Exact defensive alliances in graphs
Walter Carballosa · Applied Mathematical Sciences · 2013
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) ≥ d ¯ S (v )+ k. A defensive k-alliance S is called exact ,i fS 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