Let G = (V(G), E(G)) be a connnected simple graph. A subset S of V(G) is a dominating set of G if for every u ε V(G) \ S, there exists v ε S such that u,v ε E(G). A dominating set S is called a fair dominating set if for each distinct vertices u, v ε V(G) \ S, |NG(u) ∩ S| = |NG(v) ∩ S|. Further, if D is a minimum fair dominating set of G, then a fair dominating set S ⊆ V(G) \ D is called an inverse fair dominating set of G with respect to D. A disjoint fair dominating set of G is the set C = D ∪ S ⊆ V(G). In this paper, we give the characterizations in the join and corona of two graphs.