On SiO4 Molecular Topological Characterization of Chemical Structures
Keywords:
SiO4 in a chain, ABC polynomial and ABC index, geometric arithmetic polynomial, Randic index and reciprocal randic polynomial, sigma and Sombor index 2020 AMS Mathematics Subject Classification, 05C07, 05C09, 05C31, 05C76, 05 C 99
Abstract
In this paper, our aim is to study valency-based molecular invariants for SiO4 in a chain network. We compute the harmonic polynomial, atom bond connectivity polynomial, forgotten polynomial, geometric arithmetic polynomial, Randic polynomial, reciprocal Randic polynomial, symmetric division polynomial, inverse symmetric division polynomial, sigma polynomial, Sombor polynomial, and their degree-base topological indices for SiO4 embedded in a silicate chain network for various conditions. Physio-chemical properties of chemical compounds, such as formation enthalpies, boiling points, chromatographic retention times, vapour pressure, and surface areas, can be determined using our investigated results, such as the H-index, ABC-index, F-index, GA-index, R-index, RR-index, SDD-index, ISDD index, S-index, and SO-index. We also create graphical representations of the results that describe the dependence of topological indices on polynomial structure parameters.
References
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[25] Farrukh, Fatima, Rashid Farooq, and Mohammad R. Farahani. ”Calculating Some Topological Indices of SiO2 Layer Structure.” Journal of Informatics and Mathematical Sciences 8.3 (2016): 181-187..
[26] Ghorbani, Modjtaba, Samaneh Zangi, and Najaf Amraei. ”New results on symmetric division deg index.” Journal of Applied Mathematics and Computing 65.1 (2021): 161176.
[27] Aguilar-Snchez, R., et al. ”Analytical and computational properties of the variable symmetric division deg index.” arXiv preprint arXiv:2106.00913 (2021).
[28] Shpiz, Grigory B., and Alexander P. Kryukov. ”The method of colored graphs for simplifying expressions with indices.” Programming and Computer Software 47.1 (2021): 25-28.
[29] Gutman, Ivan. ”Geometric approach to degree-based topological indices: Sombor indices.” MATCH Commun. Math. Comput. Chem 86.1 (2021): 11-16.
[30] Kulli, V. R. ”On the product connectivity reverse index of silicate and hexagonal networks.” rn 55 (2017): 7.
[31] Hu, Min, et al. ”On distance-based topological descriptors of chemical interconnection networks.” Journal of Mathematics 2021 (2021).
[32] Kulli, V. R. ”The sum connectivity Revan index of silicate and hexagonal networks.” Annals of Pure and Applied Mathematics 14.3 (2017): 401-406.
[33] Kulli, V. R., and Ivan Gutman. ”Computation of Sombor indices of certain networks.” SSRG Int. J. Appl. Chem 8.1 (2021): 1-5.
[34] Zhou, Bo, and Ivan Gutman. ”Further properties of Zagreb indices.” MATCH Commun.
Math. Comput. Chem 54.1 (2005): 233-239.
[2] Mekapati, Suresh Babu, and Corwin Hansch. ”Comparative QSAR studies on bibenzimidazoles and terbenzimidazoles inhibiting topoisomerase I.” Bioorganic & medicinal chemistry 9.11 (2001): 2885-2893.
[3] Wiener, Harry. ”Structural determination of paraffin boiling points.” Journal of the American chemical society 69.1 (1947): 17-20.
[4] Costa, Paulo CS, et al. ”Chemical Graph Theory for Property Modeling in QSAR and QSPRCharming QSAR & QSPR.” Mathematics 9.1 (2020): 60.
[5] J.-B. Liu, C. Wang, S. Wang, and B. Wei, Zagreb indices and multiplicative zagreb indices of eulerian graphs, Bulletin of the Malaysian Mathematical Sciences Society, vol. 42, no. 1, pp. 6778, 2019.
[6] J. B. Liu, J. Zhao, J. Min, and J. Cao, ,e Hosoya index of graphs formed by a fractal graph, Fractals, vol. 27, no. 8, Article ID 1950135, 2019.
[7] J.-B. Liu and S. N. Daoud, Number of spanning trees in the sequence of some graphs, Complexity, vol. 2019, Article ID 4271783, 22 pages, 2019.
[8] J. B. Liu, J. Zhao, and Z. Q. Cai, On the generalized adjacency, Laplacian and signless Laplacian spectra of the weighted edge corona networks, Physica A: Statistical Mechanics and Its Applications, vol. 540, 2020.
[9] J. B. Liu, Z. Y. Shi, Y. H. Pan, J. Cao, M. Abdel-Aty, and U. Al-Juboori, Computing the laplacian spectrum of linear octagonal-quadrilateral networks and its applications, Polycyclic Aromatic Compounds, pp. 1-2, 2020.
[10] J. B. Liu, X. F. Pan, J. Cao, and F. F. Hu, A note on some physical and chemical indices of clique-inserted lattices, Journal of Statistical Mechanics: 7eory and Experiment, vol. 2014, no. 6, Article ID P06006, 2014.
