [[2,2,2],[]]
=> ? = 1
([(1,2),(1,3),(2,3)],4)
=> [3,1]
=> [[3,1],[]]
=> 0
([(0,3),(1,2),(1,3),(2,3)],4)
=> [3,2]
=> [[3,2],[]]
=> 0
([(0,2),(0,3),(1,2),(1,3)],4)
=> [2,2,2,2]
=> [[2,2,2,2],[]]
=> ? = 0
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [3,3]
=> [[3,3],[]]
=> ? = 0
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> [[4],[]]
=> 0
([],5)
=> [1,1,1,1,1]
=> [[1,1,1,1,1],[]]
=> 0
([(3,4)],5)
=> [2,1,1,1]
=> [[2,1,1,1],[]]
=> 0
([(2,4),(3,4)],5)
=> [2,2,1,1]
=> [[2,2,1,1],[]]
=> ? = 0
([(1,4),(2,4),(3,4)],5)
=> [2,2,2,1]
=> [[2,2,2,1],[]]
=> ? = 0
([(0,4),(1,4),(2,4),(3,4)],5)
=> [2,2,2,2]
=> [[2,2,2,2],[]]
=> ? = 0
([(1,4),(2,3)],5)
=> [2,2,1]
=> [[2,2,1],[]]
=> 0
([(1,4),(2,3),(3,4)],5)
=> [2,2,2,1]
=> [[2,2,2,1],[]]
=> ? = 1
([(0,1),(2,4),(3,4)],5)
=> [2,2,2]
=> [[2,2,2],[]]
=> ? = 0
([(2,3),(2,4),(3,4)],5)
=> [3,1,1]
=> [[3,1,1],[]]
=> 0
([(0,4),(1,4),(2,3),(3,4)],5)
=> [2,2,2,2]
=> [[2,2,2,2],[]]
=> ? = 1
([(1,4),(2,3),(2,4),(3,4)],5)
=> [3,2,1]
=> [[3,2,1],[]]
=> ? = 0
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> [3,2,2]
=> [[3,2,2],[]]
=> ? = 0
([(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2,2,2,1]
=> [[2,2,2,2,1],[]]
=> ? = 0
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> [2,2,2,2,2]
=> [[2,2,2,2,2],[]]
=> ? = 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [3,3,1]
=> [[3,3,1],[]]
=> ? = 0
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [3,2,2]
=> [[3,2,2],[]]
=> ? = 1
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [3,3,2]
=> [[3,3,2],[]]
=> ? = 0
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2,2,2,2,2]
=> [[2,2,2,2,2,2],[]]
=> ? = 0
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [3,3,3]
=> [[3,3,3],[]]
=> ? = 0
([(0,4),(1,3),(2,3),(2,4)],5)
=> [2,2,2,2]
=> [[2,2,2,2],[]]
=> ? = 1
([(0,1),(2,3),(2,4),(3,4)],5)
=> [3,2]
=> [[3,2],[]]
=> 0
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> [3,2,2]
=> [[3,2,2],[]]
=> ? = 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> [3,3]
=> [[3,3],[]]
=> ? = 0
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> [2,2,2,2,2]
=> [[2,2,2,2,2],[]]
=> ? = 2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [3,2,2,2]
=> [[3,2,2,2],[]]
=> ? = 1
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> [3,3,3]
=> [[3,3,3],[]]
=> ? = 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> [3,3,2]
=> [[3,3,2],[]]
=> ? = 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [4,1]
=> [[4,1],[]]
=> 0
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [4,2]
=> [[4,2],[]]
=> ? = 0
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [4,3]
=> [[4,3],[]]
=> ? = 0
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> [3,3,2,2]
=> [[3,3,2,2],[]]
=> ? = 0
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> [3,3,3,3]
=> [[3,3,3,3],[]]
=> ? = 0
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [4,4]
=> [[4,4],[]]
=> ? = 0
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> [[5],[]]
=> 0
([],0)
=> ?
=> ?
=> ? = 0
Description
The number of missing boxes in the first row.
