Mathematical Study of Zinc Oxide and Zinc Silicate Metal Organic Networks Via Reduce Reverse Degree Based Topological Indices
DOI:
https://doi.org/10.33411/IJIST/1968Keywords:
Topological Indices, Reduce Reverse Indices, Chemical Graph Theory, Metal Organic NetworksAbstract
In this article, some reduced reverse topological indices ((RR)TIs) are calculated based on edge partitions associated with the atomic structures of the Zinc Oxide (" ZNOX " ("h" ) and zinc silicate ("ZNSL " ("h”) metal organic networks (MON‘s’) respectively. I have calculated the reduced reverse degree-based topological indices associated with these metal organic networks like: "RRM1" ("G" )",RRM2" ("G" )",RRH M1 " ("G" )",RRH M2 " ("G" )",RRF" ("G")",RRABC(G), RRGA(G)"respectively. I have also discussed the numerical and graphical behavior of these metal organic networks. At the end, the obtained mathematical results are compared.
References
Y. Kinoshita, I. Matsubara, T. Higuchi, and Y. Saito, “The Crystal Structure of Bis(adiponitrilo)copper(I) Nitrate,” Bull. Chem. Soc. Jpn., vol. 32, no. 11, pp. 1221–1226, Nov. 1959, doi: 10.1246/BCSJ.32.1221.
B. F. Hoskins and R. Robson, “Infinite polymeric frameworks consisting of three dimensionally linked rod-like segments,” J. Am. Chem. Soc., vol. 111, no. 15, pp. 5962–5964, Jul. 1989, doi: 10.1021/JA00197A079.
Y. Cui et al., “A Luminescent Mixed-LanthanideMetal–OrganicFramework Thermometer,” J. Am. Chem. Soc., vol. 134, no. 9, pp. 3979–3982, Mar. 2012, doi: 10.1021/JA2108036.
C. Wang et al., “Dye@bio-MOF‑1Composite as a Dual-Emitting Platform for Enhanced Detection of aWide Range of Explosive Molecules,” ACS Appl. Mater. Interfaces, vol. 9, no. 23, pp. 20076–20085, Jun. 2017, doi: 10.1021/ACSAMI.7B04172.
A. S. Prasad, “Zinc in Human Health: Effect of Zinc on Immune Cells,” Mol. Med., vol. 14, no. 5–6, p. 353, May 2008, doi: 10.2119/2008-00033.PRASAD.
M. Eddaoudi et al., “Systematic Design of Pore Size and Functionality in Isoreticular MOFs and Their Application in Methane Storage,” Science (80-. )., vol. 295, no. 5554, pp. 469–472, Jan. 2002, doi: 10.1126/SCIENCE.1067208.
Y. K. Hwang et al., “Amine grafting on coordinatively unsaturated metal centers of MOFs: Consequences for catalysis and metal encapsulation,” Angew. Chemie - Int. Ed., vol. 47, no. 22, pp. 4144–4148, May 2008, doi: 10.1002/ANIE.200705998.
A. W. Thornton, K. M. Nairn, J. M. Hill, A. J. Hill, and M. R. Hill, “Metal−Organic Frameworks Impregnated with Magnesium-Decorated Fullerenes for Methane and Hydrogen Storage,” J. Am. Chem. Soc., vol. 131, no. 30, pp. 10662–10669, Aug. 2009, doi: 10.1021/JA9036302.
M. Kim, J. F. Cahill, H. Fei, K. A. Prather, and S. M. Cohen, “Postsynthetic Ligand andCation Exchangein Robust Metal–Organic Frameworks,” J. Am. Chem. Soc., vol. 134, no. 43, pp. 18082–18088, Oct. 2012, doi: 10.1021/JA3079219.
I. Ahmed and S. H. Jhung, “Composites of metal–organic frameworks: Preparation and application in adsorption,” Mater. Today, vol. 17, no. 3, pp. 136–146, Apr. 2014, doi: 10.1016/J.MATTOD.2014.03.002.
G. Ding et al., “High-performance all-polymer nonfullerene solar cells by employing an efficient polymer-small molecule acceptor alloy strategy,” Nano Energy, vol. 36, pp. 356–365, Jun. 2017, doi: 10.1016/J.NANOEN.2017.04.061.
M. H. Yap, K. L. Fow, and G. Z. Chen, “Synthesis and applications of MOF-derived porous nanostructures,” Green Energy Environ., vol. 2, no. 3, pp. 218–245, Jul. 2017, doi: 10.1016/J.GEE.2017.05.003.
R. B. Lin, S. Xiang, H. Xing, W. Zhou, and B. Chen, “Exploration of porous metal–organic frameworks for gas separation and purification,” Coord. Chem. Rev., vol. 378, pp. 87–103, Jan. 2019, doi: 10.1016/J.CCR.2017.09.027.
