On certain parameters of equitable coloring of graphs

Abstract

Coloring the vertices of a graph [Formula: see text] according to certain conditions is a random experiment and a discrete random variable [Formula: see text] is defined as the number of vertices having a particular color in the given type of coloring of [Formula: see text] and a probability mass function for this random variable can be defined accordingly. An equitable coloring of a graph [Formula: see text] is a proper coloring [Formula: see text] of [Formula: see text] which an assignment of colors to the vertices of [Formula: see text] such that the numbers of vertices in any two color classes differ by at most one. In this paper, we extend the concepts of arithmetic mean and variance, the two major statistical parameters, to the theory of equitable graph coloring and hence determine the values of these parameters for a number of standard graphs.