Identifier
Values
['A',1] => ([],1) => ([],1) => 1
['A',2] => ([(0,2),(1,2)],3) => ([(1,2)],3) => 2
['B',2] => ([(0,3),(1,3),(3,2)],4) => ([(2,3)],4) => 2
['G',2] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => ([(4,5)],6) => 2
['A',3] => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6) => ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 4
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Description
The number of minimal vertex covers of a graph.
A vertex cover of a graph $G$ is a subset $S$ of the vertices of $G$ such that each edge of $G$ contains at least one vertex of $S$. A vertex cover is minimal if it contains the least possible number of vertices.
This is also the leading coefficient of the clique polynomial of the complement of $G$.
This is also the number of independent sets of maximal cardinality of $G$.
A vertex cover of a graph $G$ is a subset $S$ of the vertices of $G$ such that each edge of $G$ contains at least one vertex of $S$. A vertex cover is minimal if it contains the least possible number of vertices.
This is also the leading coefficient of the clique polynomial of the complement of $G$.
This is also the number of independent sets of maximal cardinality of $G$.
Map
to root poset
Description
The root poset of a finite Cartan type.
This is the poset on the set of positive roots of its root system where $\alpha \prec \beta$ if $\beta - \alpha$ is a simple root.
This is the poset on the set of positive roots of its root system where $\alpha \prec \beta$ if $\beta - \alpha$ is a simple root.
Map
incomparability graph
Description
The incomparability graph of a poset.
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