Let G be non-trivial graph. A subset S of the vertex set V(G) of a graph G is called an isolate dominating set of G if every vertex in V – S is adjacent to a vertex in S such that $\delta(\langle S \rangle)=0$. The minimum cardinality of an isolate dominating set is called the isolate domination number and is denoted by $\gamma_0(G)$. If V – S contains a dominating set S′ of G, then S′ 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 investigate the inverse isolate dominating number of 4-regular graph on n vertices with girth 3 and girth 4.