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The topology of fullerenes
Author(s) -
Schwerdtfeger Peter,
Wirz Lukas N,
Avery James
Publication year - 2014
Publication title -
wiley interdisciplinary reviews: computational molecular science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 5.126
H-Index - 81
eISSN - 1759-0884
pISSN - 1759-0876
DOI - 10.1002/wcms.1207
Subject(s) - fullerene , pentagon , planar graph , cheminformatics , planar , combinatorics , computer science , topology (electrical circuits) , mathematics , computational chemistry , graph , chemistry , physics , quantum mechanics , geometry , computer graphics (images)
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.