Generalized Multiplicative Indices on Certain Chemical
Networks

Divyashree B K; Jagadeesh R; Siddabasappa

doi:https://doi.org/10.14445/22315373/IJMTT-V68I6P503

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 68 | Issue 6 | Year 2022 | Article Id. IJMTT-V68I6P503 | DOI : https://doi.org/10.14445/22315373/IJMTT-V68I6P503

Generalized Multiplicative Indices on Certain Chemical Networks

Divyashree B K, Jagadeesh R, Siddabasappa

Received	Revised	Accepted	Published
10 Apr 2022	25 May 2022	05 Jun 2022	16 Jun 2022

Citation :

Divyashree B K, Jagadeesh R, Siddabasappa, "Generalized Multiplicative Indices on Certain Chemical Networks," International Journal of Mathematics Trends and Technology (IJMTT), vol. 68, no. 6, pp. 17-32, 2022. Crossref, https://doi.org/10.14445/22315373/IJMTT-V68I6P503

Abstract

The evaluation of some indices for chemical networks, which includes the first and the second Zagreb index, generalized multiplicative indices by which we can project the stability or other properties of networks, such as ndimensional silicate networks 𝑆𝐿(𝑛), chain silicate networks (𝐶𝑛), hexagonal networks (𝐻𝑋𝑛), oxide networks(𝑂𝑛 ), cellular networks𝐻𝐶(𝑛), and Sierpinski networks 𝑆(𝐾𝑝, 𝑚). The graphical analysis is used to plot the graphs and see the effects of our results on the considered parameters.

Keywords

Silicate networks, Chain silicate networks, Hexagonal networks, Oxide networks, Cellular networks, Sierpinski networks.

References

[1] Liszka K. J, Antonio J. K, Siegel H. J, Problems with Comparing Interconnection Networks: Is an Alligator Better than an Armadillo?,IEEE Concurrency, 5(4) 18-28 (1997).
[2] Junming Xu, Topological Structure and Analysis of Interconnection Networks, Kluwer Academic Publishers, (2001).
[3] H. Wiener, Structural Determination of Paraffin Boiling Points, Journal of American Chemical Society. 69(1) 17-20.
[4] P. W. Fowler, G. Caporossi, and P. Hansen, Distance Matrices, Wiener Indices, and Related Invariants of Fullerenes, J. Phys. Chem. A, 105(25) 6232-6242.
[5] A. R. Matamala and E. Estrada, Simplex optimization of generalized topological index (GTI-simplex): a unified approach to optimize QSPR models, J. Phys. Chem. A, 109(43) (2005) 9890-9895.
[6] M. Randić, T. Pisanski, M. Novič, and D. Plavšić, Novel graph distance matrix, J. Comput.Chem.,31(9) (2010) 1832-1841.
[7] F. Yang, Z.-D. Wang, and Y.-P. Huang, Modification of the Wiener index 4, J. Comp. Chem. ,25(6 ) (2004) 881-887.
[8] I.Gutman, O.E. Polansky, Mathematical Concepts in Organic Chemistry,Springer, Berlin, (1986).
[9] V.R. Kulli, Multiplicative Connectivity Indices of Nanostructures, LAP LEMBERTAcademic Publishing, (2018).
[10] V.R. Kulli, College Graph Theory, Vishwa International Publications, Gulbarga, India, (2012).
[11] I. Gutman, B. Ruščić, N. Trinajstić, and C. F. Wilcox, Graph Theory and Molecular Orbitals. XII. Acyclic Polyenes, J. Chem.Phys., 62(9) (1975) 3399-3405.
[12] I. Gutman, Multiplicative Zagreb indices of trees, Bull. Int. Math. Virtual Inst. 1 (2011) 13-19.
[13] R. Todeschini, D. Ballabio, and V. Consonni, Novel molecular descriptors based on functions of new vertex degrees, in: Novel Molecular Structure Descriptors – Theory and Applications I, University of Kragujevac,Kragujevac, 8 (2010) 73-100.
[14] R. Todeschini and V. Consonni, New Local Vertex Invariants and Molecular Descriptors Based on Functions of the Vertex Degrees, MATCH Commun. Math. Comput. Chem. ,64 (2010) 359-372.
[15] S. Wang and B. Wei, Multiplicative Zagreb Indices of K-Trees, Discrete Applied Mathematics, 180 (2015)168-175.
[16] M. Eliasi, A. Iranmanesh, and I. Gutman, Multiplicative Versions of First Zagreb Index, MATCH Commun. Math. Comput. Chem., 68 (2012) 217-230.
[17] V. R. Kulli, Hyper-Banhatti indices and coindices of graphs, International Research Journal of Pure Algebra, 6(5) (2016) 300-304.
[18] V. R. Kulli, K1 and K2 Indices, International Journal of Mathematics Trends and Technology, 68(1) (2022) 43-52.
[19] V. R. Kulli, Banhatti − Nirmala Index of certain chemical networks, International Journal of Mathematics Trends and Technology, 68(4) (2022) 1.