Connective eccentric index of fullerenes

Document Type : Original Article

Author

Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran, 16785 – 136, I. R. Iran

Abstract

Fullerenes are carbon-cage molecules in which a number of carbon atoms are bonded in a nearly spherical configuration. The connective eccentric index of graph G is defined as C (G)= Σa V(G)deg(a)ε(a) -1, where ε(a) is defined as the length of a maximal path connecting a to another vertex of G. In the present paper we compute some bounds of the connective eccentric index and then we calculate this topological index for two infinite classes of fullerenes.

Graphical Abstract

Connective eccentric index of fullerenes

Keywords

References

REFERENCES
1. V. Sharma, R. Goswami and A. K. Madan, Eccentric connectivity index: a novel highly discriminating topological descriptor for structure property and structure activity studies, J. Chem. Inf. Comput. Sci., 37 (1997), 273 – 282.
2. B. Zhou and Z. Du, Minimum Wiener indices of trees and unicyclic graphs of given matching number, MATCH Commun. Math. Comput. Chem., 63(1) (2010), 101 – 112.
3. A. Dobrynin and A. Kochetova, Degree distance of a graph: A degree analogue of the Wiener index, J. Chem., Inf., Comput. Sci., 34(1994), 1082 – 1086.
4. I. Gutman, Selected properties of the Schultz molecular topogical index, J. Chem. Inf. Comput. Sci., 34(1994), 1087 – 1089.
5. I. Gutman and O. E. Polansky, Mathematical concepts in organic Chemistry, Springer-Verlag, New York, 1986.
6. M. A. Johnson and G. M. Maggiora, Concepts and applications of molecular similarity,Wiley Interscience, New York, 1990.
7. S. Gupta, M. Singh and A. K. Madan, Connective eccentricity Index: A novel topological descriptor for predicting biological activity, J. Mol. Graph. Model., 18 (2000), 18 – 25.
8. H. W. Kroto, J. R. Heath, S. C. O’Brien, R. F. Curl and R. E. Smalley, C60: Buckminsterfullerene, Nature, 318 (1985), 162 – 163.
9. H. W. Kroto, J. E. Fichier and D. E. Cox, The fullerene, Pergamon Press, New York, 1993.
10. N. Trinajstić and I. Gutman, Mathematical Chemistry, Croat. Chem. Acta, 75 (2002), 329 – 356.
11. A. R. Ashrafi, M. Ghorbani and M. Jalali, Computing sadhana polynomial of V -phenylenic nanotubes and nanotori, Indian J. Chem., 47 (2008), 535 – 537.
12. A. R. Ashrafi and M. Ghorbani, PI and Omega polynomials of IPR fullerenes, Fullerenes, Nanotubes and Carbon Nanostructures, 18(3) (2010), 198 – 206.
13. A. R. Ashrafi, M. Ghorbani and M. Jalali, Study of IPR fullerenes by counting polynomials, Journal of Theoretical and Computational Chemistry, 8(3) (2009), 451 – 457.
14. A. R. Ashrafi, M. Saheli and M. Ghorbani, The eccentric connectivity index of nanotubes and nanotori, Journal of Computational and Applied Mathematics, 235(16) (2011), 4561-4566.
15. The GAP Team: GAP, Groups, Algorithms and Programming, RWTH, Aachen, 1995.
16. A. R. Ashrafi and M. Ghorbani, Eccentric Connectivity Index of Fullerenes, 2008, In: I. Gutman, B. Furtula, Novel Molecular Structure Descriptors – Theory and Applications II, pp. 183 – 192.
Journal of Discrete Mathematics and Its Applications
Volume 1, 1-2
June 2011
Pages 43-50

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History

  • Receive Date: 16 January 2011
  • Revise Date: 09 February 2011
  • Accept Date: 13 March 2011
  • Publish Date: 01 June 2011

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