b-Chromatic Number of Some Operations on Cycle and Path

Abstract

A b-vertex coloring of a graph G is a proper vertex coloring of G such that each color class contains a vertex that has at least one vertex in every other color class in its  neighborhood. Here, the paper deals with the b-chromatic number of adding parallel chords in Cycle, Union of Path with Cycle and its complement, deletion and addition of vertices and edges in a Cycle.