G-graphs: A new representation of groups

An important part of computer science is focused on the links that can be established between group theory and graph theory and graphs. Cayley graphs, that establish such a link, are useful in a lot of areas of sciences. This paper introduces a new type of graph associated with a group, the G-graphs, and presents many of their properties. We show that various characteristics of a group can be seen on its associated G-graph. We also present an implementation of the algorithm constructing these new graphs, an implementation that will lead to some experimental results. Finally we show that many classical graphs are G-graphs. The relations between G-graphs and Cayley graphs are also studied.