Mp00251: Graphs clique sizesInteger partitions
Mp00179: Integer partitions to skew partitionSkew partitions
St001438: Skew partitions ⟶ ℤResult quality: 33% values known / values provided: 40%distinct values known / distinct values provided: 33%
Values
([],1)
=> [1]
=> [[1],[]]
=> 0
([],2)
=> [1,1]
=> [[1,1],[]]
=> 0
([(0,1)],2)
=> [2]
=> [[2],[]]
=> 0
([],3)
=> [1,1,1]
=> [[1,1,1],[]]
=> 0
([(1,2)],3)
=> [2,1]
=> [[2,1],[]]
=> 0
([(0,2),(1,2)],3)
=> [2,2]
=> [[2,2],[]]
=> 0
([(0,1),(0,2),(1,2)],3)
=> [3]
=> [[3],[]]
=> 0
([],4)
=> [1,1,1,1]
=> [[1,1,1,1],[]]
=> 0
([(2,3)],4)
=> [2,1,1]
=> [[2,1,1],[]]
=> 0
([(1,3),(2,3)],4)
=> [2,2,1]
=> [[2,2,1],[]]
=> 0
([(0,3),(1,3),(2,3)],4)
=> [2,2,2]
=> [[2,2,2],[]]
=> ? = 0
([(0,3),(1,2)],4)
=> [2,2]
=> [[2,2],[]]
=> 0
([(0,3),(1,2),(2,3)],4)
=> [2,2,2]
=> [[2,2,2],[]]
=> ? = 1
([(1,2),(1,3),(2,3)],4)
=> [3,1]
=> [[3,1],[]]
=> 0
([(0,3),(1,2),(1,3),(2,3)],4)
=> [3,2]
=> [[3,2],[]]
=> 0
([(0,2),(0,3),(1,2),(1,3)],4)
=> [2,2,2,2]
=> [[2,2,2,2],[]]
=> ? = 0
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [3,3]
=> [[3,3],[]]
=> ? = 0
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> [[4],[]]
=> 0
([],5)
=> [1,1,1,1,1]
=> [[1,1,1,1,1],[]]
=> 0
([(3,4)],5)
=> [2,1,1,1]
=> [[2,1,1,1],[]]
=> 0
([(2,4),(3,4)],5)
=> [2,2,1,1]
=> [[2,2,1,1],[]]
=> ? = 0
([(1,4),(2,4),(3,4)],5)
=> [2,2,2,1]
=> [[2,2,2,1],[]]
=> ? = 0
([(0,4),(1,4),(2,4),(3,4)],5)
=> [2,2,2,2]
=> [[2,2,2,2],[]]
=> ? = 0
([(1,4),(2,3)],5)
=> [2,2,1]
=> [[2,2,1],[]]
=> 0
([(1,4),(2,3),(3,4)],5)
=> [2,2,2,1]
=> [[2,2,2,1],[]]
=> ? = 1
([(0,1),(2,4),(3,4)],5)
=> [2,2,2]
=> [[2,2,2],[]]
=> ? = 0
([(2,3),(2,4),(3,4)],5)
=> [3,1,1]
=> [[3,1,1],[]]
=> 0
([(0,4),(1,4),(2,3),(3,4)],5)
=> [2,2,2,2]
=> [[2,2,2,2],[]]
=> ? = 1
([(1,4),(2,3),(2,4),(3,4)],5)
=> [3,2,1]
=> [[3,2,1],[]]
=> ? = 0
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> [3,2,2]
=> [[3,2,2],[]]
=> ? = 0
([(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2,2,2,1]
=> [[2,2,2,2,1],[]]
=> ? = 0
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> [2,2,2,2,2]
=> [[2,2,2,2,2],[]]
=> ? = 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [3,3,1]
=> [[3,3,1],[]]
=> ? = 0
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [3,2,2]
=> [[3,2,2],[]]
=> ? = 1
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [3,3,2]
=> [[3,3,2],[]]
=> ? = 0
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2,2,2,2,2]
=> [[2,2,2,2,2,2],[]]
=> ? = 0
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [3,3,3]
=> [[3,3,3],[]]
=> ? = 0
([(0,4),(1,3),(2,3),(2,4)],5)
=> [2,2,2,2]
=> [[2,2,2,2],[]]
=> ? = 1
([(0,1),(2,3),(2,4),(3,4)],5)
=> [3,2]
=> [[3,2],[]]
=> 0
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> [3,2,2]
=> [[3,2,2],[]]
=> ? = 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> [3,3]
=> [[3,3],[]]
=> ? = 0
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> [2,2,2,2,2]
=> [[2,2,2,2,2],[]]
=> ? = 2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [3,2,2,2]
=> [[3,2,2,2],[]]
=> ? = 1
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> [3,3,3]
=> [[3,3,3],[]]
=> ? = 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> [3,3,2]
=> [[3,3,2],[]]
=> ? = 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [4,1]
=> [[4,1],[]]
=> 0
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [4,2]
=> [[4,2],[]]
=> ? = 0
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [4,3]
=> [[4,3],[]]
=> ? = 0
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> [3,3,2,2]
=> [[3,3,2,2],[]]
=> ? = 0
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> [3,3,3,3]
=> [[3,3,3,3],[]]
=> ? = 0
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [4,4]
=> [[4,4],[]]
=> ? = 0
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> [[5],[]]
=> 0
([],0)
=> ?
=> ?
=> ? = 0
Description
The number of missing boxes of a skew partition.
