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Clar chains and a counterexample

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Abstract

A fullerene is a 3-regular plane graph with only pentagonal and hexagonal faces. The Fries and Clar number of a fullerene are two related parameters, and the Clar number is less understood. We introduce the Clar Structure of a fullerene, a decomposition designed to compute the Clar number for classes of fullerenes. We also settle an open question with a counterexample: we prove that the Clar and Fries number of a fullerene cannot always be obtained with the same Kekulé structure.

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Authors and Affiliations

  1. Massachusetts College of Liberal Arts, North Adams, MA, USA

    Elizabeth J. Hartung

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  1. Elizabeth J. Hartung
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Correspondence to Elizabeth J. Hartung.

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Hartung, E.J. Clar chains and a counterexample. J Math Chem 52, 990–1006 (2014). https://doi.org/10.1007/s10910-014-0305-5

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  • DOI: https://doi.org/10.1007/s10910-014-0305-5

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