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 Sn, line graph of sun let graph LðSnÞ, middle graph of sun let graph
MðSnÞ, total graph of sun let graph TðSnÞ, middle graph of wheel graph MðWnÞ and the total graph
of wheel graph TðWnÞ.