Changing and unchanging isolate domination: Edge removal

A set of S ⊆ V of vertices in a graph G is called a dominating set if every vertex of V − S is adjacent to an element of S. Further, if 〈S〉 has an isolated vertex, then S is called an isolate dominating set. The minimum cardinality of an isolate dominating set of a graph G is called the isolate domination number, denoted by γ0(G). This paper examines the effects of removal of an edge on the isolate domination number of a graph.