TY - JOUR
TI - Convex Roman Dominating Functions on Graphs under some Binary Operations
PY - 2024/04/30
Y2 - 2024/06/19
JF - European Journal of Pure and Applied Mathematics
JA - Eur. J. Pure Appl. Math.
VL - 17
IS - 2
DO - 10.29020/nybg.ejpam.v17i2.5205
UR - https://doi.org/10.29020/nybg.ejpam.v17i2.5205
SP - 1335-1351
AB - 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.
ER -