On disjunctive domination in graphs

Abstract

A set S of vertices of a graph G is a disjunctive dominating set if for every v ∈ V (G) \ S, v is adjacent to a vertex in S or S contains two vertices each of distance two from v. We say that S is a disjunctive total dominating set if for every v ∈ V (G), v is adjacent to a vertex in S or S contains two vertices each of distance two from v. In this paper, we characterize the disjunctive dominating sets and the disjunctive total dominating sets in the join, corona and composition of graphs and, as a result, obtain the values of their respective corresponding disjunctive domination numbers.