Abstract
An offensive alliance in a graph Γ = (V, E) is a set of vertices S ⊂ V where for every vertex v in its boundary it holds that the majority of vertices in v’s closed neighborhood are in S. In the case of strong offensive alliance, strict majority is required. An alliance S is called global if it affects every vertex in V \S, that is, S is a dominating set of Γ. The global offensive alliance number γo(Γ) (respectively, global strong offensive alliance number γˆ(Γ)) is the minimum cardinality of a global offensive (respectively, global strong offensive) alliance in Γ. If Γ has global independent offensive alliances, then the global independent offensive alliance number γi(Γ) is the minimum cardinality among all independent global offensive alliances of Γ. In this paper we study mathematical properties of the global (strong) alliance number of cubic graphs. For instance, we show that for all connected cubic graph of order n, 2n 5 ≤ γi(Γ) ≤
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