Convex Roman Dominating Function in Graphs

Authors

  • Rona Jane G. Fortosa MSU-Iligan Institute of Technology
  • Sergio R. Canoy, Jr. Department of Mathematics and Statistics, College of Science and Mathematics, Center for Graph Theory, Algebra, and Analysis- PRISM, MSU-Iligan Institute of Technology, 9200 Iligan City, Philippines

DOI:

https://doi.org/10.29020/nybg.ejpam.v16i3.4828

Keywords:

convex set, Roman dominating function, Roman domination number, convex Roman dominating function, convex Roman domination number

Abstract

Let $G$ be a connected graph. A function $f:V(G)\rightarrow \{0,1,2\}$ is a \textit{convex Roman dominating function} (or CvRDF) if every vertex $u$ for which $f(u)=0$ is adjacent to at least one vertex $v$ for which $f(v)=2$ and $V_1 \cup V_2$ is convex. The weight of a convex Roman dominating function $f$, denoted by $\omega_{G}^{CvR}(f)$, is given by $\omega_{G}^{CvR}(f)=\sum_{v \in V(G)}f(v)$. The minimum weight of a CvRDF on $G$, denoted by $\gamma_{CvR}(G)$, is called the \textit{convex Roman domination number} of $G$. In this paper, we determine the convex Roman domination numbers of some graphs and give some realization results involving convex Roman domination, connected Roman domination, and convex domination numbers.

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Published

2023-07-30

Issue

Section

Nonlinear Analysis

How to Cite

Convex Roman Dominating Function in Graphs. (2023). European Journal of Pure and Applied Mathematics, 16(3), 1705-1716. https://doi.org/10.29020/nybg.ejpam.v16i3.4828

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