ISOLATE DOMINATION IN THE CLASS OF UNICYCLIC GRAPHS

ISOLATE DOMINATION IN THE CLASS OF UNICYCLIC GRAPHS

S. K. Vaidya, J. B. Kelaiya

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Abstract

A subset D of the vertex set V of a graph G is called a dominating set of G if every vertex in V −D is adjacent to a vertex in D. A dominating set D such that < D > has an isolated vertex is called an isolate dominating set and the minimum cardinality of an isolate dominating set is called the isolate domination number of G and is denoted by γ0(G). In this work, we investigate an isolate domination number for unicyclic graphs in the context of various transformations.

Keywords

Dominating set, isolate dominating set, isolate domination number.