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arXiv · 1804.07113

Trees with unique minimum glolal offensive alliance sets

Mohamed Bouzefrane·Isma Bouchemakh·Mohamed Zamime·Noureddine Ikhlef-Eschouf
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Abstract

Let $G=$ $\left( V,E\right) $ be a simple graph.\ A non-empty set $S \subseteq V$ is called a global offensive alliance if $S$ is a dominating set and for every vertex $v$ in $V-S$, at least half of the vertices from the closed neighborhood of $v$ are in $S$. 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.

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Mohamed Bouzefrane, Isma Bouchemakh, Mohamed Zamime, Noureddine Ikhlef-Eschouf. 2018-04-19. Trees with unique minimum glolal offensive alliance sets. https://arxiv.org/abs/1804.07113

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