Research Interests
 Algebraic Graph Theory
 Graph Structure and Dynamics
 Random Graph Processes
 Network Optimisation
 Algebraic Combinatorics
 Operations Research
Research Groups
Extra Information
My research interest lies in (1) Network Optimization, (2) Algebraic Combinatorics, and (3) Random Graph Processes, which are very active areas in the broad subject of Discrete Mathematics. In (1) I have been working on some network optimisation problems arising from Theoretical Computer Science, Interconnection Networks and Telecommunication. These include the routing, optimal labelling, graph layout, channel assignment, domination and colouring problems. In (2) I have been studying the structure of those graphs which are symmetric with respect to vertices or/and arcs, where an arc is an edge with direction. Roughly speaking, in an arcsymmetric (a vertexsymmetric) graph all arcs (vertices) have the "same" position in the graph. My work in this area involves Permutation Group Theory, Finite Geometry, Design Theory and Regular Maps on surfaces. Intuitively, a random graph process is a process of "growing up" graphs according to some stochastic rule. My research in (3) is focused on some random graph processes which arise from the design and analysis of some randomized algorithms and from simulating the evolution of the Internet and other complex realworld networks.
Current Postgraduate Supervision
Name 
Thesis title 
Patrick ANDERSEN 
"Coverage and connectivity in wireless sensor networks" 
Nemanja POZNANOVIC 

Muhammad Adib SURANI 
"The Isoperimetric Problem in Block Designs" 
Past Postgraduate Supervision
Name 
Thesis title 
Daniel HARVEY 
"An investigation into graph minors" 
Xiaogang LIU 
"Spectral Characterisation of Graphs" 
Hamid MOKHTAR 
"Routing and wavelength assignment in communication networks" 
Michael PAYNE 
"Problems in geometric graph theory" 
Ricky ROTHERAM 
"Cayley Graphs and network optimization." 
Alison THOMSON 
"Graph theory problems arising from optical networks" 
Guangjun XU 
"Cayley graphs, network design and domination" 
Zuhe ZHANG 
"Analysis of networks: privacy in Bayesian networks and problems in lattice models" 
Current MSc Students
Name 
Project title 
Bi WEI 

Past MSc Students
Name 
Project title 
Robin LANGER 

Yang LI 

Muhammad Adib SURANI 

Pongphat TAPTAGAPORN 

Victoria WYATT 

Subject(s) Currently Teaching
Code 
Subject 
MAST30011 (620352) 
Graph theory (Semester 1) 
Recent Grant History
Year(s) 
Source 
Type 
Title 
2012  2014 
ARC 
Discovery 
Hadwiger's graph colouring conjecture 
2011  2015 
ARC 
Future Fellow 
Expander graphs, isoperimetric numbers, and forwarding indices 
Responsibilities
 Discrete Structures and Algorithms Seminar Coordinator
 MPRHMS
 Science International Advisory Committee (SIAC)
Committees
 Faculty International Advancement Committee
 Recruitment and Publicity Committee
 Strategic Planning Committee