The eccentric connectivity index of armchair polyhex nanotubes

Mahboubeh Saheli, Ali Reza Ashrafi


The eccentric connectivity index ξ(G) of the graph G is defined as ξ(G) = Σu∈V(G) deg(u)ε(u) where deg(u) denotes the degree of vertex u and ε(u) is the largest distance between u and any other vertex v of G. In this paper an exact expression for the eccentric connectivity index of an armchair polyhex nanotube is given.


eccentric connectivity index; armchair nanotube

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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, 273–282 (1997).

H. Dureja and A. K. Madan, Superaugmented eccentric connectivity indices: new-generation highly discriminating topological descriptors for QSAR/QSPR modeling, Med. Chem. Res., 16, 331–341 (2007).

V. Kumar, S. Sardana and A. K. Madan, Predicting anti- HIV activity of 2,3-diary l-1,3-thiazolidin-4-ones: computational approaches using reformed eccentric connectivity index, J. Mol. Model, 10, 399–407 (2004).

S. Sardana and A. K. Madan, Application of graph theory: Relationship of molecular connectivity index, Wiener’s index and eccentric connectivity index with diuretic activity, MATCH Commun. Math. Comput. Chem., 43, 85– 98 (2001).

M. Fischermann, A. Homann, D. Rautenbach, L. A. Szekely and L. Volkmann, Wiener Index versus maximum degree in trees, Discrete Appl. Math., 122, 127–137 (2002).

S. Gupta, M. Singh and A. K. Madan, Application of Graph Theory: Relationship of Eccentric Connectivity Index and Wiener’s Index with Anti-inflammatory Activity, J. Math. Anal. Appl., 266, 259–268 (2002).

A. Ilić and I. Gutman, Eccentric connectivity index of chemical trees, MATCH Commun. Math. Comput. Chem., to appear.

B. Zhou and Z. Du, On eccentric connectivity index, MATCH Commun. Math. Comput. Chem., 63, 181–198 (2010).

T. Doslic, M. Saheli and D. Vukičević, Eccentric connectivity index: extremal graphs and values, submitted.

A. R. Ashrafi and A. Loghman, PI index of armchair polyhex nanotubes, ARS Combinatoria, 80, 193–199 (2006).

A. Iranmanesh and A. R. Ashrafi, Balaban index of an armchair polyhex, TUC4C8(R) and TUC4C8(S) nanotorus, J. Comput. Theor. Nanosci., 4 (3), 514–517 (2007).

H. Shabani and A. R. Ashrafi, Applications of the matrix package MATLAB in computing the wiener polynomial of armchair polyhex nanotubes and nanotori, J. Comput. Theor. Nanosci., in press.

S. Yousefi and A. R. Ashrafi, Distance Matrix and Wiener Index of Armchair Polyhex Nanotubes, Studia Univ. Babes-Bolyai, Chemia, 53 (4), 111–116 (2008).

H. Deng, The PI Index of TUVC6

p; q], MATCH Commun. Math. Comput. Chem., 55, 461–476 (2006).

M. Eliasi and B. Taeri, Distance in Armchair Polyhex Nanotubes, MATCH Commun. Math. Comput. Chem. 62 295–310 (2009).

M. V. Diudea, M. Stefu, B. Parv and P. E. John, Armchair Polyhex Nanotubes, Croat. Chem. Acta, 77 (1–2), 111–115 (2004).

F. Harary, Graph Theory, Addison-Wesley, Reading MA, 1969.



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