Augmented eccentric connectivity index of Fullerenes

Document Type: Original Article

Author

Department of Mathematics, Faculty of Science, Persian Gulf University

Abstract

Fullerenes are carbon-cage molecules in which a number of carbon atoms are bonded in a nearly spherical configuration. The augmented eccentric connectivity index of graph G is defined as £(G)=∑u εV(G)M(u)ε(u)-1, where ε(u)  is defined as the length of a maximal path connecting u to another vertex of G and M(u) denotes the product of degrees of all eighbors of vertex u. In the present paper , we compute the augmented eccentric connectivity index of two classes of fullerenes C12n+2 and C20n+40.

Graphical Abstract

Augmented eccentric connectivity index of Fullerenes

Keywords


1. H. Dureja and A. K. Madan, Superaugmented eccentric connectivity indices: new generation highly discriminating topological descriptors for QSAR/QSPR modeling,Med. Chem. Res., 16 (2007), 331-341.
2. M. Ge and K. Sattler, Observation of fullerene cones, Chem. Phys. Lett., 220 (1994), 192-196.
3. A. Ilić, M. V. Diudea, F. Gholami-Nezhad and A. R. Ashrafi, Topological indices in nanocones, in I. Gutman, B. Furtula (Eds.), Novel Molecular Structure Descriptors Theory and applications I, Univ. Kragujevac, Kragujevac, 2010, pp. 217-226.

4. M. Saheli, H. Saati and A. R. Ashrafi, The eccentric connectivity index of one pentagonal carbon nanocones, toelectron. Adv. Mat., 4 (2010), 896-897.
5. T. Došlić, A. Graovac, F. Cataldo and O. Ori, Notes on some distance-based invariants for 2-dimensional square and comb lattices, Iranian J. of Math. Sci. and Informatics, 5 (2010), 61-68.
6. T. Došlić, A. Graovac, D. Vukičević, F. Cataldo, O. Ori, A. Iranmanesh, A. R. Ashrafi and F. Koorepazan Moftakhar, Topological compression factors of 2-dimensional TUC4C8(R) lattices and tori, Iranian J. Math. Chem., 1(2) (2010), 73-80.
7. T. Došlić and M. Saheli, Eccentric connectivity index of benzenoid graphs, in I.Gutman, B. Furtula, (Eds.), Novel Molecular Structure Descriptors - Theory and Applications II, Univ. Kragujevac, Kragujevac, 2010, pp. 169-182.
8. T. Došlić and M. Saheli, Augmented eccentric connectivity index of single-defect nanocones, J. Math. NanoSci., 1 (2011), 25-31.
9. 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.
10. M. Ghorbani, Connective eccentric index of fullerenes, J. Math. NanoSci, 1 (2011), 43-50.
11. Z. Yarahmadi, Ali Reza Ashrafi and S. Moradi, Extremal values of augmented eccentric connectivity index of V-phenylenic nanotorus, J. Appl. Math. Comput. 45 (2014), 35-42.
12. The GAP Team: GAP, Groups, Algorithms and Programming, RWTH, Aachen, 1995. 13. H. W. Kroto, J. R. Heath, S. C. O’Brien, R. F. Curl and R. E. Smalley, C60:Buckminsterfullerene, Nature, 318 (1985), 162-163.
Jo


Volume 4, 1-2
Winter and Spring 2014
Pages 13-18
  • Receive Date: 19 November 2013
  • Revise Date: 23 February 2014
  • Accept Date: 05 May 2014