On certain parameters of equitable coloring of graphs
Abstract
Coloring the vertices of a graph GG according to certain conditions is a random experiment and a discrete random variable XX is defined as the number of vertices having a particular color in the given type of coloring of GG and a probability mass function for this random variable can be defined accordingly. An equitable coloring of a graph GG is a proper coloring 𝒞 of G which an assignment of colors to the vertices of G 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.
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