Some results on disjunctive domination in graphs

Abstract

A set D⊆V is a disjunctive dominating set of a graph G=(V,E), if for any x not in D, x is either a neighbor of a vertex in D or there are at least two vertices in D at a distance two from x. Minimum cardinality of such a subset D of V is called the disjunctive domination number of G. In this paper we obtain the values of the disjunctive domination number of splitting graph of path and cycle graphs.