Global Defensive Alliances in the Lexicographic Product of Paths and Cycles

2018/10/18 by Rommel M. Barbosa, Mitre C. Dourado, Barbosa, Rommel M. +3
Mathematics · #05C69 #05C76 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05C69 #msc:05C76

paper · pdf · doi:10.48550/arxiv.1810.08256

25 pages, 12 tables

arxiv created 2018/10/18 · arxiv updated 2018/10/22

Abstract

A set S of vertices of graph G is a defensive alliance of G if for every v ∈ S, it holds |N[v] ∩ S| ≥ |N[v]-S|. An alliance S is called global 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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