Hyper and multiple f-index of nano star dendrimers

Ghobadi, Sirous; Ghods, Masoud; Ghorbaninejad, Mobina

doi:10.1080/09720529.2021.1923923

Open Access Research Article

Hyper and multiple f-index of nano star dendrimers

^*Sirous GhobadiCorresponding authorghobadimath46@gmail.com; s.ghobadi@qaemiau.ac.irDepartment of Mathematics Qaemshahr Branch Islamic Azad UniversityQaemshahr, Qaemshahr, 47651-61964, Iran0000-0003-4646-310XView full profile → , Masoud Ghodsmghods@semnan.ac.irDepartment of Mathematics Semnan University Faculty of Mathematics Statistics and Computer ScienceDepartment of Applied Mathematics Semnan UniversitySemnan, 35131-19111, Iran0000-0002-5006-5107View full profile → , Mobina Ghorbaninejadghorbani325@gmail.comDepartment of Mathematics Allame Tabarsi InstituteRochester, Qaemshahr, 14627, IranView full profile →

* Corresponding author · click or hover a name for details

pp. 1623–1638Vol. 26Issue 6September 2023DOI: 10.1080/09720529.2021.1923923 Crossmark XML

Received:: 01 Sep 2020
Accepted:: 01 Feb 2021
Published Online:: 24 May 2022
Article type:: Research Article
Language:: EN
Article no.:: JDMSC-1339
Pages:: 1623–1638

Abstract

Dendrimers are branching molecules that consist of a central part attached to tree-like branches which are repeatedly connected to each other. Topological indices of a molecular graph are real numbers associated with graphs, which represents some of the properties of the molecule. In this article, we obtaine precise formulas for the hyper F-index and multiple F-index of a number of nano star dendrimers.

Keywords

F-index Hyper F-index Multiple F-index Nano star dendrimer

Subject Classifications

05C0905C9005C92

References

[1] M. Alaeiyan, F. Afzal, M. R. Farahani M. A. Rostami, An exact formulas for the Wiener polarity index of nanostar dendrimers, Journal of Information and Optimization Sciences, 41:4 (2020) 933-939, DOI: 10.1080/02522667.2020.1748274.
[2] A. R. Ashrafi, M. Mirzargar, PI, Szeged and edge szeged of an infinite family of nano star dendrimers, Indian J. Chem. 47 (2008) 538-541.
[3] V. Balzani , P. Ceroni , S. Gestermann , C. Kauffmann , M. Gorka , F. Vogtle . Dendrimers as fluorescent sensors with signal amplification. Chem Commun. 9 (2000) 853-854.
[4] Cheng Yiyun, Man Na, Xu Tongwen, Fu Rongqiang, Wang Xueyuan, Wang Xiaomin, Wen Longping, Transdermal delivery of nonsteroidal anti-inflammatory drugs mediated by polyamidoamine (PAMAM) dendrimers. Journal of Pharmaceutical Sciences Volume 96, Issue 3, March 2007, Pages 595-602
[5] N. De and Sk. Md. Abo Nayeem, computing the F-index of nano star dendrimer, pasific science Review A:Natural science and engineering XXX (2016) 1-8.
[6] M. V. Diudea, A. F. Vizitiu, M. Mirzargar,A. R. Ashrafi, sadhhana polynomial in nano-dendrimers, Carpathian J. Math. 26 (2010) 59-66.
[7] M. Eliasi, A. Iranmanesh, I. Gutman, multiplicative version of first zagreb index, Match commun. Math. comput. Chem. 68 (2012) 217-230.
[8] PE. Froehling, Dendrimers and dyes - a review. Dyes Pigments. 9 (2001) 187-195.
[9] B. Furtula, I. Gutman, A forgotten topological index, J. Math. Chem. 53 (2015) 1184-1190. 10.1007/s10910-015-0480-z.
[10] W. Gao, M. R. Farahani, The hyper-zagreb index for an infinite family of nanostar dendrimer, Journal of Discrete Mathematical Sciences and Cryptography, 20:2 (2017) 515-523, DOI: 10.1080/09720529.2016.1220088
[11] M. Ghorbani, N.Azimi, Note on multiple zagreb index, Iran J. Math. Chem. 3 (2) (2012) 137-143.
[12] I. Gutman, N. Trinajstic, Graph theory and molecular orbitals total -electron energy of alternant hydrocarbons, Chem. Phys. Let. 17 (1972) 535-538. 10.1016/0009-2614(72)85099-1.
[13] A. Herrmann , G. Mihov , G. Vandermeulen , H. Klok , K. Mullen, Peptide-functionalized polyphenylene dendrimers. Tetrahedron. 9 (2003) 3925.
[14] M. Imran, M. K. Siddiqui, S. Ahmad, M. F. Hanif, M. H. Muhammad M. R. Farahani, Topological properties of benzenoid, phenylenes and nanostar dendrimers, Journal of Discrete Mathematical Sciences and Cryptography, 22:7(2019)1229-1248, DOI: 10.1080/09720529.2019.1701267
[15] X. Li, Y. Shi, A survey on the Randic index, MATCH Commun. Math. Comput. Chem. 59 (1) (2008) 127-156.
[16] HN. Patel , DRPM. Patel, Dendrimer applications - a review. Int J Pharm Bio Sci. 9(2)(2013) 454-463.
[17] G. Pasut , FM. Veronese, Polymer-drug conjugation, recent achievements and general strategies. Prog Polym Sci. 9 (2007) 933.
[18] G. H. Shirdel, H. R. Pour, A. M. Sayadi, The Hyper-Zagreb index of graph operations, Iran J. Math. Chem. 4 (2) (2013) 213-220.
[19] M. K. Siddiqui, M. Imran, A. Ahmad, On Zagreb indices, Zagreb polynomials of some nano star dendrimers, Appl. Math. Comput. 280 (2016) 132-139, http:// dx.doi.org/10.1016/j.amc.2016.01.041.
[20] D. Tathagata , G. Minakshi , NK. Jain, Poly (propyleneimine) dendrimer and dendrosome based genetic immunization against hepatitis B. Vaccine. 9(27-28) (2008) 3389-3394.
[21] M. Triesscheijn , P. Baas , JH. Schellens , FA. Stewart, Photodynamic therapy in oncology. Oncologist. 9 (2006) 1034-1044.
[22] F. Vogtle, G. Richardt, N. Werner, Dendrimer Chemistry Concepts, Syntheses, Properties, Applications (2009) ISBN 3-527-32066-0
[23] H. Wiener, Structural determination of parafin boiling points, J. Am. Chem. Soc. 69 (1947) 17-20.

Views: 242Downloads: 7Citations: 0