Let = ((), ()) be a connected simple graph. A subset of () is a dominating set of if for every ∈ () ∖ , there exists ∈ such that ∈ (). A dominating set S is called a fair dominating set if for each distinct vertices. ∈ () ∖ , | () ∩ | = | () ∩ |. Further, if is a minimum fair dominating set of , then a fair dominating set ⊆ () ∖ is called an inverse fair dominating set of with respect to. A disjoint fair dominating set of is the set = ∪ ⊆ (). In this paper, we investigate the concept and give some important results.