Abstract:<abstract><p>A nonempty subset $ D $ of vertices in a graph $ \Gamma = (V, E) $ is said is an <italic>offensive alliance</italic>, if every vertex $ v \in \partial(D) $ satisfies $ \delta_D(v) \geq \delta_{\overline{D}}(v) + 1 $; the cardinality of a minimum offensive alliance of $ \Gamma $ is called the <italic>offensive alliance number</italic> $ \alpha ^o(\Gamma) $ of $ \Gamma $. An offensive alliance $ D $ is called <italic>global</italic>, if every $ v \in V… Show more
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