A proper coloring of the graph assigns colors to the vertices, edges, or both so that proximal elements are assigned distinct colors. Concepts and questions of graph coloring arise naturally from practical problems and have found applications in many areas, including Information Theory and most notably Theoretical Computer Science. A b-coloring of a graph G is a proper coloring of the vertices of G such that there exists a vertex in each color class joined to at least one vertex in each other color class. The b-chromatic number of a graph G, denoted by uðGÞ, is the maximal integer k such that G may have a b-coloring with k colors. In this paper, we obtain the b-chromatic number for the sun let graph S n , line graph of sun let graph LðS n Þ, middle graph of sun let graph MðS n Þ, total graph of sun let graph TðS n Þ, middle graph of wheel graph MðW n Þ and the total graph of wheel graph TðW n Þ. 1991 MATHEMATICS SUBJECT CLASSIFICATION: 05C15; 05C75; 05C76 ª 2014 Production and hosting by Elsevier B.V. on behalf of Egyptian Mathematical Society.