Equitable Rings Domination in Graphs

A dominating set S of G is an equitable dominating set of G if for every v ∈ V(G) S, there exists u ∈ S such that uv ∈ V(G) and |(u) - (v)| ≤ 1. A dominating set S of G is a rings dominating set of G if every vertex v ∈ V(G) S is adjacent to atleast two vertices V(G) S. In this paper, we examine the conditions at which the equitable dominating set and the rings dominating set coincide, and thus naming the dominating set as equitable rings dominating set. The minimum cardinality of an equitable rings dominating set of a graph G is called the equitable rings domination number of G, and is denoted by γₑᵣᵢ(G). Moreover, we examine determine the equitable rings domination number of many graphs, and graphs formed by some binary operations.