Global Defensive Alliances in the Lexicographic Product of Paths and Cycles
Rommel M. Barbosa, Mitre C. Dourado, Leila R. S. da Silva

TL;DR
This paper determines the exact size of the smallest global defensive alliances in the lexicographic products of paths and cycles, contributing to graph theory and alliance analysis.
Contribution
It provides the first exact calculations of global defensive alliance numbers for lexicographic products of paths and cycles.
Findings
Exact values for global defensive alliance numbers in these graph products
Extension of alliance theory to complex graph structures
New formulas for specific graph classes
Abstract
A set of vertices of graph is a \textit{defensive alliance} of if for every , it holds . An alliance is called if it is also a dominating set. In this paper, we determine the exact values of the global defensive alliance number of lexicographic products of path and cycles.
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