Mp00251: Graphs clique sizesInteger partitions
Mp00179: Integer partitions to skew partitionSkew partitions
St001487: Skew partitions ⟶ ℤResult quality: 33% values known / values provided: 40%distinct values known / distinct values provided: 33%
Values
([],1)
=> [1]
=> [[1],[]]
=> 1 = 0 + 1
([],2)
=> [1,1]
=> [[1,1],[]]
=> 1 = 0 + 1
([(0,1)],2)
=> [2]
=> [[2],[]]
=> 1 = 0 + 1
([],3)
=> [1,1,1]
=> [[1,1,1],[]]
=> 1 = 0 + 1
([(1,2)],3)
=> [2,1]
=> [[2,1],[]]
=> 1 = 0 + 1
([(0,2),(1,2)],3)
=> [2,2]
=> [[2,2],[]]
=> 1 = 0 + 1
([(0,1),(0,2),(1,2)],3)
=> [3]
=> [[3],[]]
=> 1 = 0 + 1
([],4)
=> [1,1,1,1]
=> [[1,1,1,1],[]]
=> 1 = 0 + 1
([(2,3)],4)
=> [2,1,1]
=> [[2,1,1],[]]
=> 1 = 0 + 1
([(1,3),(2,3)],4)
=> [2,2,1]
=> [[2,2,1],[]]
=> 1 = 0 + 1
([(0,3),(1,3),(2,3)],4)
=> [2,2,2]
=> [[2,2,2],[]]
=> ? = 0 + 1
([(0,3),(1,2)],4)
=> [2,2]
=> [[2,2],[]]
=> 1 = 0 + 1
([(0,3),(1,2),(2,3)],4)
=> [2,2,2]
=> [[2,2,2],[]]
=> ? = 1 + 1
([(1,2),(1,3),(2,3)],4)
=> [3,1]
=> [[3,1],[]]
=> 1 = 0 + 1
([(0,3),(1,2),(1,3),(2,3)],4)
=> [3,2]
=> [[3,2],[]]
=> 1 = 0 + 1
([(0,2),(0,3),(1,2),(1,3)],4)
=> [2,2,2,2]
=> [[2,2,2,2],[]]
=> ? = 0 + 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [3,3]
=> [[3,3],[]]
=> ? = 0 + 1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> [[4],[]]
=> 1 = 0 + 1
([],5)
=> [1,1,1,1,1]
=> [[1,1,1,1,1],[]]
=> 1 = 0 + 1
([(3,4)],5)
=> [2,1,1,1]
=> [[2,1,1,1],[]]
=> 1 = 0 + 1
([(2,4),(3,4)],5)
=> [2,2,1,1]
=> [[2,2,1,1],[]]
=> ? = 0 + 1
([(1,4),(2,4),(3,4)],5)
=> [2,2,2,1]
=> [[2,2,2,1],[]]
=> ? = 0 + 1
([(0,4),(1,4),(2,4),(3,4)],5)
=> [2,2,2,2]
=> [[2,2,2,2],[]]
=> ? = 0 + 1
([(1,4),(2,3)],5)
=> [2,2,1]
=> [[2,2,1],[]]
=> 1 = 0 + 1
([(1,4),(2,3),(3,4)],5)
=> [2,2,2,1]
=> [[2,2,2,1],[]]
=> ? = 1 + 1
([(0,1),(2,4),(3,4)],5)
=> [2,2,2]
=> [[2,2,2],[]]
=> ? = 0 + 1
([(2,3),(2,4),(3,4)],5)
=> [3,1,1]
=> [[3,1,1],[]]
=> 1 = 0 + 1
([(0,4),(1,4),(2,3),(3,4)],5)
=> [2,2,2,2]
=> [[2,2,2,2],[]]
=> ? = 1 + 1
([(1,4),(2,3),(2,4),(3,4)],5)
=> [3,2,1]
=> [[3,2,1],[]]
=> ? = 0 + 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> [3,2,2]
=> [[3,2,2],[]]
=> ? = 0 + 1
([(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2,2,2,1]
=> [[2,2,2,2,1],[]]
=> ? = 0 + 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> [2,2,2,2,2]
=> [[2,2,2,2,2],[]]
=> ? = 1 + 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [3,3,1]
=> [[3,3,1],[]]
=> ? = 0 + 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [3,2,2]
=> [[3,2,2],[]]
=> ? = 1 + 1
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [3,3,2]
=> [[3,3,2],[]]
=> ? = 0 + 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2,2,2,2,2]
=> [[2,2,2,2,2,2],[]]
=> ? = 0 + 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [3,3,3]
=> [[3,3,3],[]]
=> ? = 0 + 1
([(0,4),(1,3),(2,3),(2,4)],5)
=> [2,2,2,2]
=> [[2,2,2,2],[]]
=> ? = 1 + 1
([(0,1),(2,3),(2,4),(3,4)],5)
=> [3,2]
=> [[3,2],[]]
=> 1 = 0 + 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> [3,2,2]
=> [[3,2,2],[]]
=> ? = 1 + 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> [3,3]
=> [[3,3],[]]
=> ? = 0 + 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> [2,2,2,2,2]
=> [[2,2,2,2,2],[]]
=> ? = 2 + 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [3,2,2,2]
=> [[3,2,2,2],[]]
=> ? = 1 + 1
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> [3,3,3]
=> [[3,3,3],[]]
=> ? = 1 + 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> [3,3,2]
=> [[3,3,2],[]]
=> ? = 1 + 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [4,1]
=> [[4,1],[]]
=> 1 = 0 + 1
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [4,2]
=> [[4,2],[]]
=> ? = 0 + 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [4,3]
=> [[4,3],[]]
=> ? = 0 + 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> [3,3,2,2]
=> [[3,3,2,2],[]]
=> ? = 0 + 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> [3,3,3,3]
=> [[3,3,3,3],[]]
=> ? = 0 + 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [4,4]
=> [[4,4],[]]
=> ? = 0 + 1
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> [[5],[]]
=> 1 = 0 + 1
([],0)
=> ?
