Restrained Domination Excellent Trees

Abstract

A set \(S\) of vertices in a graph \(G = (V, E)\) is a restrained dominating set of \(G\) if every vertex not in \(S\) is adjacent to a vertex in \(S\) and to a vertex in \(V \setminus S\). The graph \(G\) is called restrained domination excellent if every vertex belongs to some minimum restrained dominating set of \(G\). We provide a characterization of restrained domination excellent trees.