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 |deg(u) − deg(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 and determine the equitable domination numbers of many graphs, as well as graphs formed by some binary operations.