=> ?
=> ? = 0 + 1
Description
The number of inner corners of a skew partition.
Mp00251: Graphs clique sizesInteger partitions
Mp00179: Integer partitions to skew partitionSkew partitions
St001490: Skew partitions ⟶ ℤResult quality: 33% values known / values provided: 40%distinct values known / distinct values provided: 33%
Values
([],1)
=> [1]
=> [[1],[]]
=> 1 = 0 + 1
([],2)
=> [1,1]
=> [[1,1],[]]
=> 1 = 0 + 1
([(0,1)],2)
=> [2]
=> [[2],[]]
=> 1 = 0 + 1
([],3)
=> [1,1,1]
=> [[1,1,1],[]]
=> 1 = 0 + 1
([(1,2)],3)
=> [2,1]
=> [[2,1],[]]
=> 1 = 0 + 1
([(0,2),(1,2)],3)
=> [2,2]
=> [[2,2],[]]
=> 1 = 0 + 1
([(0,1),(0,2),(1,2)],3)
=> [3]
=> [[3],[]]
=> 1 = 0 + 1
([],4)
=> [1,1,1,1]
=> [[1,1,1,1],[]]
=> 1 = 0 + 1
([(2,3)],4)
=> [2,1,1]
=> [[2,1,1],[]]
=> 1 = 0 + 1
([(1,3),(2,3)],4)
=> [2,2,1]
=> [[2,2,1],[]]
=> 1 = 0 + 1
([(0,3),(1,3),(2,3)],4)
=> [2,2,2]
=> [[2,2,2],[]]
=> ? = 0 + 1
([(0,3),(1,2)],4)
=> [2,2]
=> [[2,2],[]]
=> 1 = 0 + 1
([(0,3),(1,2),(2,3)],4)
=> [2,2,2]
=> [[2,2,2],[]]
=> ? = 1 + 1
([(1,2),(1,3),(2,3)],4)
=> [3,1]
=> [[3,1],[]]
=> 1 = 0 + 1
([(0,3),(1,2),(1,3),(2,3)],4)
=> [3,2]
=> [[3,2],[]]
=> 1 = 0 + 1
([(0,2),(0,3),(1,2),(1,3)],4)
=> [2,2,2,2]
=> [[2,2,2,2],[]]
=> ? = 0 + 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [3,3]
=> [[3,3],[]]
=> ? = 0 + 1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> [[4],[]]
=> 1 = 0 + 1
([],5)
=> [1,1,1,1,1]
=> [[1,1,1,1,1],[]]
=> 1 = 0 + 1
([(3,4)],5)
=> [2,1,1,1]
=> [[2,1,1,1],[]]
=> 1 = 0 + 1
([(2,4),(3,4)],5)
=> [2,2,1,1]
=> [[2,2,1,1],[]]
=> ? = 0 + 1
([(1,4),(2,4),(3,4)],5)
=> [2,2,2,1]
=> [[2,2,2,1],[]]
=> ? = 0 + 1
([(0,4),(1,4),(2,4),(3,4)],5)
=> [2,2,2,2]
=> [[2,2,2,2],[]]
=> ? = 0 + 1
([(1,4),(2,3)],5)
=> [2,2,1]
=> [[2,2,1],[]]
=> 1 = 0 + 1
([(1,4),(2,3),(3,4)],5)
=> [2,2,2,1]
=> [[2,2,2,1],[]]
=> ? = 1 + 1
([(0,1),(2,4),(3,4)],5)
=> [2,2,2]
=> [[2,2,2],[]]
=> ? = 0 + 1
([(2,3),(2,4),(3,4)],5)
=> [3,1,1]
=> [[3,1,1],[]]
=> 1 = 0 + 1
([(0,4),(1,4),(2,3),(3,4)],5)
=> [2,2,2,2]
=> [[2,2,2,2],[]]
=> ? = 1 + 1
([(1,4),(2,3),(2,4),(3,4)],5)
=> [3,2,1]
=> [[3,2,1],[]]
=> ? = 0 + 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> [3,2,2]
=> [[3,2,2],[]]
=> ? = 0 + 1
([(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2,2,2,1]
=> [[2,2,2,2,1],[]]
=> ? = 0 + 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> [2,2,2,2,2]
=> [[2,2,2,2,2],[]]
=> ? = 1 + 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [3,3,1]
=> [[3,3,1],[]]
=> ? = 0 + 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [3,2,2]
=> [[3,2,2],[]]
=> ? = 1 + 1
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [3,3,2]
=> [[3,3,2],[]]
=> ? = 0 + 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2,2,2,2,2]
=> [[2,2,2,2,2,2],[]]
=> ? = 0 + 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [3,3,3]
=> [[3,3,3],[]]
=> ? = 0 + 1
([(0,4),(1,3),(2,3),(2,4)],5)
=> [2,2,2,2]
=> [[2,2,2,2],[]]
=> ? = 1 + 1
([(0,1),(2,3),(2,4),(3,4)],5)
=> [3,2]
=> [[3,2],[]]
=> 1 = 0 + 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> [3,2,2]
=> [[3,2,2],[]]
=> ? = 1 + 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> [3,3]
=> [[3,3],[]]
=> ? = 0 + 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> [2,2,2,2,2]
=> [[2,2,2,2,2],[]]
=> ? = 2 + 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> [3,2,2,2]
=> [[3,2,2,2],[]]
=> ? = 1 + 1
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> [3,3,3]
=> [[3,3,3],[]]
=> ? = 1 + 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> [3,3,2]
=> [[3,3,2],[]]
=> ? = 1 + 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [4,1]
=> [[4,1],[]]
=> 1 = 0 + 1
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [4,2]
=> [[4,2],[]]
=> ? = 0 + 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [4,3]
=> [[4,3],[]]
=> ? = 0 + 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> [3,3,2,2]
=> [[3,3,2,2],[]]
=> ? = 0 + 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> [3,3,3,3]
