<![CDATA[Let G be a graph. A proper k-coloring of G is coloring all vertices of G with k colors such that every two adjacent vertices are assigned different colors. The minimum value of k for which a proper k-coloring of G exist is called the chromatic number of G. A b-coloring of G is a proper k-coloring of G such that each color class has a representative that is adjacent to at least one vertex in each of the other color classes. The largest positive integer k such that there is a b-coloring of G is called the b-chromatic number of G, denoted . In this article, we establish the b-chromatic number of the central graph on the star graph , the b-chromatic number of the middle graph on the star graph and the b-chromatic number of total graph on the star graph . Keywords : Chromatic Number; B-chromatic Number; Star Graf]]>
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