[11] J.-B. Liu, X.-F. Pan, J. Cao, and X. Huang, ,e kirchhoff index of toroidal meshes and variant networks, Mathematical Problems in Engineering, vol. 2014, Article ID 286876, 8 pages, 2014.
[12] J.-B. Liu, X.-F. Pan, and J. Cao, Some properties on Estrada index of folded hypercubes networks, Abstract and Applied Analysis, vol. 2014, Article ID 167623, 6 pages, 2014.
[13] Ghani, Muhammad Usman, et al. ”A Paradigmatic Approach to Find the ValencyBased K-Banhatti and Redefined Zagreb Entropy for Niobium Oxide and a MetalOrganic Framework.” Molecules 27.20 (2022): 6975.
[14] Zhang, Ying-Fang, et al. ”Connecting SiO 4 in Silicate and Silicate Chain Networks to Compute Kulli Temperature Indices.” Molecules 27.21 (2022): 7533.
[15] Sourav Mondal, Arindam Dey, Nilanjan De, and Anita Pal, Qspr analysis of some novel neighbourhood degree-based topological descriptors, Complex & Intelligent Systems 7 (2021), no. 2, 977996.
[16] Alam, Ashraful, et al. ”Degree-Based Entropy for a Non-Kekulean Benzenoid Graph.” Journal of Mathematics 2022 (2022).
[17] Al-Ahmadi, Bashair, Anwar Saleh, and Wafa Al-Shammakh. ”Downhill Zagreb Topological Indices and M dn-Polynomial of Some Chemical Structures Applied for the Treatment of COVID-19 Patients.” Open Journal of Applied Sciences 10.04 (2021): 395.
[18] Anton B Zakharov, Dmytro K Tsarenko, and Vladimir V Ivanov, Topological characteristics of iterated line graphs in the qsar problem: a multigraph in the description of properties of unsaturated hydrocarbons, Structural Chemistry (2021), 111.
[19] Natarajan, Vanasundaram, et al. ”Effect of electron-phonon interaction and valence band edge shift for carrier-type reversal in layered ZnS/rGO nanocomposites.” Journal of Colloid and Interface Science 586 (2021): 39-46.
[20] Zhong, Lingping. ”The harmonic index for graphs.” Applied Mathematics Letters 25.3 (2012): 561-566.
[21] Estrada, Ernesto, et al. ”An atom-bond connectivity index: modelling the enthalpy of formation of alkanes.” (1998).
[22] Furtula, Boris, and Ivan Gutman. ”A forgotten topological index.” Journal of mathematical chemistry 53.4 (2015): 1184-1190.
[23] Vukicevic, Damir, and Boris Furtula. ”Topological index based on the ratios of geometrical and arithmetical means of end-vertex degrees of edges.” Journal of mathematical chemistry 46.4 (2009): 1369-1376.
[24] Li, Xu, et al. ”Bounds on general randic index for F-sum graphs.” Journal of Mathematics 2020 (2020). Kulli, V. R., B. Chaluvaraju, and H. S. Boregowda. ”Connectivity Banhatti indices for certain families of benzenoid systems.” Journal of Ultra Chemistry 13.4 (2017): 81-
[25] Farrukh, Fatima, Rashid Farooq, and Mohammad R. Farahani. ”Calculating Some Topological Indices of SiO2 Layer Structure.” Journal of Informatics and Mathematical Sciences 8.3 (2016): 181-187..
[26] Ghorbani, Modjtaba, Samaneh Zangi, and Najaf Amraei. ”New results on symmetric division deg index.” Journal of Applied Mathematics and Computing 65.1 (2021): 161176.
[27] Aguilar-Snchez, R., et al. ”Analytical and computational properties of the variable symmetric division deg index.” arXiv preprint arXiv:2106.00913 (2021).
[28] Shpiz, Grigory B., and Alexander P. Kryukov. ”The method of colored graphs for simplifying expressions with indices.” Programming and Computer Software 47.1 (2021): 25-28.
[29] Gutman, Ivan. ”Geometric approach to degree-based topological indices: Sombor indices.” MATCH Commun. Math. Comput. Chem 86.1 (2021): 11-16.
[30] Kulli, V. R. ”On the product connectivity reverse index of silicate and hexagonal networks.” rn 55 (2017): 7.
[31] Hu, Min, et al. ”On distance-based topological descriptors of chemical interconnection networks.” Journal of Mathematics 2021 (2021).
[32] Kulli, V. R. ”The sum connectivity Revan index of silicate and hexagonal networks.” Annals of Pure and Applied Mathematics 14.3 (2017): 401-406.
[33] Kulli, V. R., and Ivan Gutman. ”Computation of Sombor indices of certain networks.” SSRG Int. J. Appl. Chem 8.1 (2021): 1-5.
[34] Zhou, Bo, and Ivan Gutman. ”Further properties of Zagreb indices.” MATCH Commun.
Math. Comput. Chem 54.1 (2005): 233-239.
Published
2025-04-30
How to Cite
Mj, J., & shivashankara, k. (2025). On SiO4 Molecular Topological Characterization of Chemical Structures. IJO - International Journal of Mathematics (ISSN: 2992-4421 ), 8(04), 01-21. Retrieved from https://ijojournals.com/index.php/m/article/view/1071
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