b –Coloring of the Comb product of Extended Duplicate graph of Cycle graph Networks with Path graph

Abstract

The b – chromatic number which is ????(????), the highest k such that graph can be b – colored using k colors. At least one vertex in every color group is adjacent to a vertex in every other color group. In this work we acquire b – chromatic number of the middle graph of an extension of duplicate graph of cycle graph (M[EDG(Cn)]), total graph of an extension of duplicate graph of cycle graph (T[EDG(Cn)]), Comb Product of middle graph of an extension of duplicate graph of cycle with (Pn) and Comb Product of total graph of an extension of duplicate graph of cycle with (Pn).