Isolate domination in graphs

Abstract

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 γ0 and the upper isolate domination number Γ0 respectively. In this paper we initiate a study on these parameters.

Keywords

• Dominating set
• Isolate dominating set
• Isolate domination number
• Upper isolate domination number