Let G = (V(G), E(G)) be a connected nontrivial graph. A nonempty set  is defined as a restrained global offensive alliance in G if S 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.

dominating set, restrained dominating set, offensive alliance, global offensive alliance, restrained global offensive alliance.

Received: August 19, 2024; Accepted: November 13, 2024; Published: January 2, 2025

How to cite this article: Klarice Shaira R. Tan and Isagani S. Cabahug, Jr., Restrained global offensive alliances in some graphs, Advances and Applications in Discrete Mathematics 42(3) (2025), 191-204. https://doi.org/10.17654/0974165825013

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

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