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The topology of fullerenes

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 grap...

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Detalles Bibliográficos
Autores principales: Schwerdtfeger, Peter, Wirz, Lukas N, Avery, James
Formato: Online Artículo Texto
Lenguaje:English
Publicado: John Wiley & Sons, Ltd. 2015
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4313690/
https://www.ncbi.nlm.nih.gov/pubmed/25678935
http://dx.doi.org/10.1002/wcms.1207
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author Schwerdtfeger, Peter
Wirz, Lukas N
Avery, James
author_facet Schwerdtfeger, Peter
Wirz, Lukas N
Avery, James
author_sort Schwerdtfeger, Peter
collection PubMed
description 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 Sci 2015, 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.
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spelling pubmed-43136902015-02-10 The topology of fullerenes Schwerdtfeger, Peter Wirz, Lukas N Avery, James Wiley Interdiscip Rev Comput Mol Sci Focus Article 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 Sci 2015, 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. John Wiley & Sons, Ltd. 2015-01 2014-10-27 /pmc/articles/PMC4313690/ /pubmed/25678935 http://dx.doi.org/10.1002/wcms.1207 Text en © 2014 The Authors. WIREs Computational Molecular Science published by John Wiley & Sons, Ltd. http://creativecommons.org/licenses/by-nc-nd/3.0/ This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.
spellingShingle Focus Article
Schwerdtfeger, Peter
Wirz, Lukas N
Avery, James
The topology of fullerenes
title The topology of fullerenes
title_full The topology of fullerenes
title_fullStr The topology of fullerenes
title_full_unstemmed The topology of fullerenes
title_short The topology of fullerenes
title_sort topology of fullerenes
topic Focus Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4313690/
https://www.ncbi.nlm.nih.gov/pubmed/25678935
http://dx.doi.org/10.1002/wcms.1207
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