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Dominating Set
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Domination in graphoidal covers of a graph
Domination in graphoidal covers of a graph,10.1016/S0012365X(98)003896,Discrete Mathematics,B. Devadas Acharya,Purnima Gupta
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Domination in graphoidal covers of a graph
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B. Devadas Acharya
,
Purnima Gupta
A graphoidal cover of a given graph G=(V,E) is a set of its paths of length at least one, not necessarily open, such that no two paths have a common internal vertex and every edge of G is in exactly one of these paths. Graphoidal covers provide a fresh ground for generalizing results in
graph theory
and this paper is the first attempt to demonstrate the fruitfulness of this contention taking the notion of domination in graphs. Given a graphoidal cover ψ of G we define a set D of vertices of G to be a ψdominating set (ψdomset, for short) of G whenever for every vertex v in V⧹D there exists a vertex u in D and a path P in ψ such that u and v are the endvertices of P. This paper initiates a study of this concept in graphs which may not be necessarily finite.
Journal:
Discrete Mathematics  DM
, vol. 206, no. 13, pp. 333, 1999
DOI:
10.1016/S0012365X(98)003896
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