ON GLOBAL VERTEX-EDGE DOMINATION OF JOIN AND CORONA OF SIMPLE GRAPHS

A subset $S$ of the vertex set $V(G)$ of a graph $G$ is a vertex-edge dominating set of $G$ if, for all edges $e \in E(G)$, there exists a vertex $v \in S$ that vertex-edge dominates $e$. If the same set $S$ is a vertex-edge dominating set of the complement $\bar{G}$ of $G$, then $S$ is called a globalvertex edge dominating set of $G$. The minimum cardinality of a global vertex-edge dominating set is called a global vertex-edge domination number of $G$, denoted by $\gamma_{g v e}(G)$. This paper characterises global vertex-edge dominating sets of join and corona of graphs. Bounds for global vertex-edge domination numbers are also determined. Received: January 26, 2025 Revised: February 12, 2025 Accepted: March 6, 2025