Gilles Caporossi

A constructive enumeration of fusenes and benzenoids

In this paper, a fast and complete method to constructively enumerate fusenes and benzenoids is given. It is fast enough to construct several million nonisomorphic structures per second. The central idea is to represent fusenes as labelled inner duals and generate them in a two step approach using the canonical construction path method and the homomorphism principle.

Facts and Conjectures about Fullerene Graphs: Leapfrog, Cylinder and Ramanujan Fullerenes

The definition of a fullerene as a cubic polyhedron made up entirely of pentagons and hexagons is compatible with a huge variety of isomeric forms for structures of chemically achievable size (n ~ 100 or fewer vertices ≡ carbon atoms). Generation of complete sets of structures in this size range allows evaluation of conjectures, both chemical and mathematical, on energetics and graph-theoretical properties of this class of molecular graphs. Counterexamples to conjectures of GRAFFITI, including some on fullerenes that are Ramanujan graphs (ramafullerenes) are provided. Graph-theoretical indicators for closure of π shells and low overall energy of fullerenes are also briefly discussed.