Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001799
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Mapping
St001799: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => 0
([],2)
 => 1
([(0,1)],2)
 => 0
([],3)
 => 6
([(1,2)],3)
 => 3
([(0,2),(1,2)],3)
 => 1
([(0,1),(0,2),(1,2)],3)
 => 0
([],4)
 => 25
([(2,3)],4)
 => 16
([(1,3),(2,3)],4)
 => 10
([(0,3),(1,3),(2,3)],4)
 => 6
([(0,3),(1,2)],4)
 => 9
([(0,3),(1,2),(2,3)],4)
 => 5
([(1,2),(1,3),(2,3)],4)
 => 7
([(0,3),(1,2),(1,3),(2,3)],4)
 => 3
([(0,2),(0,3),(1,2),(1,3)],4)
 => 2
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 0
([],5)
 => 90
([(3,4)],5)
 => 63
([(2,4),(3,4)],5)
 => 45
([(1,4),(2,4),(3,4)],5)
 => 33
([(0,4),(1,4),(2,4),(3,4)],5)
 => 25
([(1,4),(2,3)],5)
 => 42
([(1,4),(2,3),(3,4)],5)
 => 30
([(0,1),(2,4),(3,4)],5)
 => 28
([(2,3),(2,4),(3,4)],5)
 => 36
([(0,4),(1,4),(2,3),(3,4)],5)
 => 20
([(1,4),(2,3),(2,4),(3,4)],5)
 => 24
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 16
([(1,3),(1,4),(2,3),(2,4)],5)
 => 21
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 12
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 18
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 14
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 10
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 7
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 6
([(0,4),(1,3),(2,3),(2,4)],5)
 => 18
([(0,1),(2,3),(2,4),(3,4)],5)
 => 21
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 13
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => 9
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 10
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 7
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => 5
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => 9
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 15
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 7
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => 4
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 2
Description
The number of proper separations of a graph. A separation of a graph with vertex set $V$ is a set $\{A, B\}$ of subsets of $V$ such that $A\cup B = V$ and there is no edge between $A\setminus B$ and $B\setminus A$. A separation $\{A, B\}$ is proper $A\setminus B$ and $B\setminus A$ are non-empty. For example, the number of proper separations of the empty graph on $n$ vertices $\{1,\dots,n\}$ is the Stirling number of the second kind $S(n+1, 3)$, i.e., the number of set partitions of $\{0,1,\dots,n\}$ into three subsets, where the subset containing $0$ corresponds to $A \cap B$.