Let G be a finite group and X a subset of G. The commuting graph C(G,X) is the graph whose vertex set is X with two distinct elements of X joined by an edge whenever they commute in the group G. This thesis studies the structure of commuting graphs C(G,X) when G is either a symmetric group Sym(n) or a sporadic group McL, and X a conjugacy class for elements of order three. We describe how this graph can be useful in understanding various aspects of the structure of the group with a particular emphasis on the connectivity of the graph, the properties of the discs around some fixed vertex and the diameter of the graph.
Date of Award  1 Aug 2013 

Original language  English 

Awarding Institution   The University of Manchester


Supervisor  Peter Rowley (Supervisor) & Louise Walker (Supervisor) 

 connectivity
 commuting graph
 elements of order three
 symmetric group
 diameter
Commuting graphs for elements of order three in finite groups
Nawawi, A. (Author). 1 Aug 2013
Student thesis: Phd