Isolate domination in the class of unicyclic graphs

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.