Processing math: 100%

Identifier
Values
['A',1] => ([],1) => ([],1) => 1
['A',2] => ([(0,2),(1,2)],3) => ([(0,2),(1,2)],3) => 2
['B',2] => ([(0,3),(1,3),(3,2)],4) => ([(0,3),(1,3),(2,3)],4) => 3
['G',2] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 4
['A',3] => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 4
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Description
The upper irredundance number of a graph.
A set S of vertices is irredundant, if there is no vertex in S, whose closed neighbourhood is contained in the union of the closed neighbourhoods of the other vertices of S.
The upper irredundance number is the largest size of a maximal irredundant set.
The smallest graph with different upper irredundance number and upper domination number St001337The upper domination number of a graph. has eight vertices. It is obtained from the disjoint union of two copies of K4 by joining three of the four vertices of the first with three of the four vertices of the second. For bipartite graphs the two parameters always coincide [2].
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 α≺β if β−α is a simple root.
Map
to graph
Description
Returns the Hasse diagram of the poset as an undirected graph.