A new method for computing ABC index of nanostar dendrimers

Document Type: Original Article

Author

Department of Mathematics, Tarbiat Modarres University, P. O. Box: 14115-137, Tehran, I. R. Iran

Abstract

The ABC index is a topological index was defined as $ABC(G)=\sum_{uv\in E}\sqrt{(d_G (u) +d_G (v )- 2)/d_G (u)d_G (v )}  $, where $d_G(u)$  denotes degree of vertex u. The second version of ABC index is defined as $ABC_2(G)=\sum_{uv\in E}\sqrt{(n_u+n_v-2)/n_un_v}  $ where $n_u $is the number of vertices closer to vertex u than v. In this paper we study some properties of these new topological indices.

Graphical Abstract

A new method for computing ABC index of nanostar dendrimers


REFERENCES
[1] M. V. Diudea, (Ed.), QSPR/QSAR Studies by Molecular Descriptors, NOVA, New
York (2001).
[2] M. V. Diudea, I. Gutman and L. Jäntschi, Molecular Topology, NOVA, New York
(2002).
[3] M. V. Diudea, M. S. Florescu and P. V. Khadikar, Molecular Topology and Its
Applications, EFICON, Bucharest (2006).
[4] I. Gutman and O. E. Polansky, Mathematical Concepts in Organic Chemistry,
Springer - Verlag, New York (1986).
[5] M. A. Johnson, G. M. Maggiora, Concepts and Applications of Molecular Similarity, Wiley Interscience, New York, (1990).
[6] H. Wiener, J. Am. Chem. Soc., 69 (1947) 17.
[7] B. Furtula, A. Graovac, D. Vukičević, Disc. Appl. Math., 157 (2009) 2828.
[8] D. Vukicevic and B. Furtula, J. Math. Chem. 46 (2009) 1369 .
[9] Ante Graovac and Modjtaba Ghorbani. Acta Chim. Slov., 57 (2010) 609.
[10] B. Zhou, I. Gutman, B. Furtula, and Z. Du, Chem. Phys. Lett., 482 (2009) 153.

[11] M. A. Hosseinzadeh and M. Ghorbani, J. Optoelectron. Adv. Mater., 11 (11) (2009)
1671.
[12] N. Trinajstić and I. Gutman, Croat. Chem. Acta, 75 (2002) 329.
[13] D. B. West, Introduction to Graph theory, Prentice Hall, Upper Saddle River
(1996).
[14] A. R. Ashra i, M. Ghorbani and M. Jalali, J. Theor. Comput. Chem., 7, 221 (2008).
[15] A. R. Ashra i, M. Ghorbani and M. Jalali, J. Theor. Comput. Chem., 8, 451 (2009).
[16] A. R. Ashra i, M. Jalali, M. Ghorbani and M. V. Diudea, MATCH Commun. Math.
Comput. Chem., 60, 905 (2008).
[17] M. Ghorbani and M. Jalali, MATCH Commun. Math. Comput. Chem., 62 (2009) 353.
[18] M. Ghorbani, A. R. Ashra i and M. Hemmasi, Optoelectron. Adv. Mater. – Rapid Comm., 3 (2009) 1306.
[19] A. R. Ashrafi, M. Ghorbani and M. Jalali, Optoelectron. Adv. Mater. – Rapid Comm., 3 (2009) 823.
[20] A. R. Ashrafi and M. Ghorbani, Optoelectron. Adv. Mater. – Rapid Comm., 3 (2009)
596.