Computing Some Topological Indices of the Molecular Graphs of Benzyl Ether with $C_{60}H$ Core and Benzyl Ether with Porphyrin Core

محورهای موضوعی : مجله بین المللی ریاضیات صنعتی

B. Solaymani ¹ (Department of Mathematics, Shahrekord Branch, Islamic Azad University, Shahrekord, Iran.)
SH. Heidarian ² (Department of Mathematics, Shahrekord Branch, Islamic Azad University, Shahrekord, Iran.)
F. Khaksar Haghani ³ (Department of Mathematics, Shahrekord Branch, Islamic Azad University, Shahrekord, Iran.)

تاریخ دریافت : 1399/10/13 تاریخ پذیرش : 1400/06/15 تاریخ انتشار : 1400/07/09

کلید واژه: Zagreb coindices, F-polynomial, F-index, Multiplicative Zagreb coindices, Multiplicative Zagreb indices, Zagreb indices,

چکیده مقاله :

In this paper, the first, second and third Zagreb indices, the first and second multiplicative Zagreb indices, the F-index and F-polynomial of benzyl ether dendrimer with C60H core and benzyl ether dendrimer with porphyrin core are calculated. In addition, the first and second Zagreb coindices, the first and second multiplicative Zagreb coindices of these graphs are computed as well. Finally, the multiplicative Zagreb index of these graphs is computed through the link of graphs.

چکیده انگلیسی:

در این مقاله شاخص های اول، دوم و سوم زاگرب، شاخص های اول و دوم ضربی زاگرب، F-شاخص و F-چندجمله ای دیندریمرهای بنزیل اتر با هسته C_60H و بنزیل اتر با هسته پروفرین محاسبه شده اند. علاوه بر این هم شاخص های اول و دوم زاگرب و هم شاخص های ضربی اول و دوم زاگرب این گرافها محاسبه شده اند. در پایان شاخص ضربی این گراف ها از طریق اتصال گرافها بدست آمده است.

منابع و مأخذ:

[1] H. Abdo, D. Dimitrov, I. Gutman, On extremal trees with respect to the Findex,Kuwait Journal of Science 44 (2017) 1-8.
[2] V. Ahmadi, M. R. Darafsheh, J. Hashemi, Zagreb, multiplicative Zagreb Indices and Coindices of graphs, International Journal of Industrial Mathematics 9 (2017) 47-57.
[3] V. Ahmadi, M. R. Darafsheh, Zagreb, Multiplicative Zagreb indices and coindices of NCn(k) and Ca3(C6) graphs,  Bulletin of Parana’s Mathematical Society 36 (2018) 9-15.
[4] A. R. Ashrafi, T. Doili, A. Hamzeh, The Zagreb coindices of graph operations, Discrete Applied Mathematics 158 (2010) 1571-1578.
[5] A. R. Ashrafi, T. Doili, A. Hamzeh, Extremal graphs with respect to the Zagreb coindices, MATCH Communications in Mathematical and in Computer Chemistry 65 (2011) 85-92.
[6] M. Bhanumathi, K. Easu, J. Rani, Computation of multiplicative topological indices of Dutch windmill graph, International Journal of Engineering 8 (2017) 185-196.
[7] M. Cancan, M. S. Aldemir, On ve-Degree and ev-Degree Zagreb indices of Titania nanotubes, American Journal of Chemical Engineering 5 (2017) 163-168.
[8] M. R. Farahani, The hyper-Zagreb index of T USC4C8(S) nanotubes, International Journal of Engineering Research and Technology 3 (2015) 1-6.
[9] G. H. Fath-Tabar, Old and new Zagreb indices of graphs, MATCH Communications in Mathematical and in Computer Chemistry 65 (2011) 79-84.
[10] I. Gutman, B. Furtula, On Zagreb indices and coindices,MATCH Communications in Mathematical and in Computer Chemistry 74 (2015) 189-198.
[11] I. Gutman, O. E. Polansky, Mathematical Concepts in Organic Chemistry, Springer, Berlin, 1986.
[12] I. Gutman, N. Trinajsti, Graph theory and molecularorbitals III, Total π-electron energy of allernant hydrocarbons, Chemical Physics Letters 17 (1972) 535-538.
[13] S. M. Hosmani, I. Gutman, A forgotten topological index, Journal of Mathematical Chemistry 53 (2015) 1184-1190.
[14] A. Iranmanesh, M. A. Hosseinzadeh, I. Gutman, On multiplicative Zagreb indices of graphs, Iranian Journal of Mathematical Chemistry 3 (2012) 115-154.
[15] M. Rezaei, W. Gao, M. K. Siddiqui, M. R. Farahani, Computing hyoer Zagreb index and M-polynomial of Titania nanotubes Tio2[m; n], Sigma Journal of Engineering and Natural Sciences 35 (2017) 707-714.
[16] R. Todeschin, D. Ballabio, V. Consonni, Novel molecular descriptors based on functions of new vertex degrees. in: I. Gutman and B. Furtula, Eds., Novel Molecular Stucture Descriptors-Theory and Applications I, University Kragujevac, Kragujevac 55 (2010) 73-100.
[17] R. Todeschini, V. Consonni, Handbook of Molecular Descriptors, Wiley-VCH, Weinheim, 2000.
[18] R. Todeschini, V. Consonni, New local vertex invariants and molecular descriptors based on functions of the vertex degrees, MATCH MATCH Communications in Mathematical and in Computer Chemistry 64 (2010) 359-372.
[19] K. Xu, K. Ch. Das, K. Tang, On the multiplicative Zagreb coindex of graphs, Opuscula Mathematica 33 (2013) 191-204.
[20] S. Zhang, Unicyclic graphs with the first three smalest and largest first general Zagreb index, MATCH  Communications in Mathematical and in Computer Chemistry 55 (2006) 427-438.