Abstract
The recently developed idea of analyzing complex networks in terms of node displacement due to vibration (Estrada and Hatano, Chem Phys Lett 486:166–170, 2010a) is applied to fullerenes. The fact that the ramafullerenes (fullerenes of Ramanujan graphs) are limited to fullerenes with relatively small number of C atoms is explained from the point of view of the node displacement. The node displacement is also shown to indicate the stability of isomers of C40 fullerenes. It is suggested from the analysis of local node displacement that instability of fullerenes mainly comes from pentagon-rich areas of the molecules.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Albertazzi A, Domene C, Fowler PW, Heine T, Seifert G, Van Alsenoy C, Zerbetto F (1999) Phys Chem Chem Phys 1:2913
Aldersey-Williams H (1995) The most beautiful molecule: the discovery of the buckyball. Wiley, London
Alon N (1986) Combinatorica 6:83
Alon N, Milman VD (1985) J Combin Theory Ser B 38:73
Balaban AT, Liu X, Klein DJ, Babić D, Schmalz TG, Seitz WA, Randić M (1995) J Chem Inf Comput Sci 35:396
Campbell EEB, Fowler PW, Mitchell D, Zerbetto F (1996) Chem Phys Lett 250:544
Doslić T (2005) Chem Phys Lett 412:336
Doslić T (2008) J Math Chem 43:647
Estrada E, Hatano N (2010a) Chem Phys Lett 486:166–170
Estrada E, Hatano N (2010b) In: Gutman I, Furtula B (eds) Novel molecular descriptors. Theory and applications I. Mathematical chemistry monographs No. 8. University of Kragujevac, Serbia, p 3
Fajtlowitz S, Larson SE (2003) Chem Phys Lett 377:485
Fowler PW (2002) Croat Chem Acta 75:401
Fowler PW (2003) MATCH Commun Math Comput Chem 48:87–96
Fowler PW, Manolopoulos DE (1995) An atlas of fullerenes. Clarendon Press, Oxford. Reprinted: Dover, New York, NY (2006)
Fowler PW, Rogers KM, Fajtlowick S, Hansen P, Capporosi G (1999) Facts and conjectures about fullerene graphs: leapfrog, cylinder and ramanujan fullerenes. Les Cahiers du GERAD, G-99-66
Hoory S, Linial N, Wigderson A (2006) Bull Am Math Soc 43:439
Klein DJ, Randić M (1993) J Math Chem 12:81
Lubotzky A, Phillips R, Sarnak P (1988) Combinatorica 9:261
Manolopoulos DE, May JC, Down SE (1991) Chem Phys Lett 181:105
Pierson HO (1993) Handbook of carbon, graphite, diamond and fullerenes. properties, processing and applications. Noyes Pub, New Jersey
Ram Murty M (2003) J Ramanujan Math Soc 18:1
Réti T, László I (2009) Acta Polytech Hung 6:85
Xiao W, Gutman I (2003) Theor Chem Acc 110:284–289
Zhang H, Balasubramanian K (1993) J Phys Chem 97:10341
Acknowledgements
EE thanks P. Fowler for providing the dataset of C40 isomers used in this study. EE thanks New Professor’s Fund of the University of Strathclyde for partial financial support. ARM thanks FONDECYT (Chile) under grant No. 1080561
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer Netherlands
About this chapter
Cite this chapter
Estrada, E., Hatano, N., Matamala, A.R. (2011). A Graph Theoretic Approach to Atomic Displacements in Fullerenes. In: Cataldo, F., Graovac, A., Ori, O. (eds) The Mathematics and Topology of Fullerenes. Carbon Materials: Chemistry and Physics, vol 4. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0221-9_9
Download citation
DOI: https://doi.org/10.1007/978-94-007-0221-9_9
Published:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-007-0220-2
Online ISBN: 978-94-007-0221-9
eBook Packages: Chemistry and Materials ScienceChemistry and Material Science (R0)