Efficient secure domination in graphs

Let G = (V,E) be a graph. A dominating set S ⊆ V (G) is an efficient dominating set if S is a 2-packing set. The set S is a secure dominating set of G if for each u ∈ V S there exists a vertex v ∈ S such that uv belongs to the edge set of G and (S{v}) ∪ {u} is a dominating set of G. In this paper we introduce efficient secure domination in graphs. We define and study the parameter efficient secure domination number of G.