Some new results on equitable coloring parameters of graphs

Abstract

An equitable colouring of a graph $G$ is a proper vertex coloring $\C$ of $G$ such that the cardinalities of any two color classes in $G$ with respect to $\C$ differ by at most one.  Coloring the vertices of a graph $G$ subject to given conditions can be considered as a random experiment. In this context, a discrete random variable $X$ can be defined as the color of a vertex chosen at random, with respect to the given type of coloring of $G$ and a probability mass function for this random variable can be defined accordingly.   In this paper, we discuss two statistical parameters of the powers of certain graph classes, with respect to their equitable colorings.