I. Gutman, “Selected properties of the Schultz molecular topological index,” J. Chem. Inf. Comput. Sci., vol. 34, no. 5, pp. 1087–1089, Sep. 1994, doi: 10.1021/CI00021A009.
G. Rücker and C. Rücker, “On Topological Indices, Boiling Points, and Cycloalkanes,” J. Chem. Inf. Comput. Sci., vol. 39, no. 5, pp. 788–802, Sep. 1999, doi: 10.1021/CI9900175.
H. Gonzalez-Diaz, S. Vilar, L. Santana, and E. Uriarte, “Medicinal chemistry and bioinformatics--current trends in drugs discovery with networks topological indices,” Curr. Top. Med. Chem., vol. 7, no. 10, pp. 1015–1029, Jun. 2007, doi: 10.2174/156802607780906771.
M. K. Siddiqui, M. Imran, and A. Ahmad, “On Zagreb indices, Zagreb polynomials of some nanostar dendrimers,” Appl. Math. Comput., vol. 280, pp. 132–139, Apr. 2016, doi: 10.1016/J.AMC.2016.01.041.
I. Gutman and N. Trinajstić, “Graph theory and molecular orbitals. Total φ-electron energy of alternant hydrocarbons,” Chem. Phys. Lett., vol. 17, no. 4, pp. 535–538, Dec. 1972, doi: 10.1016/0009-2614(72)85099-1.
V. Ravi and K. Desikan, “On computation of the reduced reverse degree and neighbourhood degree sum-based topological indices for metal-organic frameworks,” Main Gr. Met. Chem., vol. 45, no. 1, pp. 92–99, Jan. 2022, doi: 10.1515/MGMC-2022-0009.
T. Došli´došli´c, M. A. Hosseinzadeh, S. Hossein-Zadeh, A. Iranmanesh, and F. Rezakhanlou, “On Generalized Zagreb Indices of Random Graphs”.
L. Buyantogtokh, B. Horoldagva, and K. C. Das, “On reduced second Zagreb index,” J. Comb. Optim. 2020 393, vol. 39, no. 3, pp. 776–791, Jan. 2020, doi: 10.1007/S10878-019-00518-7.
“Riverbank Erosion & Consequent Land Settlement Issues: A Case of River Chenab, District Hafizabad | International Journal of Innovations in Science & Technology.” Accessed: Aug. 03, 2026. [Online]. Available: https://journal.50sea.com/index.php/IJIST/Riverbank-Erosion-Consequent-Land-Sett
W. Gao, H. Wu, M. K. Siddiqui, and A. Q. Baig, “Study of biological networks using graph theory,” Saudi J. Biol. Sci., vol. 25, no. 6, pp. 1212–1219, Sep. 2018, doi: 10.1016/J.SJBS.2017.11.022.
F. Javaid, M. K. Jamil, and I. Tomescu, “Extremal k-generalized quasi unicyclic graphs with respect to first and second Zagreb indices,” Discret. Appl. Math., vol. 270, pp. 153–158, Nov. 2019, doi: 10.1016/J.DAM.2019.06.006.
Sadia Noureen, Akhlaq Ahmad Bhatti, “Extremal trees for the modified first Zagreb connection index with fixed number of segments or vertices of degree 2,” J. Taibah Univ. Sci., vol. 14, no. 1, 2020, [Online]. Available: https://www.tandfonline.com/doi/full/10.1080/16583655.2019.1699227
Z. Wang, F. Chaudhry, M. Naseem, and A. Asghar, “Reverse Zagreb and Reverse Hyper-Zagreb Indices for Crystallographic Structure of Molecules,” J. Chem., vol. 2020, 2020, doi: 10.1155/2020/9805829.
V. R. Kulli, “Reverse Zagreb and Reverse Hyper-Zagreb Indices and their Polynomials of Rhombus Silicate Networks,” Ann. Pure Appl. Math., vol. 16, no. 1, pp. 47–51, Jan. 2018, doi: 10.22457/APAM.V16N1A6.
C. Y. Jung, M. A. Gondal, N. Ahmad, and S. M. Kang, “Reverse degree based indices of some nanotubes,” J. Discret. Math. Sci. Cryptogr., vol. 22, no. 7, pp. 1289–1294, Oct. 2019, doi: 10.1080/09720529.2019.1700921.
D. Zhao et al., “On Reverse Degree Based Topological Indices of Polycyclic Metal Organic Network,” Polycycl. Aromat. Compd., vol. 42, no. 7, pp. 4386–4403, Jan. 2022, doi: 10.1080/10406638.2021.1891105.
R. S. Haoer and A. U. R. Virk, “Some reverse topological invariants for metal-organic networks,” J. Discret. Math. Sci. Cryptogr., vol. 24, no. 2, pp. 499–510, Feb. 2021, doi: 10.1080/09720529.2021.1899208.
