Convex Roman Dominating Functions on Graphs under some Binary Operations (European Journal of Pure and Applied Mathematics, 2024)
Let $G$ be a connected graph. A function $f:V(G)→ \{0,1,2\}$ is a 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 $ω_{G}^{CvR}(f)$, is given by $ω_{G}^{CvR}(f)=\sum_{v \in V(G)}f(v)$. The minimum weight of a CvRDF on $G$, denoted by $γ_{CvR}(G)$, is called the 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.
Keywords: Roman dominating function; Roman domination number; convex Roman dominating function; convex Roman domination number; corona; edge corona; complementary prism; lexicographic product; and Cartesian product