=> [[3,3,3,3],[]]
=> ? = 0 + 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [4,4]
=> [[4,4],[]]
=> ? = 0 + 1
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> [[5],[]]
=> 1 = 0 + 1
([],0)
=> ?
=> ?
=> ? = 0 + 1
Description
The number of connected components of a skew partition.
Mp00250: Graphs clique graphGraphs
Mp00154: Graphs coreGraphs
Mp00111: Graphs complementGraphs
St000259: Graphs ⟶ ℤResult quality: 36% values known / values provided: 36%distinct values known / distinct values provided: 67%
Values
([],1)
=> ([],1)
=> ([],1)
=> ([],1)
=> 0
([],2)
=> ([],2)
=> ([],1)
=> ([],1)
=> 0
([(0,1)],2)
=> ([],1)
=> ([],1)
=> ([],1)
=> 0
([],3)
=> ([],3)
=> ([],1)
=> ([],1)
=> 0
([(1,2)],3)
=> ([],2)
=> ([],1)
=> ([],1)
=> 0
([(0,2),(1,2)],3)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> ? = 0
([(0,1),(0,2),(1,2)],3)
=> ([],1)
=> ([],1)
=> ([],1)
=> 0
([],4)
=> ([],4)
=> ([],1)
=> ([],1)
=> 0
([(2,3)],4)
=> ([],3)
=> ([],1)
=> ([],1)
=> 0
([(1,3),(2,3)],4)
=> ([(1,2)],3)
=> ([(0,1)],2)
=> ([],2)
=> ? = 0
([(0,3),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? = 0
([(0,3),(1,2)],4)
=> ([],2)
=> ([],1)
=> ([],1)
=> 0
([(0,3),(1,2),(2,3)],4)
=> ([(0,2),(1,2)],3)
=> ([(0,1)],2)
=> ([],2)
=> ? = 1
([(1,2),(1,3),(2,3)],4)
=> ([],2)
=> ([],1)
=> ([],1)
=> 0
([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> ? = 0
([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ([],2)
=> ? = 0
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> ? = 0
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([],1)
=> ([],1)
=> ([],1)
=> 0
([],5)
=> ([],5)
=> ([],1)
=> ([],1)
=> 0
([(3,4)],5)
=> ([],4)
=> ([],1)
=> ([],1)
=> 0
([(2,4),(3,4)],5)
=> ([(2,3)],4)
=> ([(0,1)],2)
=> ([],2)
=> ? = 0
([(1,4),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? = 0
([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([],4)
=> ? = 0
([(1,4),(2,3)],5)
=> ([],3)
=> ([],1)
=> ([],1)
=> 0
([(1,4),(2,3),(3,4)],5)
=> ([(1,3),(2,3)],4)
=> ([(0,1)],2)
=> ([],2)
=> ? = 1
([(0,1),(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ([(0,1)],2)
=> ([],2)
=> ? = 0
([(2,3),(2,4),(3,4)],5)
=> ([],3)
=> ([],1)
=> ([],1)
=> 0
([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? = 1
([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ([(0,1)],2)
=> ([],2)
=> ? = 0
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? = 0
([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ([],2)
=> ? = 0
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? = 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ([(0,1)],2)
=> ([],2)
=> ? = 0
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> ([(0,1)],2)
=> ([],2)
=> ? = 1
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? = 0
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? = 0
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? = 0
([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,1)],2)
=> ([],2)
=> ? = 1
([(0,1),(2,3),(2,4),(3,4)],5)
=> ([],2)
=> ([],1)
=> ([],1)
=> 0
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> ([(0,1)],2)
=> ([],2)
=> ? = 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> ? = 0
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> 2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ([],2)
=> ? = 1
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? = 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> ([(0,1)],2)
=> ([],2)
=> ? = 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],2)
=> ([],1)
=> ([],1)
=> 0
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> ? = 0
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> ? = 0
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ([],2)
=> ? = 0
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([],4)
=> ? = 0
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> ? = 0
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 0
([],0)
=> ?
