Let G = (V, E) be a graph. A subset S of V is a dominating set of G if every vertex in V \ S is adjacent to a vertex in S. A dominating set S is called a secure dominating set if for each v ∈ V \ S there exists u ∈ S such that v is adjacent to u and S1 = (S \ {u}) ∪ {v} is a dominating set. If further the vertex u ∈ S is unique, then S is called a perfect secure dominating set. The minimum cardinality of a perfect secure dominating set of G is called the perfect secure domination number of G

more »

... is denoted by γ ps (G). In this paper we initiate a study of this parameter and present several basic results.