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