On the Maximum Number of Dominating Classes in Graph Coloring

Abstract

In this paper we investigate the dominating- -color number، of a graph <em>G</em>. That is the maximum number of color classes that are also dominating when <em>G</em> is colored using colors. We show that where is the join of <em>G</em> and H. This result allows us to construct classes of graphs such that and thus provide some information regarding two questions raised in [1] and [2].