Isolate domination in graphs
I. Sahul Hamid, S. Balamurugan · Arab Journal of Mathematical Sciences · 2015
A set D of vertices of a graph G is called a dominating set of G if every vertex in V ( G ) − D is adjacent to a vertex in D . A dominating set S such that the subgraph 〈 S 〉 induced by S has at least one isolated vertex is called an isolate dominating set . An isolate dominating set none of whose proper subset is an isolate dominating set is a minimal isolate dominating set . The minimum and maximum cardinality of a minimal isolate dominating set are called the isolate domination number γ 0 and the upper isolate domination number Γ 0 respectively. In this paper we initiate a study on these parameters.