[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.11568/kjm.2019.27.3.613

EDGE SZEGED INDICES OF BENZENE RING

Baig, Abdul Qudair (Department of Mathematics The University of Lahore Pakpattan Campus)
Naeem, Muhammad (Department of Mathematics The University of Lahore Pakpattan Campus)
Mushtaq, Muhammad (Department of Mathematics The University of Lahore Pakpattan Campus)
Gao, Wei (School of Information Science and Technology Yunnan Normal University)

Publication Information

Korean Journal of Mathematics / v.27, no.3, 2019 , pp. 613-627 More about this Journal

Abstract

Consider a connected molecular graph G = (V, E) where V is the set of vertices and E is the set of edges. In G, vertices represent the atoms and edges represent the covalent bonds between atoms. In graph G, every edge (say) e = uv will be connected by two atoms u and v. The edge Szeged index is a topological index which has been introduced by Ivan Gutman. In this paper, we have computed edge Szeged indices of a hydrocarbon family called Benzene ring and is denoted by $(BR)_{n{\times}n}$ .

Keywords

Edge Szeged index; Padmakar Iven index; Geometric Arithmetic index; Mostar index; Benzene ring;

Citations & Related Records

Reference

1	K. Ch. Dasa, I. Gutmanb, and B. Furtulab, Survey on Geometric-Arithmetic Indices of Graphs, MATCH Commun. Math. Comput. Chem. 65 (2011), 595-644
2	A. Das, G. Domotor, I. Gutman, S. Joshi, S. Karmarkar, D. Khaddar, T. Khaddar, P.V. Khadikar, L. Popovic, N.S. Sapre, N. Sapre, and A. Shirhatti, A Comparative Study of the Wiener, Schultz and Szeged Indices of Cycloalkanes, J. Serb. Chem. Soc. 62 (1997), 235-239.
3	H. Deng and J. Hou, P I indices of nanotubes $SC_4C_8$ [q; 2p] covering by $C_4$ and $C_8$ , MATCH Commun. Math. Comput. Chem. 57, (2007), 503-516.
4	A. A. Dobrynin, I. Gutman, S. Klavzar, and P. Zegiret, Wiener index of hexagonal systems, Acta Appl. Math. 72 (2002), 247-294. DOI
5	T. Doslic, I. Martinjak, R. Skrekovski, S. T. Spuzevic, and I. Zubac, Mostar index, J. Math. Chem. 56 (2018), 2995-3013. DOI
6	M. Eliasi and B. Taeri, Szeged index of armchair polyhex nanotubes, MATCH Commun. Math. Comput. Chem. 59 (2008), 437-450.
7	I. Gutman and A. R. Ashrafi, The edge version of the Szeged index, Croat. Chem. Acta 81 (2008), 263-266.
8	I. Gutman,Y. N. Yeh, S. L. Lee, and Y. L. Luo, Some Recent Results in the Theory of the Wiener Number, Indian J. Chem. 1993, 32A, 651-661
9	I. Gutman and J.H. Potgieter, Wiener Index and Intermolecular Forces, J. Serb.Chem. Soc. 62 (1997), 185-192.
10	A. Heydari and B. Taeri, Szeged index of $TUC_4C_8$ (R) nanotubes, MATCH Commun. Math. Comput. Chem. 57 (2007), 463-477.
11	A. Iranmanesh and O. Khormali, Szeged index of $HAC_5C_7$ [r, p] nanotubes, J. Comput. Theor. Nanosci., in press.
12	S. Karmarkar, S. Karmarkar, S. Joshi, A. Das, and P.V Khadikar, Novel Application of Wiener vis-a-vis Szeged Indices in Predicting Polychlorinated Biphenyls in the Environment, J. Serb. Chem. Soc. 62 (1997), 227-234.
13	P.V. Khadikar, S. Karmarkar, S. Joshi, and I. Gutman, Estimation of the Protonation Constants of Salicylhydroxamic Acids by Means of the Wiener Topological Index, J. Serb. Chem. Soc. 61 (1996), 89-95.
14	H. Wiener, Stractural determination of paraffin boiling points, J. Amer. Chem. Soc., 69 (1947), 17-20. DOI