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Caay, Mark. (1404). EQUITABLE RINGS DOMINATION IN GRAPHS. , 13(2), 157-168. doi: 10.22044/jas.2023.12812.1693
Mark Lantaca Caay. "EQUITABLE RINGS DOMINATION IN GRAPHS". , 13, 2, 1404, 157-168. doi: 10.22044/jas.2023.12812.1693
Caay, Mark. (1404). 'EQUITABLE RINGS DOMINATION IN GRAPHS', , 13(2), pp. 157-168. doi: 10.22044/jas.2023.12812.1693
Caay, Mark. EQUITABLE RINGS DOMINATION IN GRAPHS. , 1404; 13(2): 157-168. doi: 10.22044/jas.2023.12812.1693

EQUITABLE RINGS DOMINATION IN GRAPHS

Journal of Algebraic Systems
دوره 13، شماره 2، مهر 2025، صفحه 157-168    اصل مقاله (396.73 K)
نوع مقاله: Original Manuscript
شناسه دیجیتال (DOI): 10.22044/jas.2023.12812.1693
نویسنده
Mark Lantaca Caay*
Department of Mathematics and Physics, Adamson University, P.O. Box 1013, Ermita Manila City, Metro Manila, Philippines.
چکیده
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.
کلیدواژه‌ها
domination؛ equitable domination؛ rings domination؛ equitable domination rings domination
مراجع
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آمار
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