# Topology of Interconnection Networks as Modelled by Graphs

*by Professor Mirka Miller*

*Institution:*School of ITMS, University of Ballarat

*Date: Fri 20th May 2005*

*Time: 1:05 PM*

*Location: Room 213, Richard Berry Building, Department of Mathematics and Statistics, University of Melbourne*

*Abstract*: Networks govern all aspects of society, including transportation,

communication networks, computer networks, social networks, and networks

for the distribution of goods etc. and the theoretical analysis of such

networks has become a subject of fundamental importance. Networks can be

modelled by graphs.

Such a network (graph) consists of a number of nodes and some connections

(either unidirectional or bidirectional) between nodes. An interesting

measure related to the performance of a network is its diameter which is

the maximum distance between any two nodes of the network. Given a limited

number of connections (degree) available at any node and given the desired

value of the network diameter, the following problem has been of

interest:

Degree/diameter problem: Given maximum degree and diameter, what is the

largest possible number of nodes in a network?

In this talk we give an overview of the degree/diameter problem and we

present some recent new results.

*For More Information:* Mark Fackrell tel: 8344-8053 email: m.fackrell@ms.unimelb.edu.au