Fair domination polynomial of a graph

A dominating set of a simple graph G = (V, E) is a subset D ⊆ V such that every vertex not in D is adjacent to at least one vertex in D. ##The cardinality of a smallest dominating set of G, denoted by γ(G), is the domination number of G. ##The neighbourhood of a vertex v in G, N(v) is the set of all of the vertices adjacent to v. For k ≥ 1, a k-fair dominating set (kFD-set) in G, is a dominating set S such that |N(v) ∩ D| = k for every vertex v ∈ V D. ##A fair dominating set, in G is a kFD-set for some integer k ≥ 1