Modified eccentric connectivity index of fullerenes

Document Type: Original Article


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


The eccentric connectivity index of a graph is defined as E(Γ)=∑uεV(Γ)degΓ(u)e(u), where degΓ(u) denotes the degree of the vertex u in Γ and e(u) is the eccentricity of vertex u. In this paper, the modified eccentric connectivity index of two infinite classes of fullerenes is computed.

Graphical Abstract

Modified eccentric connectivity index of fullerenes


[1] 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) 183-192.
[2] A. R. Ashrafi, M. Saheli and M. Ghorbani, The eccentric connectivity index of  nanotubes and nanotori, J. Comput. Appl. Math. 235 (2011) 4561- 4566.
[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] T. Došlić, M. Ghorbani and M. A. Hosseinzadeh, Eccentric connectivity polynomial of some graph operations, Util. Math. 84 (2011) 197-209.
[5] P. W. Fowler and D. E. Manolopoulos, An Atlas of Fullerenes, Oxford Univ. Press, Oxford, 1995.
[6] A. Graovać and T. Pisanski, On the Wiener index of a graph, J. Math. Chem. 8 (1991) 53-62.
[7] M. Ghorbani, Connective eccentric index of fullerenes, J. Math. Nanosci. 1 (2011) 43-50.
[8] M. Ghorbani, A. R. Ashrafi and M. Hemmasi, Eccentric connectivity polynomials of fullerenes, Optoelectronics and Advanced Materials-(RC), 3(12) (2009) 1306 - 1308.
[9] M. Ghorbani and M. Hakimi-Nezhaad, A note on modified eccentric connectivity index, submitted.
[10] 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.
[11] H. W. Kroto, J. R. Heath, S. C. O’Brien, R. F. Curl and R. E. Smalley, C60: buckminsterfullerene, Nature 318 (1985) 162-163.
[12] 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.

Volume 5, 1-2
Summer and Autumn 2015
Pages 1-10
  • Receive Date: 25 December 2014
  • Revise Date: 08 February 2015
  • Accept Date: 01 July 2015