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Domination in graphoidal covers of a graph

Domination in graphoidal covers of a graph,10.1016/S0012-365X(98)00389-6,Discrete Mathematics,B. Devadas Acharya,Purnima Gupta

Domination in graphoidal covers of a graph  
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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 ψ-dominating set (ψ-domset, 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 end-vertices 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. 1-3, pp. 3-33, 1999
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