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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...
Autores principales: | , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
John Wiley & Sons, Ltd.
2015
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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. |
format | Online Article Text |
id | pubmed-4313690 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2015 |
publisher | John Wiley & Sons, Ltd. |
record_format | MEDLINE/PubMed |
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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