Computing the Hosoya Index of Some Nanostar Dendrimers


  • Fateme Movahedi Department of Mathematics, Faculty of Sciences, Golestan University, Gorgan, Iran
  • Mohamad Hadi Akhbari bDepartment of Mathematics, Islamic Azad University, Estahban Branch, Estahban, Iran
  • Roslan Hasni Special Interest Group of Modeling and Data Analytics (SIGMDA), Faculty of Computer Science and Mathematics, Universiti Malaysia Terengganu 21030 Kuala Nerus, Terengganu, Malaysia



Topological index, Hosoya index, Dendrimers, Mathematical Chemistry


Dendrimers are highly branched macromolecules built up from a monomer, with new branches added in steps until a tree structure is created. The various biological characteristics of dendrimers are a good choice in chemistry, biology, the medical field, and nano-science. A topological index is a type of molecular descriptor that is calculated based on the molecular graph of a chemical structure. The Hosoya index is a well-known topological index that is used to predict some of their physico-chemical properties from the structure of molecules. The Hosoya index of a graph is defined as the total number of its independent edge sets. In this paper, we study the Hosoya index of some families of nanostar dendrimers. We obtain the formulas of the Hosoya index for two infinite classes of dendrimers, namely, nanostar dendrimer  and tetrathiafulvalene dendrimer. We use the Mathematica program to evaluate the results and accuracy of calculations. Our results can be used in analyzing the molecular topology of these families of nanostar dendrimers.


N. E. Arif, R. Hasni, A. Kalaf. (2013). Chromatic polynomial of POPAM and siloxane dendrimers. J. Comput. Theor. Nanosci., 10, 285-287.

S. C. Basak, K. Balasubramanian, B. D. Gute, D. Mills, A. Gorczynska, S. Roszak. (2003). Prediction of cellular toxicity of halocarbons from computed chemodescriptors: A hierarchical QSAR approach. J. Chem. Inf. Comput. Sci., 43(4), 1103-1109.

A. Bharali, A. Pegu, J. Buragohain and B. Deka. (2021). Generalized ISI index of certain families of nanostar dendrimers. J. Interdiscip. Math., 24(7), 2021-2034.

J. Devillers, A. T. Balaban. (1999). Topological indices and related descriptors in QSAR and QSPR. Gordon and Breach, Amsterdam.

I. Gutman and O. E. Polansky. (1986). Mathematical concepts in organic chemistry. Springer, Berlin.

H. Hosoya. (1971). Topological index, a newly proposed quantity characterizing the topological nature of structural isomers of saturated hydrocarbons. Bull. Chem. Soc. Jpn., 44, 2332-2339.

H. Hosoya. (2002). The topological index Z before and after 1971. Internet Electron. J. Mol. Des., 1, 428-442.

H. Hosoya. (2007). Important mathematical structures of the topological index Z for tree graphs. J. Chem. Inf. Model., 47, 744-75.

H. Hosoya. (2007). Mathematical meaning and importance of the topological index Z. Croat. Chem. Acta., 80, 239-249.

Y. Liu, W. Zhuang and Z. Liang. (2015). Largest Hosoya index and smallest Merrifield-Simmons index in tricyclic graphs. MATCH Commun. Math. Comput. Chem., 73, 195-224.

M. Mirzagar. (2009). PI Szeged and edge Szeged polynomial of a dendrimers. MATCH Commun. Math. Comput. Chem., 23, 363-370.

F. Movahedi, M. H. Akhbari and H. Kamarulhaili. (2021). On the Hosoya index of some families of graph. Math. Interdisc. Res., 6, 225-234.

F. Movahedi. (2021). Matching polynomials for some Nanostar Dendrimers. Asian-European Journal of Mathematics, 14(10), 2150188.

F. Movahedi. (2021). Matching polynomials for some nanostar dendrimers. Asian-Eur. J. Math., 14(10), 2150188.

J. Ou. (2009). On extremal unicyclic molecular graphs with maximal Hosoya index. Discrete Appl. Math., 157(2), 391-397.

A. Sattar, M. Javaid and E. Bonyah. (2022). Computing connection-based topological indices of Dendrimers, J. Chem., 7204641.