Gilles Caporossi and Pierre Hansen - Variable neighborhood search for extremal graphs B.  automated search for relations between graph invariants

The AutoGraphiX system is designed to find (heuristically) extremal graphs for some invariant, possibly subject to constraints. Using parametrisation, a set of presumably extremal graphs may be produced from which some conjectures may be found. We aim here to automate this process, thus making the system completely automated. Three approaches used are to be described here: A numerical one, using principal component analysis in a particular way, a geometric one based on the definition of a convex hull of the graphs in the space of chosen invariants, and an algebraic one based upon recognition of famillies of extremal graphs and known relations for the so found famillies of graphs.