Let G = (V(G), E(G)) be a connected simple graph. A subset S of V(G) is a dominating set of G if for every u ∈ V(G) \ S, there exists v ∈ S such that uv ∈ E(G). A dominating set S is called a secure dominating set if for each u ∈ V(G) \ S there exists v ∈ S such that u is adjacent to v and (S {v}) ∪ {u} is a dominating set. A secure dominating set S is called a perfect secure dominating set of G if each u ∈ V(G) \ S is dominating by exactly one element of S. Further, if D is a minimum perfect secure dominating set of G, then a perfect secure dominating set S ⊆ V(G) \ D is called an inverse perfect secure dominating set of G with respect to D. In this paper, we investigate the concept and give some important results.