S. Zaman, K. H. Hakami, S. Rasheed, and F. T. Agama, “Reduced reverse degree-based topological indices of graphyne and graphdiyne nanoribbons with applications in chemical analysis,” Sci. Reports 2024 141, vol. 14, no. 1, pp. 547-, Jan. 2024, doi: 10.1038/s41598-023-51112-1.
D. L and V. K. M, “Reduced Reversed Degree-Based Topological Indices Of Line Graph Of Alkanes,” Int. J. Environ. Sci., vol. 11, no. 15, pp. 410–418, Jun. 2025, doi: 10.64252/2A6QGQ64.
G. Hong, Z. Gu, M. Javaid, H. M. Awais, and M. K. Siddiqui, “Degree-based topological invariants of metal-organic networks,” IEEE Access, vol. 8, pp. 68288–68300, 2020, doi: 10.1109/ACCESS.2020.2985729.
“(PDF) A Study of Indium phosphide and line graph of subdivision graph of H-naphtalenic nano-sheet via irregularity indices.” Accessed: Aug. 03, 2026. [Online]. Available: https://www.researchgate.net/publication/391487375_A_Study_of_Indium_phosphide_and_line_graph_of_subdivision_graph_of_H-naphtalenic_nano-sheet_via_irregularity_indices
iftikhar Ali, M. H. Aftab, T. Khalifa, and H. Kanj, “Topological attributes of Caffeine [C8H10N4O2] and Subdivided Aztec diamond Networks Via Revan Indices,” Tech. J., vol. 30, no. 04, pp. 46–54, Dec. 2025, Accessed: Aug. 03, 2026. [Online]. Available: https://tj.uettaxila.edu.pk/index.php/technical-journal/article/view/2265
S. M. Hosamani, “Correlation of domination parameters with physicochemical properties of octane isomers,” Appl. Math. Nonlinear Sci., vol. 1, no. 2, pp. 345–352, Aug. 2016, doi: 10.21042/AMNS.2016.2.00029.
J. Rada, J. M. Rodríguez, and J. M. Sigarreta, “Geometric properties of chemical graphs,” Int. J. Quantum Chem., vol. 121, no. 23, p. e26798, Dec. 2021, doi: 10.1002/QUA.26798.
H. M. Awais, M. Jamal, and M. Javaid, “Topological properties of metal-organic frameworks,” Main Gr. Met. Chem., vol. 43, no. 1, pp. 67–76, Jan. 2020, doi: 10.1515/MGMC-2020-0007.
P. Horcajada et al., “Flexible Porous Metal-Organic Frameworks for a Controlled Drug Delivery,” J. Am. Chem. Soc., vol. 130, no. 21, pp. 6774–6780, May 2008, doi: 10.1021/JA710973K.
L. Sarkisov, “Toward Rational Designof Metal–Organic Frameworksfor Sensing Applications: Efficient Calculation of Adsorption Characteristicsin Zero Loading Regime,” J. Phys. Chem. C, vol. 116, no. 4, pp. 3025–3033, Feb. 2012, doi: 10.1021/JP210633W.
M. An, “The first Zagreb index, reciprocal degree distance and Hamiltonian-connectedness of graphs,” Inf. Process. Lett., vol. 176, p. 106247, Jun. 2022, doi: 10.1016/J.IPL.2022.106247.
G. H. SHIRDEL, H. REZAPOUR, and A. M. SAYADI, “The Hyper-Zagreb Index of Graph Operations,” Iran. J. Math. Chem., vol. 4, no. 2, pp. 213–220, May 2013, doi: 10.22052/IJMC.2013.5294.
V. Ravi, M. K. Siddiqui, N. Chidambaram, and K. Desikan, “On Topological Descriptors and Curvilinear Regression Analysis of Antiviral Drugs Used in COVID-19 Treatment,” Polycycl. Aromat. Compd., vol. 42, no. 10, pp. 6932–6945, Nov. 2022, doi: 10.1080/10406638.2021.1993941.
B. Furtula and I. Gutman, “A forgotten topological index,” J. Math. Chem. 2015 534, vol. 53, no. 4, pp. 1184–1190, Feb. 2015, doi: 10.1007/S10910-015-0480-Z.
E. Estrada, L. A. Torres, L. Rodríguez, and I. Gutman, “An Atom-Bond Connectivity Index : Modelling The Enthalpy of Formation of Alkanes,” Indian J. Chem. Sect. A Inorganic, Phys. Theor. Anal., 1998.
D. Vukičević and B. Furtula, “Topological index based on the ratios of geometrical and arithmetical means of end-vertex degrees of edges,” J. Math. Chem. 2009 464, vol. 46, no. 4, pp. 1369–1376, Jan. 2009, doi: 10.1007/S10910-009-9520-X
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