On b-chromatic number of sun let graph and wheel graph families

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 φ(G)φ(G), 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 SnSn, line graph of sun let graph L(Sn)L(Sn), middle graph of sun let graph M(Sn)M(Sn), total graph of sun let graph T(Sn)T(Sn), middle graph of wheel graph M(Wn)M(Wn) and the total graph of wheel graph T(Wn)T(Wn).