The topology of fullerenes

Peter Schwerdtfeger, Lukas Wirz, James Emil Avery

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    Abstract

    Fullerenes are carbon molecules that form polyhedral cages. Their bond structures are exactly the planar cubic graphs that have only pentagon and hexagon faces. Strikingly, a number of chemical properties of a fullerene can be derived from its graph structure. A rich mathematics of cubic planar graphs and fullerene graphs has grown since they were studied by Goldberg, Coxeter, and others in the early 20th century, and many mathematical properties of fullerenes have found simple and beautiful solutions. Yet many interesting chemical and mathematical problems in the field remain open. In this paper, we present a general overview of recent topological and graph theoretical developments in fullerene research over the past two decades, describing both solved and open problems.
    Original languageEnglish
    JournalWiley Interdisciplinary Reviews: Computational Molecular Science
    Volume5
    Issue number1
    Pages (from-to)96-145
    ISSN1759-0876
    DOIs
    Publication statusPublished - 1 Nov 2014

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