Shahrood University of Technology Journal of Algebraic Systems 2345-5128 13 2 2025 07 01 EQUITABLE RINGS DOMINATION IN GRAPHS 157 168 3107 10.22044/jas.2023.12812.1693 EN Mark Lantaca Caay Department of Mathematics and Physics, Adamson University, P.O. Box 1013, Ermita Manila City, Metro Manila, Philippines. Journal Article 2023 03 07 A dominating set $S$ of $G$ is an \textit{equitable dominating set} of $G$ if for every $v \in V(G) \setminus S$, there exists $u \in S$ such that $uv \in V(G)$ and $\displaystyle{\left|\deg(u) - \deg(v)\right| \leq 1.}$ A dominating set $S$ of $G$ is a \textit{rings dominating set} of $G$ if every vertex $v \in V(G) \setminus S$ is adjacent to atleast two vertices $V(G) \setminus S$. 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 \textit{equitable rings dominating set}. The minimum cardinality of an equitable rings dominating set of a graph $G$ is called the \textit{equitable rings domination number} of $G$, and is denoted by $\gamma_{eri}(G)$. Moreover, we examine determine the equitable rings domination number of many graphs, and graphs formed by some binary operations. https://jas.shahroodut.ac.ir/article_3107_85db498e78e0e83d51387a231bf4d645.pdf