Domination‐balanced graphs

Abstract

Abstract A set D of vertices in a graph is said to be a dominating set if every vertex not in D is adjacent to some vertex in D. The domination number β( G ) of a graph G is the size of a smallest dominating set. G is called domination balanced if its vertex set can be partitioned into β( G ) subsets so that each subset is a smallest dominating set of the complement G of G. The purpose of this paper is to characterize these graphs.