Upper k-Alliances in Graphs
نویسندگان
چکیده
A nonempty set S ⊆ V is a defensive k-alliance in Γ = (V,E), k ∈ [−Δ,Δ] ∩ Z, if for every v ∈ S, δS(v) ≥ δS̄(v) + k. An defensive kalliance S is called critical if no proper subset of S is an defensive k-alliances in Γ = (V,E). The upper defensive k-alliance number of Γ, denoted by Ak(Γ), is defined as the maximum cardinality of a critical defensive k-alliance in Γ. In this paper we study the mathematical properties of upper defensive k-alliance in graphs. In particular, we obtain several tight bounds on upper defensive k-alliance numbers of a graph. Mathematics Subject Classification: 05C69; 05A20; 05C50
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