Some Results on the $b$-Colouring Parameters of Graphs

Abstract

A vertex colouring of a given graph G can be considered as a random experiment. A discrete random variable X, corresponding to this random experiment, can be defined as the colour of a randomly chosen vertex of G and a probability mass function for this random variable can be defined accordingly. In this paper, we study the concepts of mean and variance corresponding to the b-colouring of G and hence determine the values of these parameters for a number of standard graphs.