=> ?
=> ?
=> ? = 0
Description
The diameter of a connected graph. This is the greatest distance between any pair of vertices.
Mp00250: Graphs clique graphGraphs
Mp00154: Graphs coreGraphs
Mp00111: Graphs complementGraphs
St000260: Graphs ⟶ ℤResult quality: 36% values known / values provided: 36%distinct values known / distinct values provided: 67%
Values
([],1)
=> ([],1)
=> ([],1)
=> ([],1)
=> 0
([],2)
=> ([],2)
=> ([],1)
=> ([],1)
=> 0
([(0,1)],2)
=> ([],1)
=> ([],1)
=> ([],1)
=> 0
([],3)
=> ([],3)
=> ([],1)
=> ([],1)
=> 0
([(1,2)],3)
=> ([],2)
=> ([],1)
=> ([],1)
=> 0
([(0,2),(1,2)],3)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> ? = 0
([(0,1),(0,2),(1,2)],3)
=> ([],1)
=> ([],1)
=> ([],1)
=> 0
([],4)
=> ([],4)
=> ([],1)
=> ([],1)
=> 0
([(2,3)],4)
=> ([],3)
=> ([],1)
=> ([],1)
=> 0
([(1,3),(2,3)],4)
=> ([(1,2)],3)
=> ([(0,1)],2)
=> ([],2)
=> ? = 0
([(0,3),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? = 0
([(0,3),(1,2)],4)
=> ([],2)
=> ([],1)
=> ([],1)
=> 0
([(0,3),(1,2),(2,3)],4)
=> ([(0,2),(1,2)],3)
=> ([(0,1)],2)
=> ([],2)
=> ? = 1
([(1,2),(1,3),(2,3)],4)
=> ([],2)
=> ([],1)
=> ([],1)
=> 0
([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> ? = 0
([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ([],2)
=> ? = 0
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> ? = 0
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([],1)
=> ([],1)
=> ([],1)
=> 0
([],5)
=> ([],5)
=> ([],1)
=> ([],1)
=> 0
([(3,4)],5)
=> ([],4)
=> ([],1)
=> ([],1)
=> 0
([(2,4),(3,4)],5)
=> ([(2,3)],4)
=> ([(0,1)],2)
=> ([],2)
=> ? = 0
([(1,4),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? = 0
([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([],4)
=> ? = 0
([(1,4),(2,3)],5)
=> ([],3)
=> ([],1)
=> ([],1)
=> 0
([(1,4),(2,3),(3,4)],5)
=> ([(1,3),(2,3)],4)
=> ([(0,1)],2)
=> ([],2)
=> ? = 1
([(0,1),(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ([(0,1)],2)
=> ([],2)
=> ? = 0
([(2,3),(2,4),(3,4)],5)
=> ([],3)
=> ([],1)
=> ([],1)
=> 0
([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? = 1
([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ([(0,1)],2)
=> ([],2)
=> ? = 0
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? = 0
([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ([],2)
=> ? = 0
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? = 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ([(0,1)],2)
=> ([],2)
=> ? = 0
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> ([(0,1)],2)
=> ([],2)
=> ? = 1
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? = 0
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? = 0
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? = 0
([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,1)],2)
=> ([],2)
=> ? = 1
([(0,1),(2,3),(2,4),(3,4)],5)
=> ([],2)
=> ([],1)
=> ([],1)
=> 0
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> ([(0,1)],2)
=> ([],2)
=> ? = 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> ? = 0
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> 2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ([],2)
=> ? = 1
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? = 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> ([(0,1)],2)
=> ([],2)
=> ? = 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],2)
=> ([],1)
=> ([],1)
=> 0
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> ? = 0
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> ? = 0
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ([],2)
=> ? = 0
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([],4)
=> ? = 0
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> ? = 0
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 0
([],0)
=> ?
=> ?
=> ?
=> ? = 0
Description
The radius of a connected graph. This is the minimum eccentricity of any vertex.
