Inverse Rings Domination

A. Let X = V (G) \ S, where S is a ri-set of G.A subset Y X is said to be an inverse rings dominating set of G with respect to S if Y is a rings dominating set of G.The minimum cardinality of an inverse rings dominating set of G with respect to a ri-set S of G is said to be an inverse rings domination number of G with respect to a ri-set S of G, and we denote such as -1 ri (G) S .An inverse rings dominating set of G with respect to S whose cardinality is equal to -1 ri (G) S is said to be a -1 ri S -set of G.In this study, we show that the graph may have a rings dominating set and no inverse rings dominating set.Moreover, we study the inverse rings dominating set in the join and corona of graphs.