On equality in an upper bound for the equivalence domination number

Abstract

Let G = (V, E) be a graph. A subset S of V is called an equivalence set if every component of the induced subgraph ⟨S⟩ is complete. The equivalence domination number γ_e(G) is the minimum cardinality of an equivalence dominating set of G. In this paper we investigate the structure of graphs G satisfying γ_e(G) = |V (G)| − Δ(G).

Keywords: Dominating set, equivalence set, independent set, equivalence domination number.