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 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)∣ – ∆(G).