Analysis of Bridge Graph through K-Banhatti Sombor Invariants
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Graph invariant is a numeric quantity, which is often associative with a molecular graph. During the last few years countless mathematical graph invariants have been characterized and used for the prediction of different
properties of chemical compounds. In any case, no solid assessment has been embraced to choose, how much these invariants are connected with a molecular graph. The current study introduces two new topological invariants, namely multiplicative k banhatti sombor index and multiplicative k banhatti reduce sombor index to calculate the results for three variants of bridge networks. Bridge graphs have a good potential for
prediction in the field of computer science, mathematics, chemistry, pharmacy, informatics, and biology in relation to physical, chemical structures, and networks. These deduced results can be used for the
computer network modelling, bio-informatics, and chemical compounds.
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Mansour T, Schork M. The vertex PI index and Szeged index of bridge graphs. Disc Appl Math. 2009;157(7):1600–1606. https://doi.org.10.1016/j.dam.2008.09.008
Khalaf AJM, Farhan M, Siddiqui M, Farahani M. On degree based topological indices of bridge graphs. J Dis Math Sci Crypto. 2020;23:1139–1156. https://doi.org/10.1080/09720529.2020.1822040
Gutman I. Some basic properties of Sombor indices. Open J Discret Appl Math. 2021;4(1):1–3. https://doi.org/10.30538/psrp-odam2021.0047
Rasulev BF, Abdullaev ND, Syrov VN, Leszczynski J. A quantitative structure‐activity relationship (QSAR) study of the antioxidant activity of flavonoids. QSAR & Combin Sci. 2005;24(9):1056-1065. https://doi.org/10.1002/qsar.200430013
Kiralj R, Ferreira M. Basic validation procedures for regression models in QSAR and QSPR studies: theory and application. J Braz Chem Soc. 2009;20(4):770-787. https://doi.org/10.1590/S0103-50532009000400021
Huo CG, Azhar F, Virk AR, Ismaeel T. Investigation of dendrimer structures by means of K-Banhatti invariants. J Math. 2022;2022:e4451899. https://doi.org/10.1155/2022/4451899
Sultan S, Gharibi W, Ahmad A. Computing the topological indices for certain families of graphs. Sci Int. 2015;27(6):3795-3810. https://doi.org/10.32604/cmc.2023.033976
Das KC, Bhatti FM, Lee SG, Gutman I. Spectral properties of the He matrix of hexagonal systems. MATCH Commun Math Comput Chem. 2011;65:753-774.
Imran M, Iqbal MA, Liu Y, Baig AQ, Khalid W, Zaighum MA. Computing eccentricity-Based topological indices of 2-Power interconnection networks. J Chem. 2020;2020:e379459. https://doi.org/10.1155/2020/3794592
Liu J, Cai L, Akhtar W, Maitla SA, Wei Y. Computation of irregularity indices of certain computer networks. 2020;2020:e2797286. https://doi.org/10.1155/2020/2797286
Cancan M, Ahmad I, Ahmad S, “Study of topology of block shift networks via topological indices. Proyecciones (Antofagasta). 2020;39(4):887–902. http://dx.doi.org/10.22199/issn.0717-6279-2020-04-0055
Ahmad MS, Nazeer W, Kang SM, Imran M, Gao W. Calculating degree-based topological indices of dominating David derived networks. Open Phy. 2017;15(1):1015–1021. https://doi.org/10.1515/phys-2017-0126
Wei C-C, Ali H, Binyamin MA, Naeem MN, Liu J-B. Computing degree based topological properties of third type of hex-derived networks. Math. 2019;7(4):e368. https://doi.org/10.3390/math7040368
Ahmad MS, Afzal D, Nazeer W, Kang SM. On topological indices of octagonal network. Far East J Math Sci. 2017;102(11):2563-2571. http://dx.doi.org/10.17654/MS102112563
Naeem M, Siddiqui MK, Guirao JLG, Gao W. New and modified eccentric indices of octagonal grid Omn. Appl Math Nonlinear Sci. 2018:3(1):209–228. https://doi.org/10.21042/AMNS.2018.1.00016
Hussain Z, Munir M, Rafique S, Min Kang S. Topological characterizations and index-analysis of new degree-based descriptors of honeycomb networks. Symmetry. 2018;10(10):e478. https://doi.org/10.3390/sym10100478
Riaz M, Gao W, Baig AQ. M-polynomials and degree-based topological indices of some families of convex polytopes. Open J Math Sci. 2018;2(1):18–28.
