Which fullerenes are stable?

Document Type: Original Article

Author

University of Kashan

Abstract

A fullerene is a molecule composed of carbon in the shape of a hollow sphere, ellipsoid, tube, and many other forms. The spherical ones are called buckyballs and they look like the balls used in football game. The first stable cluster of fullerenes was discovered by Kroto and his co-authors who received the Nobel Prize. In this paper, we introduced some classes of stable fullerene graphs.

Graphical Abstract

Which fullerenes are stable?

Keywords

Main Subjects


[1] D. Babić, D.J. Klein, and C.H. Sah, Symmetry of fullerenes, Chem. Phys. Lett. 211(1993) 235–241.
[2] A. Behmaram, Matching in fullerene and molecular graphs, Ph. D thesis, University of Tehran, 2013.
[3] P.R. Cromwell, Polyhedra, Cambridge University Press, Cambridge, 1997.

[4] M. Deza, M. Dutour Sikirić and P. W. Fowler, Zigzags, railroads, and knots in fullerenes, J. Chem. Inf. Comp. Sci. 44 (2004) 1282-1293.
[5] P.W. Fowler, D.E. Manolopoulos, D.B. Redmond, and R.P. Ryan, Possible Symmetries of Fullerene Structures, Chem. Phys. Lett. 202 (1993) 371–378.
[6] P.W. Fowler and D.E. Manolopoulos, An Atlas of Fullerenes, Clarendon Press, Oxford, 1995.
[7] C. Godsil, G. Royle, Algebraic Graph Theory, Springer, New York, 2001.
[8] J. E. Graver, Kekulé structures and the face independence number of a fullerene, Eur. J. Combin. 28 (2007) 1115–1130.

[9] J. E. Graver, Encoding fullerenes and geodesic domes, SIAM. J. Discr.Math. 17 (2004) 596–614.
[10] B. King, M. V. Diudea, The chirality of icosahedral fullerenes: a comparison of the tripling (leapfrog), quadrupling (chamfering), and septupling (capra) trasformations, J. Math. Chem. 39 (2006) 597–604.
[11] H. W. Kroto, J. R. Heath, S. C. Obrien, R. F. Curl, R.E. Smalley, C60: Buckminsterfullerene, Nature 318 (1985) 162-163.
[12] H. W. Kroto, J. E. Fichier, D. E Cox, The Fullerene, Pergamon Press, New York, 1993.
[13] K. Kutnar, D. Marusic, On cyclic edge-connectivity of fullerenes, Discr. Appl. Math.156 (2008) 1661–1669.
[14] K. Kutnar, D. Marusic, D. Janezic, Fullerenes via their automorphism groups, MATCH Commun. Math. Comput. Chem., 63 (2010) 267-282.
[15] P. Mani, Automorphismen von polyedrischen Graphen, Math. Annalen. 192 (1971) 279–303.
[16] H. Zhang and D. Ye, An upper bound for the Clar number of fullerene graphs, J. Math. Chem. 41 (2007) 123 – 133.


Volume 5, 1-2
Summer and Autumn 2015
Pages 23-29
  • Receive Date: 11 December 2014
  • Revise Date: 05 February 2015
  • Accept Date: 16 May 2015