Volume 55, 2021Regular articles published in advance of the transition of the journal to Subscribe to Open (S2O). Free supplement sponsored by the Fonds National pour la Science Ouverte
|Page(s)||S863 - S872|
|Published online||02 March 2021|
Trees with unique minimum global offensive alliance
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: firstname.lastname@example.org
Accepted: 19 February 2020
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, |NG [ν] ∩ D|≥|NG [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.
Mathematics Subject Classification: 05C69 / 05C70
Key words: Tree / domination / global offensive alliance / characterization
© EDP Sciences, ROADEF, SMAI 2021
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