Web of Science (Emerging Sources Citation Index)

Document Type: Original Research Article

Authors

1 Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran,

2 Department of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16844, Iran.

10.33945/SAMI/ECC.2020.7.4

Abstract

Dendrimers are the highly branched organic macromolecules with successive layers or generations of branch units surrounding a central core. In mathematical chemistry, a particular attention has been given to degree-based graph invariant. The Narumi-Katayama index and its modified version of a graph G, denoted by NK(G) and NK*(G) are equal to the product of the degrees of the vertices of G. In this work we calculated the Narumi-Katayama Indices and its Modified version for some families of dendrimers such as NS1[n], NS2[n] and NS3[n]. The exact formulas of the Narumi-Katayama and Modified Narumi-Katayama indices of these dendrimers nano structures are presented in this paper.

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[1] A.R. Ashrafi, M. Mirzargar, Indian J. Chem., 2008, 47A, 538-541.

[2] B. Klajnert, M. Bryszewska, Acta Biochim. Polonica., 2001, 48, 199-208.

[3] H. Narumi, M. Katayama. Mem. Fac. Engin. Hokkaido Univ., 1984, 16, 209-214.

[4] H. Wiener, J Amer. Chem. Soc., 1947, 69, 1, 17-20.

[5] I. Gutman, M. Ghorbani. Appl. Math. Lett., 2012, 25, 1435-1438.

[6] I. Goli Farkoush, M. Alaeiyan, M. Maghasedi. J Dis. Math. Sci. Crypt., 2019, 22, 1189-1197.

[7] N. Dorostic, A. Iranmanesh, M.V. Diudea, Math Commun. Match. Comput. Chem., 2009, 062, 389-395.

[8] N.E. Arif, R. Hasni, S. Alikhani, Dig. J. Nano. Biostr., 2011, 6, 1551-1556.

[9] S. Alikhani, M.A. Iranmanesh, J. Comput. Theor. Nanosc., 2010, 7, 2314-2316.

[10] A. Iranmanesh, N.A. Gholami, MATCH Commun. Math. Comput. Chem., 2009, 62, 371-379.

[11] M. Mirzagar, MATCH Commun. Math. Comput. Chem., 2009, 62, 363-370.

[12] H. Yousefi-Azari, A.R. Ashrafi, A. Baharin, Y. Yazdani, Asian J. Chem., 2008, 20, 15-20.

[13] W. Gao, L. Liang, Y. Gao. Energy Edu. Sci Tec: Part A., 2014, 32, 8961-8970.

[14] W. Gao, L. Liang, Y. Gao. Bio Technology: An Indian J., 2014, 10, 3837-3845.

[15] W. Gao, M.R. Farahani. J Adv Chem., 2015, 12, 3934-3939.

[16] E.G.A. Gomaa, M.A. Berghout, M.R. Moustafa, F.M. El Taweel, H.M. Farid, Prog. Chem. Biochem. Res., 2018, 1, 19-28.

[17] M. Nabati, V. Bodaghi-Namileh, S. Sarshar, Prog. Chem. Biochem. Res., 2019, 2, 108-119.

[18] M.E. Khan, A.S. Adeiza, T.A. Tor-Anyiin, A. Alexander, Prog. Chem. Biochem. Res., 2019, 2, 68-73.

[19] J.-B. Liu, A.Q. Baig, M. Imran, W. Khalid, M. Saeed, M.R. Farahani, Eurasian Chem. Commun., 2020, 2, 672-679.

[20] M. Imran, S.A. Ul Haq Bokhary, S. Manzoor, M.K. Siddiqui, Eurasian Chem. Commun., 2020, 2, 680-687.

[21] Y. Gao, M.R. Farahani, W. Nazeer, Chem. Methodol., 2018, 3, 39-45.

[22] D.X. Li, J.-B. Liu, M. Rezaei, M.R. Farahani, J. Comput. Theor. Nanosci., 2016, 13, 9136–9139.

[23] W. Gao, M.R. Farahani, J. Dis. Math. Sci. Crypt., 2017,20, 515-523.

[24] W. Gao, L. Shi, M.R. Farahani, IAENG Int. J. App. Math., 2016, 46, 168-186.

[25] Z. Foruzanfar, M.K. Jamil, M.R. Farahani, M. Imran, X. Zhang, Int. J. Pur. App. Math., 2017, 117, 173-183.

[26] M.R. Farahani, A.Q. Baig, W. Sajjad, J. Math. Nanosci., 2017,7, 23–28.