ON THE LANZHOU INDEX OF GRAPHS

Qinghe  Tong; Chenxu Yang; Wen   Li

doi:10.29121/granthaalayah.v10.i11.2022.4916

Authors

Qinghe Tong School of Mathematics and Statistics, Qinghai Normal University, Xining, Qinghai 810008, China
Chenxu Yang School of Computer, Qinghai Normal University, Xining, Qinghai 810008, China
Wen Li School of Computer, Qinghai Normal University, Xining, Qinghai 810008, China

DOI:

https://doi.org/10.29121/granthaalayah.v10.i11.2022.4916

Keywords:

Lanzhou Index, Silicate Network, Graph operation

Abstract [English]

Let be a simple graph with vertex set and edge set . The Lanzhou index of a graph is defined by , where denoted by the degree of the vertex v in . In a chemical graph, the topological index can help determine chemical, biological, pharma-cological, toxicological, and technically relevant information on molecules. In this paper, we get exact formulas for , where is some certain chemical graphs, like silicate, chain silicate, oxide, and graphene networks. Moreover, we determine the Lanzhou index of several graph operations.

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Author Biographies

Qinghe Tong, School of Mathematics and Statistics, Qinghai Normal University, Xining, Qinghai 810008, China

Qinghe Tong received the
bachelor degree in Mathematica science
from Bohai University, Jinzhou, China, in 2020.
She is currently pursuing the master’degree with
the School of Mathematics and Statistics, Qinhai Normal University, Xining, China.
her research interests include Factor, Somber index,
Laznzhou index, she has published 3 academic research papers.

Wen Li, School of Computer, Qinghai Normal University, Xining, Qinghai 810008, China

Wen Li received the master’degree in Mathematica science from Qinhai Normal University, Qinhai, China, in 2014. She is currently pursuing the doctors degree in the School of Computer Science, Qinhai Normor University, Xining, China. Her research interests include chemical graphh theory, graph algorithm, he has published 3 academic research papers.

References

Chartrand, G., Lesniak, L., and Zhang, P. (1996). Graphs and Digraphs. Chapman & Hall.

Furtula, B., and Gutman, I. (2015). A Forgotten Topological Index. Journal of Mathematical Chemistry, 53(4), 1184–1190. https://doi.org/10.1007/s10910-015-0480-z. DOI: https://doi.org/10.1007/s10910-015-0480-z

Hinz, A. M., and Schief, A. (1990). The Average Distance on the Sierpiński Gasket. Probability Theory and Related Fields, 87(1), 129–138. https://doi.org/10.1007/BF01217750. DOI: https://doi.org/10.1007/BF01217750

Husimi, K. (1950). Note on Mayer’S Theory of Cluster Integrals. Journal of Chemical Physics, 18(5), 682–684. https://doi.org/10.1063/1.1747725. DOI: https://doi.org/10.1063/1.1747725

Kaimanovich, V. A. (2001). Random Walks on Sierpiński Graphs : Hyperbolicity and Stochastic Hom-Ögbenization, Fractals in Graz, 145–183. DOI: https://doi.org/10.1007/978-3-0348-8014-5_5

Kazemi, R., and Behtoei, A. (2017). The First Zagreb and Forgotten Topological Indices of D-Ary Trees, Hac-Ettepe. Journal of Mathematics and Statistics, 46(4), 603–611. DOI: https://doi.org/10.15672/HJMS.20174622758

Klix, F., and Goede, K. R. (1967). Struktur and Komponenten analyse von Problem lö sungsprozersen. Zeitschrift für Psychologie, 174, 167–193.

Manuel, P., and Rajasingh, I. (2009). Topological Properties of Silicate Networks, IEEE.GC.Confe.Exhi, 5, 1–5. https://doi.org/10.1109/IEEEGCC.2009.5734286. DOI: https://doi.org/10.1109/IEEEGCC.2009.5734286

Nadeem, M. F., Zafar, S., and Zahid, Z. (2015). On Certain Topological Indices of the Line Graph of Subdivision Graphs. Applied Mathematics and Computation, 271, 790–794. https://doi.org/10.1016/j.amc.2015.09.061. DOI: https://doi.org/10.1016/j.amc.2015.09.061

Pisanski, T., and Tucker, T. W. (2001). Growth in Repeated Truncations of Maps, Atti Sem. Mat. Fis. Univ. Modena, 49, 167–176.

Teguia, A. M., and Godbole, A. (2006). Sierpiński Gasket Graphs and Some of their Properties, Australasia-n. J. Combin, 35, 181–192. https://doi.org/10.48550/arXiv.math/0509259.

Vukičević, D., Li, Q., Sedlar, J., and Dǒslić, T. (2018). Lanzhou Index, MATCH Commun. Match. Computers and Chemistry, 80, 863–876.

Zmazek, B., and Zerovnik, J. (2003). Computing the Weighted Wiener and Szeged Number on Weighted Cactus Graphs in Linear Time. Croatica Chemica Acta, 76, 137–143.

Zmazek, B., and Zerovnik, J. (2005). Estimating the Trac on Weighted Cactus Networks in Linear Time, Ni-nth International Conference on Information Visualisation, 536–541.