Ext. Number:
  • Algebraic Graph Theory
  • Graph Structure and Dynamics
  • Random Graph Processes
  • Network Optimisation
  • Algebraic Combinatorics
  • Operations Research
Recent Publications:
  • Radio number of trees (2017) more
  • Networking for Big Data: A Survey (2017) more
  • Perfect codes in circulant graphs (2017) more
  • Radio number of trees (2017) more
  • Recursive cubes of rings as models for interconnection networks (2017) more

Selected Publications

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 arc-symmetric (a vertex-symmetric) 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 real-world networks.
Current Postgraduate Supervision:
Patrick ANDERSEN "Coverage and connectivity in wireless sensor networks"
Muhammad Adib SURANI "The Isoperimetric Problem in Block Designs"
Past Postgraduate Supervision:
Daniel HARVEY "An investigation into graph minors"
Xiaogang LIU "Spectral Characterisation of Graphs"
Hamid MOKHTAR "Routing and wavelength assignment in communication networks"
Michael Stuart 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 "Entropy Constants of Lattices on Plane, Cylinder and Torus"
Current MSc Students:
Subject(s) Currently Teaching:
MAST30011 (620-352) Graph theory (Semester 1, 2017)
Recent Grant History:
Year(s) Source Type Title
2011 - 2015 ARC Future Fellow Expander graphs, isoperimetric numbers, and forwarding indices
2012 - 2014 ARC Discovery Hadwiger's graph colouring conjecture
2005 - 2007 ARC Discovery Channel Assignment in Cellular Communication Systems and Optical Networks
2003 - 2005 ARC Discovery Interconnection Network Routing and Graph Symmetry
Discrete Structures and Algorithms Seminar Coordinator
Faculty International Advancement Committee (Member)
Recruitment and Publicity Committee