  We present Digenes, a new discovery system that aims to help researchers in
graph theory. While its main task is to find extremal graphs for a given
(function of) invariants, it also provides some basic support in proof
conception. This has already been proved to be very useful to find new
conjectures since the AutoGraphiX system of Caporossi and Hansen (Discrete
Math. 212-2000). However, unlike existing systems, Digenes can be used both
with directed or undirected graphs. In this paper, we present the principles
and functionality of Digenes, describe the genetic algorithms that have been
designed to achieve them, and give some computational results and open
questions. This do arise some interesting questions regarding genetic
algorithms design particular to this field, such as crossover definition.
