A subset S of the vertex set  of a graph G is a vertex-edge dominating set of G if, for all edges  there exists a vertex  that vertex-edge dominates e. If the same set S is a vertex-edge dominating set of the complement  of G, then S is called a global-vertex 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  This paper characterises global vertex-edge dominating sets of join and corona of graphs. Bounds for global vertex-edge domination numbers are also determined.

domination, vertex-edge domination, global vertex-edge domination

Received: January 26, 2025; Revised: February 12, 2025; Accepted: March 6, 2025; Published: March 11, 2025

How to cite this article: Cristover N. Vidal and Analen A. Malnegro, On global vertex-edge domination of join and corona of simple graphs, Advances and Applications in Discrete Mathematics 42(4) (2025), 385-393. https://doi.org/10.17654/0974165825024

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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