A b-coloring is a proper k-coloring of the vertices of a graph such that each color class has a vertex that is adjacent to a vertex of every other color class. The b-chromatic number of a graph G is the largest integer k such that G admits a b-coloring with k colors. A graph G is said to be stable b-chromatic graph if b(G.uv) = b(G) for every u,v ε V (G) with u is adjacent to v. In this paper we obtain some basic properties of bs-chromatic graphs. © 2016 Academic Publications, Ltd.