In this article we introduce a new graph coloring called the b_q-coloring. A b_q-coloring of a graph G is a proper vertex coloring of G with k colors such that every color class c admits a set of vertices S, of size at most q, such that every color except c appears in the neighborhood of S. The aim of this coloring is to generalize the domination constraint given in the b-coloring of a graph where every color admits only one dominating vertex (adjacent to every other color). The largest positive integer k for which a graph has a b_q-coloring using k colors is the b_q-chromatic number. We present some classes of graphs for which the b_q-chromatic number has maximum value and we give exact values of this parameter for paths and cycles. We also present some bounds for Cartesian products of graphs.