For a graph G = ( V , E ) , a set S ? V is a dominating set if every vertex in V ? S has at least a neighbor in S . A dominating set S is a global offensive alliance if for each vertex v in V ? S at least half the vertices from the closed neighborhood of v are in S . The domination number γ ( G ) is the minimum cardinality of a dominating set of G , and the global offensive alliance number γ o ( G ) is the minimum cardinality of a global offensive alliance of G . We show that if G is a connected unicycle graph of order n with l ( G ) leaves and s ( G ) support vertices then γ o ( G ) ≥ n ? l ( G ) + s ( G ) 3 . Moreover, we characterize all extremal unicycle graphs attaining this bound.
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