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

Patrick W. Fowler, Kevin M. Rogers, Siemion Fajtlowicz, Pierre Hansen and Gilles Caporossi
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Patrick W. Fowler: University of Exeter, School of Chemistry
Kevin M. Rogers: University of Exeter, School of Chemistry
Siemion Fajtlowicz: University of Houston, Department of Mathematics
Pierre Hansen: GERAD and École des Hautes Études Commerciales
Gilles Caporossi: GERAD and École des Hautes Études Commerciales

A chapter in Algebraic Combinatorics and Applications, 2001, pp 134-146 from Springer

Abstract: 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.

Keywords: Large Separator; Black Vertex; Eigenvalue Spectrum; Fullerene Graph; High Fullerene (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1007/978-3-642-59448-9_10

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