On Certain Colouring Parameters of Mycielski Graphs of Some Graphs

TL;DR

This paper investigates the statistical properties of vertex colourings in Mycielski graphs derived from standard graphs, focusing on mean and variance of colour distributions.

Contribution

It introduces the analysis of colouring parameters, specifically mean and variance, for the Mycielski graphs of certain standard graphs, extending previous graph colouring studies.

Findings

Calculated mean and variance of colour distributions for Mycielski graphs.

Extended statistical graph colouring concepts to Mycielski constructions.

Provided new insights into colouring parameters of complex graph classes.

Abstract

Colouring the vertices of a graph $G$ according to certain conditions can be considered as a random experiment and a discrete random variable $X$ can be defined as the number of vertices having a particular colour in the proper colouring of $G$. The concepts of mean and variance, two important statistical measures, have also been introduced to the theory of graph colouring and determined the values of these parameters for a number of standard graphs. In this paper, we discuss the colouring parameters of the Mycielskian of certain standard graphs.