Eccentric connectivity index of fullerene graphs

Document Type: Original Article

Author

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

Abstract

The eccentric connectivity index of the molecular graph is defined as $\zeta^c(G)=\sum_{uv\in E}degG(u)ε(u)$ , where degG(x) denotes the degree of the vertex x in G and ε(u)=max{d(x,u) |x ε V(G)}. In this paper this polynomial is computed for an infinite class of fullerenes.

Graphical Abstract

Eccentric connectivity index of fullerene graphs

Keywords


1. H. Wiener, Structural determination of paraffin boiling points, J. Amer. Chem. Soc.,69 (1947), 17-20.

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. 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.

4. A. Dobryninand A. Kochetova, Degree distance of a graph: A degree analogue of the Wiener index, J. Chem., Inf., Comput. Sci., 34(1994), 1082 – 1086.

5. 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.

6. 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.

7. M. Ghorbani, Connective Eccentric Index of Fullerenes, J. Math. Nano. Sci., 1 (2011), 43 – 52.

8. A. R. Ashrafi and M. Ghorbani, Eccentric Connectivity Index of Fullerenes, In: I. Gutman, B. Furtula, Novel Molecular Structure Descriptors – Theory and Applications II, (2008), pp.183 – 192.

9. T. Doslić, M. Ghorbani and M. A. Hosseinzadeh, Eccentric connectivity polynomial of some graph operations, Utilitas Mathematica, 84 (2011), 297 – 309.

10. H. W. Kroto and J. R. Heath, S. C. O’Brien, R. F. Curl, R. E. Smalley, C60: Buckminsterfullerene, Nature, 318 (1985), 162 – 163.

11. H. W. Kroto, J. E. Fichier and D. E. Cox, The fulerene, Pergamon Press, New York, 1993.

12. N. Trinajstić and I. Gutman, Mathematical Chemistry, Croat. Chem. Acta, 75 (2002), 329 – 356.

13. The Hyper Chem package, Release 7.5 for Windows, Hypercube Inc., Florida, USA, 2002.

14. 17. M. V. Diudea, O. Ursu and Cs. L. Nagy, TOPOCLUJ, Babes-Bolyai University, Cluj, 2002.

15. The GAP Team: GAP, Groups, Algorithms and Programming, RWTH, Aachen, 1995.