Inverse isolate domination number on a vertex switching of cycle related graphs

Abstract

Let \(G\) be non-trivial graph. A subset \(S \subset V(G)\) is called a isolate dominating set of \(G\) if is a dominating set and \(\delta(<S>)=0\). The set \(S^{\prime} \subset V(G)-S\) such that \(S^{\prime}\) is a dominating set of \(G\) and \(\delta\left(<S^{\prime}>\right)=0\), then \(S^{\prime}\) is called an inverse isolate dominating set with respect to \(S\). The minimum cardinality of an inverse isolate dominating set is called an inverse isolate dominating number and is denoted by \(\gamma_0^{-1}(G)\). In this paper we find inverse isolate dominating number on vertex switching of some cycle related graphs.