Trees with unique minimum global offensive alliance

¹ Department of Mathematics, B.P. 270, Lamda-RO Laboratory, University of Blida, Blida, Algeria
² Faculty of Mathematics, Laboratory L’IFORCE, University of Sciences and Technology Houari Boumediene (USTHB), B.P. 32 El-Alia, Bab-Ezzouar 16111, Algiers, Algeria
³ Faculty of Technology, University of Médéa, Médéa, Algeria
⁴ Faculty of Sciences, Department of Mathematics and Computer Science, University of Médéa, Médéa, Algeria

^* Corresponding author: mohamedbouzefrane@gmail.com

Received: 18 July 2018
Accepted: 19 February 2020

Abstract

Let G = (V, E) be a simple graph. A non-empty set D ⊆ V is called a global offensive alliance if D is a dominating set and for every vertex ν in V − D, |N_G [ν] ∩ D|≥|N_G [ν] − D|. The global offensive alliance number is the minimum cardinality of a global offensive alliance in G. In this paper, we give a constructive characterization of trees having a unique minimum global offensive alliance.