On the number of fair dominating sets of graphs
Saeid Alikhani, Maryam Safazadeh · Advanced Studies Euro-Tbilisi Mathematical Journal · 2023
Let 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.