The objective of this proposal is to bring to Europe a high-level conference reviewing the recent developments in algebraic graph theory, looking in particular at applications to chemistry. Algebraic graph theory has prospered in small groups spread throughout the world and the proposed meeting will bring these researchers together for the first time since 1993. The meeting is timely in that recent research resulting from a workshop in discrete mathematical chemistry (held in 1998 in the USA) clearly demonstrates that algebraic graph theory has important application for aspects or chemical research, namely the understanding of the molecular structure of fullerenes. This meeting will complement that held in the USA. At that meeting the majority of participants had a background in chemistry. The intention is that this meeting will consist largely of mathematicians, with a small number of chemists and mathematical chemists invited to help outline the most fruitful areas for interdisciplinary collaboration.