Relatively Prime Inverse Domination on Jump Graph

Abstract

Let  be non-trivial graph. A subset  of the vertex set  of a graph  is called a dominating set of  if every vertex in  is adjacent to a vertex in . The minimum cardinality of a dominating set is called the domination number and is denoted by . If  contains a dominating set  of , then  is called an inverse dominating set with respect to . In an inverse dominating set , every pair of vertices  and  in  such that , then  is called relatively prime inverse dominating set. The minimum cardinality of a relatively prime inverse dominating set is called relatively prime inverse dominating number and is denoted by . In this paper we find relatively prime inverse dominating number of some jump graphs.