Relatively prime inverse domination on vertex switching of some graphs

Abstract

Let G = (V, E) be a non-trivial graph. A subset D of the vertex set V of a graph G is called a dominating set of G if every vertex in V − D is adjacent to a vertex in D. The domination number is the lowest cardinality of a dominating set, and it is denoted by γ(G). If V − D contains a dominating set S of G, then S is called an inverse dominating set with respect to D. In an inverse dominating set S, every pair of vertices u and v in S such that (deg(u), deg(v)) = 1, then S is called relatively prime inverse dominating set. The lowest cardinality of a relatively prime inverse dominating set is called the relatively prime inverse domination number and is denoted by γ−1rp (G). In this paper, we find relatively prime inverse domination number on vertex switching of some graphs.