Secure Domination in Digraphs

Given a graph G = (V,E), a subset S of V is dominating if for every v in V - S there exists u in S such that uv is in E. A dominating subset S of V is secure if for every v in V - S there exists u in S such that (S - {u}) U {v} is dominating. In this work we extend the concept of secure dominating set to digraphs in four different ways, all of them with interesting applications, and prove some results regarding each of them.