On Equitable Coloring Parameters of Certain Cycle Related Graphs

Abstract

Coloring the vertices of a graph G subject to given conditions can be considered as a random experiment and corresponding to this experiment, a discrete random variable X can be defined as the colour of a vertex chosen at random, with respect to the given type of colouring of G and a probability mass function for this random variable can be defined accordingly. A proper coloring C of a graph G, which assigns colors to the vertices of G such that the numbers of vertices in any two colour classes differ by at most one, is called an equitable colouring of G. In this paper, we study two statistical parameters of certain cycle related graphs, with respect to their equitable colorings.