On the domination number of graphs with minimum degree at least seven

A dominating set in a graph G is a set S⊆V(G) such that every vertex that is not in S is adjacent to a vertex from it. The domination number γ(G) is the minimum cardinality of a dominating set in G. For k≥1, let G_k denote the class of all connected graphs with minimum degree at least k. The problem to determine or estimate the best possible constants c_dom,k (which depend only on k) such that γ(G)≤c_dom,k⋅n(G) for all G∈G_k is well studied, where n(G) denotes the order of G. In this paper we establish best known lower and upper bounds to date on the constant c_dom,7, namely [Formula presented]≤c_dom,7≤[Formula presented].