@article{Convex Roman Dominating Functions on Graphs under some Binary Operations_2024, place={Maryland, USA}, volume={17}, url={https://www.ejpam.com/index.php/ejpam/article/view/5205}, DOI={10.29020/nybg.ejpam.v17i2.5205}, abstractNote={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 specifically study the concept of convex Roman domination in the corona and edge corona of graphs, complementary prism, lexicographicproduct, and Cartesian product of graphs.}, number={2}, journal={European Journal of Pure and Applied Mathematics}, year={2024}, month={Apr.}, pages={1335–1351} }