Global Defensive Alliances in the Lexicographic Product of Paths and Cycles

Rommel M. Barbosa; Mitre C. Dourado; Leila R. S. da Silva

paper

Global Defensive Alliances in the Lexicographic Product of Paths and Cycles

arXiv:1810.08256

Abstract

A set $S$ of vertices of graph $G$ is a \textit{defensive alliance} of $G$ if for every $v \in S$ , it holds $∣ N [v] \cap S ∣ \geq ∣ N [v] - S ∣$ . An alliance $S$ is called $g l o ba l$ 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.

25 pages, 12 tables