Exact Defensive Alliances in Graphs
نویسنده
چکیده
A nonempty set S ⊂ V is a defensive k-alliance in G = (V,E), k ∈ [−Δ,Δ] ∪ Z, if for every v ∈ S, dS(v) ≥ dS̄(v) + k. A defensive k-alliance S is called exact, if S is defensive k-alliance but is no defensive (k+1)-alliance in G. In this paper we study the mathematical properties of exact defensive k-alliances in graphs. In particular, we obtain several bounds for defensive k-alliance of a graph. Furthermore, we characterize the exact defensive alliances in graph join G1 G2 in terms of G1, G2. Mathematics Subject Classification: 05C69; 05A20; 05C50
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