On the number of fair dominating sets of graphsS. Alikhani, M. SafazadehLet G = (V, E) be a simple graph. A dominating set of G 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. For k ≥ 1, a k-fair dominating set (kFD-set) in G, is a dominating set D 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. In this paper, after presenting preliminaries, we count the number of fair dominating sets of some specific graphs.Advanced Studies: Euro-Tbilisi Mathematical Journal, Vol. 16, supplement issue 1 (2023), pp. 59-69 |