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Schwerdtfeger P, Wirz LN, Avery J. The topology of fullerenes. Wiley Interdiscip Rev Comput Mol Sci. 2015;5(1):96-145doi: 10.1002/wcms.1207.
Schwerdtfeger, P., Wirz, L. N., & Avery, J. (2015). The topology of fullerenes. Wiley interdisciplinary reviews. Computational molecular science, 5(1), 96-145. https://doi.org/10.1002/wcms.1207
Schwerdtfeger, Peter, et al. "The topology of fullerenes." Wiley interdisciplinary reviews. Computational molecular science vol. 5,1 (2015): 96-145. doi: https://doi.org/10.1002/wcms.1207
Schwerdtfeger P, Wirz LN, Avery J. The topology of fullerenes. Wiley Interdiscip Rev Comput Mol Sci. 2015 Jan;5(1):96-145. doi: 10.1002/wcms.1207. PMID: 25678935; PMCID: PMC4313690.
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Wiley Interdiscip Rev Comput Mol Sci. 2015 Jan;5(1):96-145. doi: 10.1002/wcms.1207.

The topology of fullerenes.

Wiley interdisciplinary reviews. Computational molecular science

Peter Schwerdtfeger, Lukas N Wirz, James Avery

Affiliations

  1. 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.
  2. Centre for Theoretical Chemistry and Physics, The New Zealand Institute for Advanced Study, Massey University Auckland Auckland, New Zealand.
  3. Niels Bohr Institute, University of Copenhagen Copenhagen, Denmark.

PMID: 25678935 PMCID: PMC4313690 DOI: 10.1002/wcms.1207

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.

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