A dominated coloring of a graph G is a proper vertex coloring where each color class is dominated by at least one vertex of G. The dominated chromatic number of G, denoted ?dom (G), is the m inimum number of colors required for a dominated coloring of G. In this paper, we provide new bounds for ?dom (G) and characterize all graphs that achieve some of these bounds. Also we investigate graphs G for which ?dom (G) = ?(G) where ?(G) is the chromatic number of G, in particular we give a characterization o ? cubic graphs G such that ?dom (G) = ?(G).
Benkaci et al. (Wed,) studied this question.