On unique realizations of domination chain parameters

摘要

The domination chain ir{G) ≤ γ(G) ≤ i(G) ≤ β_0{G) ≤ Γ(G) ≤ I R(G), which holds for any graph G, is the subject of much research. In this paper, we consider the maximum number of edges in a graph having one of these domination chain parameters equal to 2 through a unique realization. We show that a specialization of the domination chain still holds in this setting.