RESTRAINED GLOBAL OFFENSIVE ALLIANCES IN SOME GRAPHS
Klarice Shaira R. Tan, Isagani S. Cabahug · Advances and Applications in Discrete Mathematics · 2025
Let be a connected nontrivial graph. A nonempty set is defined as a restrained global offensive alliance in if is a global offensive alliance and the subgraph has no isolated vertices. In this study, we investigate the necessary and sufficient conditions for the existence of a restrained global offensive alliance in various graph structures, including paths, cycles, and specific graph families. Additionally, we explore the minimum cardinality of such alliances within these graph types. Furthermore, this research generates the exact values and characterizations of the restrained global offensive alliance in the join graphs, providing deeper understanding of their properties.