b –Coloring of Comb Product of Extended Duplicate graph of Path Networks

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 Path graph (M[EDG(Pn)]), total graph of an extension of duplicate graph of Path graph (T[EDG(Pn)]), Comb Product of middle graph of an extension of duplicate graph of path with (Pn) and Comb Product of total graph of an extension of duplicate graph of path with (Pn).