Convex Roman Dominating Function in Graphs


  • 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



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


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.






Nonlinear Analysis

How to Cite

Convex Roman Dominating Function in Graphs. (2023). European Journal of Pure and Applied Mathematics, 16(3), 1705-1716.

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