Mp00250: Graphs clique graphGraphs
Mp00154: Graphs coreGraphs
Mp00111: Graphs complementGraphs
St000777: Graphs ⟶ ℤResult quality: 36% values known / values provided: 36%distinct values known / distinct values provided: 67%
Values
([],1)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1 = 0 + 1
([],2)
=> ([],2)
=> ([],1)
=> ([],1)
=> 1 = 0 + 1
([(0,1)],2)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1 = 0 + 1
([],3)
=> ([],3)
=> ([],1)
=> ([],1)
=> 1 = 0 + 1
([(1,2)],3)
=> ([],2)
=> ([],1)
=> ([],1)
=> 1 = 0 + 1
([(0,2),(1,2)],3)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> ? = 0 + 1
([(0,1),(0,2),(1,2)],3)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1 = 0 + 1
([],4)
=> ([],4)
=> ([],1)
=> ([],1)
=> 1 = 0 + 1
([(2,3)],4)
=> ([],3)
=> ([],1)
=> ([],1)
=> 1 = 0 + 1
([(1,3),(2,3)],4)
=> ([(1,2)],3)
=> ([(0,1)],2)
=> ([],2)
=> ? = 0 + 1
([(0,3),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? = 0 + 1
([(0,3),(1,2)],4)
=> ([],2)
=> ([],1)
=> ([],1)
=> 1 = 0 + 1
([(0,3),(1,2),(2,3)],4)
=> ([(0,2),(1,2)],3)
=> ([(0,1)],2)
=> ([],2)
=> ? = 1 + 1
([(1,2),(1,3),(2,3)],4)
=> ([],2)
=> ([],1)
=> ([],1)
=> 1 = 0 + 1
([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> ? = 0 + 1
([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ([],2)
=> ? = 0 + 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> ? = 0 + 1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1 = 0 + 1
([],5)
=> ([],5)
=> ([],1)
=> ([],1)
=> 1 = 0 + 1
([(3,4)],5)
=> ([],4)
=> ([],1)
=> ([],1)
=> 1 = 0 + 1
([(2,4),(3,4)],5)
=> ([(2,3)],4)
=> ([(0,1)],2)
=> ([],2)
=> ? = 0 + 1
([(1,4),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? = 0 + 1
([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([],4)
=> ? = 0 + 1
([(1,4),(2,3)],5)
=> ([],3)
=> ([],1)
=> ([],1)
=> 1 = 0 + 1
([(1,4),(2,3),(3,4)],5)
=> ([(1,3),(2,3)],4)
=> ([(0,1)],2)
=> ([],2)
=> ? = 1 + 1
([(0,1),(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ([(0,1)],2)
=> ([],2)
=> ? = 0 + 1
([(2,3),(2,4),(3,4)],5)
=> ([],3)
=> ([],1)
=> ([],1)
=> 1 = 0 + 1
([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? = 1 + 1
([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ([(0,1)],2)
=> ([],2)
=> ? = 0 + 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? = 0 + 1
([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ([],2)
=> ? = 0 + 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? = 1 + 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(1,2)],3)
=> ([(0,1)],2)
=> ([],2)
=> ? = 0 + 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> ([(0,1)],2)
=> ([],2)
=> ? = 1 + 1
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? = 0 + 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? = 0 + 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? = 0 + 1
([(0,4),(1,3),(2,3),(2,4)],5)
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,1)],2)
=> ([],2)
=> ? = 1 + 1
([(0,1),(2,3),(2,4),(3,4)],5)
=> ([],2)
=> ([],1)
=> ([],1)
=> 1 = 0 + 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> ([(0,1)],2)
=> ([],2)
=> ? = 1 + 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> ? = 0 + 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> 3 = 2 + 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ([],2)
=> ? = 1 + 1
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? = 1 + 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> ([(0,1)],2)
=> ([],2)
=> ? = 1 + 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],2)
=> ([],1)
=> ([],1)
=> 1 = 0 + 1
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> ? = 0 + 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> ? = 0 + 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ([],2)
=> ? = 0 + 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([],4)
=> ? = 0 + 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> ? = 0 + 1
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1 = 0 + 1
([],0)
=> ?
=> ?
=> ?
=> ? = 0 + 1
Description
The number of distinct eigenvalues of the distance Laplacian of a connected graph.
