title: The topology of fullerenes.
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.WIREs Comput Mol Sci2015, 5:96-145. doi: 10.1002/wcms.1207 Conflict of interest: The authors have declared no conflicts of interest for this article. For further resources related to this article, please visit the WIREs website.
authors: Centre for Theoretical Chemistry and Physics, The New Zealand Institute for Advanced Study, Massey University Auckland Auckland, New Zealand ; Fachbereich Chemie, Philipps-Universität Marburg Marburg, Germany.
authors: Peter
authors: P
authors: Schwerdtfeger
authors: Centre for Theoretical Chemistry and Physics, The New Zealand Institute for Advanced Study, Massey University Auckland Auckland, New Zealand.
authors: Lukas N
authors: LN
authors: Wirz
authors: Niels Bohr Institute, University of Copenhagen Copenhagen, Denmark.
authors: James
authors: J
authors: Avery