Abstract
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.
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Fowler, P.W., Rogers, K.M., Fajtlowicz, S., Hansen, P., Caporossi, G. (2001). Facts and Conjectures about Fullerene Graphs: Leapfrog, Cylinder and Ramanujan Fullerenes. In: Betten, A., Kohnert, A., Laue, R., Wassermann, A. (eds) Algebraic Combinatorics and Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59448-9_10
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