Graphical and computational representation of groups

Abstract

An important part of the computer science is focused on the links that can be established between group theory and graph theory. CAYLEY graphs can establish such a link but meet some limitations. This paper introduces a new type of graph associated to a group: the G-graphs. We present an implementation of the algorithm constructing these new graphs. We establish a library of the most common G-graphs, using GAP and the SmallGroups library. We give some experimental results with GAP and we show that many classical graphs are G-graphs. © Springer-Verlag Berlin Heidelberg 2004.