﻿ 富勒烯C10n的化学拓扑指数计算 Calculation of Topological Index for Fullerene C10n

Advances in Applied Mathematics
Vol.05 No.01(2016), Article ID:17036,8 pages
10.12677/AAM.2016.51020

Calculation of Topological Index for Fullerene C10n

Niannian Han, Wei Gao

School of Information, Yunnan Normal University, Kunming Yunnan

Received: Feb. 1st, 2016; accepted: Feb. 22nd, 2016; published: Feb. 29th, 2016

Copyright © 2016 by authors and Hans Publishers Inc.

ABSTRACT

In computational chemistry, the molecular structures are modelled as graphs which are called the molecular graphs. In these graphs, each vertex represents an atom and each edge denotes covalent bound between atoms. It is shown that the topological indices defined on the molecular graphs can reflect the chemical characteristics of chemical compounds and drugs. In this paper, we present the second ABC index, the second GA index and modified Szeged index of fullerenes by means of chemical structure analysis and edge dividing techniques.

Keywords:Chemical Graph Theory, Fullerene, The Second ABC Index, The Second GA Index, Modified Szeged Index

1. 引言

Graovac和Ghorbani在文献 [11] 中定义了第二类化学键连通指数(the second atom-bond connectivity index，简称第二类ABC指数)如下：

Rostami等 [12] 得到关于第二类ABC指数的上界。

Fath-Tabar等 [13] 定义了第二类几何算术指数(the second geometric-arithmetic index，简称为第二类GA指数)如下：

Zhan和Qiao [14] 研究了树结构的最大和最小第二类GA指数，并给出对应的极图。

Xing和Zhou [15] 给出了n个顶点的单圈图的修改Szeged指数的极值。Chen等 [16] 对维纳指数和修改Szeged指数的差值进行了分析。Dong等 [17] 得到一些特殊分子结构族类的修改Szeged指数。Faghani和Ashrafi [18] 给出计算修改Szeged指数的新公式。

2. 主要结果

Figure 1. The dividing of

Table 1. The related data for each edge class in fullerene C10n

3. 总结

Calculation of Topological Index for Fullerene C10n[J]. 应用数学进展, 2016, 05(01): 150-157. http://dx.doi.org/10.12677/AAM.2016.51020

1. 1. Farahani, M.R., Gao, W. and Kanna, M.R.R. (2015) On The Omega Polynomials of A Family of Hydrocarbon Mole-cules “Polycyclic Aromatic Hydrocarbons Pank”. Asian Academic Research Journal of Multidisciplinary, 2, 263-268.

2. 2. Gao, W. and Shi, L. (2014) Wiener Index of Gear Fan Graph And Gear Wheel Graph. Asian Journal of Chemistry, 26, 3397-3400.

3. 3. Farahani, M.R. and Gao, W. (2015) The Schultz Index and Schultz Polynomial of the Jahangir Graphs . Applied Mathematics, 6, 2319-2325. http://dx.doi.org/10.4236/am.2015.614204

4. 4. Xi, W.F. and Gao, W. (2014) Geometric-Arithmetic Index and Zagreb Indices of Certain Special Molecular Graphs. Journal of Advances in Chemistry, 10, 2254-2261.

5. 5. Gao, W. and Shi, L. (2015) Szeged Related Indices of Unilateral Polyomino Chain and Unilateral Hexagonal Chain. IAENG International Journal of Applied Mathematics, 45, 138-150.

6. 6. Gao, W. and Farahani, M.R. (2016) Degree-Based Indices Computation for Special Chemical Molecular Structures Using Edge Dividing Method. Applied Mathematics and Nonlinear Sciences, 1, 94-117.

7. 7. Estrada, E., Torres, L., Rodrguez, L. and Gutman, I. (1998) An Atom-Bond Connectivity Index: Modelling the Enthalpy of Formation of Alkanes. Indian Journal of Chemistry A, 37, 849-855.

8. 8. Ghorbani, M. and Jalili, M. (2009) Computing A New Topological Index of Nano Structures. Digest Journal of Nanomaterials and Biostructures, 4, 681-685.

9. 9. Ghorbani, M. and Hosseinzadeh, M.A. (2010) Computing ABC4 Index of Nanostar Dendrimers. Op-toelectronics and Advanced Materials-Rapid Communications, 4, 1419-1422.

10. 10. Ghorbani, M. and Ghazi, M. (2010) Computing Some Topological Indices of Triangular Benzenoid. Digest Journal of Nanomaterials and Bios-tructures, 5, 1107-1111.

11. 11. Graovac, A. and Ghorbani, M. (2010) A New Version of Atom-Bond Connectivity Index. Acta Chimica Slovenica, 57, 609-612.

12. 12. Rostami, M., Haghighat, M.S. and Ghorbani, M. (2013) On Second Atom-Bond Connectivity Index. Iranian Journal of Mathematical Chemistry, 4, 265-270.

13. 13. Tabar, G.F., Purtula, B. and Gutman, I. (2010) A New Geometric-Arithmetic Index. Journal of Mathematical Chemistry, 47, 477-486. http://dx.doi.org/10.1007/s10910-009-9584-7

14. 14. Zhan, F.Q. and Qiao, Y.F. (2014) The Second Geometric-Arithmetic Index of the Starlike Tree with k-Component. Mathematics in Practice and Theory, 44, 226-229.

15. 15. Xing, R. and Zhou, B. (2011) On the Revised Szeged Index. Discrete Applied Mathematics, 159, 69-78. http://dx.doi.org/10.1016/j.dam.2010.09.010

16. 16. Chen, L., Li, X. and Liu, M. (2014) The (Revised) Szeged Index and the Wiener Index of a Nonbipartite Graph. European Journal of Combinatorics, 36, 237-246. http://dx.doi.org/10.1016/j.ejc.2013.07.019

17. 17. Dong, H., Zhou, B. and Trinajstic, N. (2011) A Novel Version of the Edge-Szeged Index. Croatica Chemica Acta, 84, 543-545. http://dx.doi.org/10.5562/cca1889

18. 18. Faghani, M. and Ashrafi, A.R. (2014) Revised and Edge Revised Szeged Indices of Graphs. Ars Mathematica contemporanea, 7, 153-160.