Document Type : Original Article


1 College of Pharmacy and Biological Engineering, Chengdu University, Chengdu, 610106, China

2 Department of Applied Mathematics of Iran University of Science and Technology (IUST), Narmak, Tehran 16844, Iran.

3 Division of Science and Technology, University of Education, Lahore 54000, Pakistan


Let G be a connected graph with vertex and edge sets V (G) and E(G), respectively. The first Zagreb index M1(G) was originally defined as the sum of the squares of the degrees of all vertices of G. Recently, we know a new version of the first Zagreb index as the Multiplicative Zagreb Eccentricity index that introduced by Nilanjan De and ε(u) is the largest distance between u and any other vertex v of G. In this paper we compute this new topological index of famous molecular graph “Circumcoronene Series of Benzenoid Hk”.

Graphical Abstract

On Topological Indices of Circumcoronene Series of Benzenoid


Main Subjects

[1] West D.B., Introduction to Graph Theory, Prentice Hall, Upper Saddle River, 1996
[2] Todeschini R., Consonni V. Handbook of Molecular Descriptors. Wiley, Weinheim. 2000
[3] Balaban A.T.  (Ed.), From Chemical Topology to Three-dimensional Geometry, Plenum, New York, 1997
[4] Gutman I., Trinajstić N. Chem. Phys. Lett., 1972, 17:535
[5] Gutman I., Das K.C. MATCH Commun. Math. Comput. Chem., 2004, 50:83
[6] Todeschini R., Consonni V. MATCH Commun. Math. Comput. Chem., 2010, 64:359
[7] Todeschini R., Ballabio D., Consonni V., Novel molecular descriptors based on functions of the vertex degrees, in: I.Gutman, B. Furtula (Eds.), Novel Molecular Structure Descriptors - Theory and Applications I, Univ. Kragujevac, Kragujevac, 2010, 73-100
[8] Ghorbani M., Hosseinzadeh M.A., Filomat, 2012, 26:93
[9] Vukicevic D., Graovac A. Acta. Chim. Slov., 2010, 57;524
[10] Sharma V., Goswami R., Madan A.K. J. Chem. Inf. Comput. Sci., 1997, 37:273
[11] Sardana S., Madan A.K. MATCH Commun. Math. Comput. Chem., 2001, 43:85
[12] Gupta S., Singh M., Madan A.K. J. Math. Anal. Appl., 2002, 266: 259
[13] Furtula B., Graovac A., Vukičević D. Disc. Appl. Math., 2009, 157:2828
[14] Fischermann M., Homann A., Rautenbach D., Szekely L.A., Volkmann L. Discrete Appl. Math., 2002, 122:127
[15] Farahani M.R. Annals of West University of Timisoara-Mathematics and Computer Science., 2013, 51:29
[16] De N. South Asian J. Math., 2012, 2:570
[17] Nikolic S., Kovacevic G., Milicevic A., Trinajstić N. Croat. Chem. Acta, 2003, 76:113
[18] Braun J., Kerber A., Meringer M., Rucker C. MATCH Commun. Math. Comput. Chem., 2005, 54:163
[19] Khalifeh M.H., Yousefi–Azari H., Ashrafi A.R. Discr. Appl. Math., 2009, 157:804
[20] Gutman I. Bull. Internat. Math. Virt. Inst., 2011, 1:13
[21] Xu K., Hua H. MATCH Commun. Math. Comput. Chem., 2012, 68: 241
[22] Liu J., Zhang Q. MATCH Commun. Math. Comput. Chem., 2012, 68:231
[23] Reti T., Gutman I. Bull. Internat. Math. Virt. Inst., 2012, 2: 133
[24] Luo Z., Wu J. Trans. Comb., 2014, 3:21
[25] Wang H., Bao H. South Asian J Math, 2012, 2:578
[26] Farahani M.R. Journal of Chemistry and Materials Research, 2015, 2:67
[27] Farahani M.R. Int. Lett.Chem. Phy. Ast., 2015, 52:147
[28] Farahani M.R. New. Front. Chem., 2014, 23:141
[29] Farahani M.R. Chem. Phy. Res. J., 2014, 7:277
[30] Farahani M.R. Adv. Mater. Corr., 2013, 2:16
[31] Farahani M.R. Chem. Phy. Res. J., 2013, 6:27
[32] Farahani M.R. J. Adv. Phy., 2013, 2:48
[33] Farahani M.R, World Appl. Sci. J., 2013, 21:1260
[34] Zigert P., Klavžar S., Gutman I. ACH Models Chem., 2000, 137:83
[35] Soncini A., Steiner E., Fowler P.W., Havenith R.W.A., Jenneskens L.W. Chem. Eur. J., 2003, 9:2974
[36] John P.E., Khadikar P.V., Singh J. J. Math. Chem., 2007, 42:27
[37] Klavžar S., Gutman I., Mohar B. J. Chem. Int Comput. Sci., 1995, 35:590
[38] Klavžar S. MATCH Commun. Math. Comput. Chem., 2008, 60:255