Global defensive k-alliances in graphs
Rodriguez, J. A. · Sigarreta, J. M.
Original · EN
Let Γ=(V,E) be a simple graph. For a nonempty set X V, and a vertex v∈ V, δₓ(v) denotes the number of neighbors v has in X. A nonempty set S V is a defensive k-alliance in Γ=(V,E) if δₛ(v)≥ δS(v)+k, ∀ v∈ S. A defensive k-alliance S is called global if it forms a dominating set. The global defensive k-alliance number of Γ, denoted by γₖᵃ(Γ), is the minimum cardinality of a defensive k-alliance in Γ. We study the mathematical properties of γₖᵃ(Γ).
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