The following 95 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St001301The first Betti number of the order complex associated with the poset. St000181The number of connected components of the Hasse diagram for the poset. St000908The length of the shortest maximal antichain in a poset. St001634The trace of the Coxeter matrix of the incidence algebra of a poset. St001001The number of indecomposable modules with projective and injective dimension equal to the global dimension of the Nakayama algebra corresponding to the Dyck path. St001208The number of connected components of the quiver of $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra $A$ of $K[x]/(x^n)$. St001371The length of the longest Yamanouchi prefix of a binary word. St001730The number of times the path corresponding to a binary word crosses the base line. St001803The maximal overlap of the cylindrical tableau associated with a tableau. St001195The global dimension of the algebra $A/AfA$ of the corresponding Nakayama algebra $A$ with minimal left faithful projective-injective module $Af$. St001804The minimal height of the rectangular inner shape in a cylindrical tableau associated to a tableau. St001307The number of induced stars on four vertices in a graph. St001325The minimal number of occurrences of the comparability-pattern in a linear ordering of the vertices of the graph. St001496The number of graphs with the same Laplacian spectrum as the given graph. St000264The girth of a graph, which is not a tree. St001578The minimal number of edges to add or remove to make a graph a line graph. St000287The number of connected components of a graph. St001518The number of graphs with the same ordinary spectrum as the given graph. St001765The number of connected components of the friends and strangers graph. St001877Number of indecomposable injective modules with projective dimension 2. St001630The global dimension of the incidence algebra of the lattice over the rational numbers. St001878The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L. St001095The number of non-isomorphic posets with precisely one further covering relation. St000914The sum of the values of the Möbius function of a poset. St001570The minimal number of edges to add to make a graph Hamiltonian. St000661The number of rises of length 3 of a Dyck path. St000791The number of pairs of left tunnels, one strictly containing the other, of a Dyck path. St000931The number of occurrences of the pattern UUU in a Dyck path. St000936The number of even values of the symmetric group character corresponding to the partition. St000938The number of zeros of the symmetric group character corresponding to the partition. St000940The number of characters of the symmetric group whose value on the partition is zero. St000980The number of boxes weakly below the path and above the diagonal that lie below at least two peaks. St001124The multiplicity of the standard representation in the Kronecker square corresponding to a partition. St001141The number of occurrences of hills of size 3 in a Dyck path. St000284The Plancherel distribution on integer partitions. St000704The number of semistandard tableaux on a given integer partition with minimal maximal entry. St000735The last entry on the main diagonal of a standard tableau. St000901The cube of the number of standard Young tableaux with shape given by the partition. St001128The exponens consonantiae of a partition. St001876The number of 2-regular simple modules in the incidence algebra of the lattice. St001651The Frankl number of a lattice. St001875The number of simple modules with projective dimension at most 1. St000175Degree of the polynomial counting the number of semistandard Young tableaux when stretching the shape. St000205Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and partition weight. St000206Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and integer composition weight. St000225Difference between largest and smallest parts in a partition. St000319The spin of an integer partition. St000320The dinv adjustment of an integer partition. St000749The smallest integer d such that the restriction of the representation corresponding to a partition of n to the symmetric group on n-d letters has a constituent of odd degree. St000944The 3-degree of an integer partition. St001175The size of a partition minus the hook length of the base cell. St001178Twelve times the variance of the major index among all standard Young tableaux of a partition. St001248Sum of the even parts of a partition. St001279The sum of the parts of an integer partition that are at least two. St001280The number of parts of an integer partition that are at least two. St001392The largest nonnegative integer which is not a part and is smaller than the largest part of the partition. St001541The Gini index of an integer partition. St001586The number of odd parts smaller than the largest even part in an integer partition. St001587Half of the largest even part of an integer partition. St001657The number of twos in an integer partition. St001918The degree of the cyclic sieving polynomial corresponding to an integer partition. St000207Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer composition weight. St000208Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer partition weight. St000618The number of self-evacuating tableaux of given shape. St000667The greatest common divisor of the parts of the partition. St000755The number of real roots of the characteristic polynomial of a linear recurrence associated with an integer partition. St000781The number of proper colouring schemes of a Ferrers diagram. St001283The number of finite solvable groups that are realised by the given partition over the complex numbers. St001284The number of finite groups that are realised by the given partition over the complex numbers. St001389The number of partitions of the same length below the given integer partition. St001432The order dimension of the partition. St001571The Cartan determinant of the integer partition. St001599The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on rooted trees. St001780The order of promotion on the set of standard tableaux of given shape. St001899The total number of irreducible representations contained in the higher Lie character for an integer partition. St001900The number of distinct irreducible representations contained in the higher Lie character for an integer partition. St001901The largest multiplicity of an irreducible representation contained in the higher Lie character for an integer partition. St001908The number of semistandard tableaux of distinct weight whose maximal entry is the length of the partition. St001924The number of cells in an integer partition whose arm and leg length coincide. St001934The number of monotone factorisations of genus zero of a permutation of given cycle type. St001199The dominant dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001722The number of minimal chains with small intervals between a binary word and the top element. St001118The acyclic chromatic index of a graph. St000302The determinant of the distance matrix of a connected graph. St000466The Gutman (or modified Schultz) index of a connected graph. St000467The hyper-Wiener index of a connected graph. St001846The number of elements which do not have a complement in the lattice. St000771The largest multiplicity of a distance Laplacian eigenvalue in a connected graph. St000772The multiplicity of the largest distance Laplacian eigenvalue in a connected graph. St001060The distinguishing index of a graph. St001645The pebbling number of a connected graph. St001719The number of shortest chains of small intervals from the bottom to the top in a lattice. St001820The size of the image of the pop stack sorting operator. St001330The hat guessing number of a graph. St000782The indicator function of whether a given perfect matching is an L & P matching.