Mondal S, Nilanjan DE, Anita PAL. Topological Properties of Networks Using M-Polynomial Approach. Konuralp J Math. 2020;8(1):97–105.
Deng F, Zhang X, Alaeiyan M, Mehboob A, Farahani MR. Topological Indices of the Pent-Heptagonal Nanosheets VC5C7 and HC5C7. Adv Mater Sci Eng. 2019;2019:e9594549. https://doi.org/10.1155/2019/9594549
Mirehi N, Tahmasbi M, Targhi AT. Hand gesture recognition using topological feature. Multi Tools Appl. 2019;78(10):13361–13386. https://doi.org/10.1007/s11042-019-7269-1
M. K. Siddiqui, M. Naeem, N. A. Rahman, and M. Imran, “Computing topological indices of certain networks. J Optoelec Advan Mate. 2016;18(September-October):884–892.
Deria P, Gómez-Gualdrón DA, Hod I, Snurr RQ, Hupp JT, Farha OK. Framework-topology-dependent catalytic activity of zirconium-based (porphinato) zinc (II) MOFs. J Am Chem Soc. 2016;138(43):14449–14457.
Rajan B, William A, Grigorious C, Stephen S. On certain topological indices of silicate, honeycomb and hexagonal networks. J Comp Math Sci. 2012;3(5):498–556.
Liu J-B, Zhang T, S. Hayat S. The calculations of topological indices on certain networks. J Math. 2021;2021:e6694394. https://doi.org/10.1155/2021/6694394
Aslam A, Ahmad S, Binyamin MA, Gao W. Calculating topological indices of certain OTIS interconnection networks. Open Chem. 2019;17(1):220–228. https://doi.org/10.1515/chem-2019-0029
Bordoloi S, Kalita B. Designing graph database models from existing relational databases. Int J Comput Appl. 2013;74(1):25-31.
Duardo-Sanchez A, Patlewicz G, Gonzalez-Diaz H. Network topological indices from chem-bioinformatics to legal sciences and back. Curr Bioinfo. 2011;6(1):53–70. https://doi.org/10.2174/157489311795222347
Singh RP. Application of graph theory in computer science and engineering. Int J Comput Appl. 2014;104(1):10-13.
Marx D. Graph colouring problems and their applications in scheduling. Period Polytech Elec Eng. 2004;48(1-2):1-16.
Tosuni B. Graph theory in computer science–an overview. Int J Acad Res Ref. 2015;3(4):55–62.
Brückler FM, Došlić T, Graovac A, Gutman I. On a class of distance-based molecular structure descriptors. Chem Phy Letters. 20122;503:336–338. https://doi.org/10.1016/j.cplett.2011.01.033
Ajmal M, Nazeer W, Munir M, Kang SM, Jung, CY. The M-polynomials and topological indices of toroidal polyhex network. Int J Math Ana. 2017;11(7):305-315. https://doi.org/10.12988/ijma.2017.7119
Munir M, Nazeer W, Shahzadi Z, Kang SM. Some invariants of circulant graphs. Symmetry. 2016;8(11):e134. https://doi.org/10.3390/sym8110134
Wiener H. Structural determination of paraffin boiling points. J Am Chem Soc. 1947;69(1):17–20. https://doi.org/10.1021/ja01193a005
Randic M. Characterization of molecular branching. J Am Chem Soc. 1975;97(23):6609–6615. https://doi.oeg/10.1021/ja00856a001
Virk AR, Rehman MA, Nazeer W. New definition of atomic bond connectivity index to overcome deficiency of structure sensitivity and abruptness in existing definition. 2019;3(4):1-20. https://doi.org/10.32350/sir.34.01
Hashmi M, Chaudhry F, Khalaf AJM, Farahani M. Investigation of dendrimer structures by means of reverse atomic bond connectivity index. J Disc Math Sci Crypto. 2021;24:473–485. https://doi.org10.1080/09720529.2021.1882161
Kwun YC, Virk AR, Nazeer W, Rehman MA, Kang SM. On the multiplicative degree-based topological indices of silicon-carbon Si2C3-I[p,q] and Si2C3-II[p,q]. Symmetry. 2018;10(8):e320. https://doi.org/10.3390/sym10080320
Virk AUR, Jhangeer MN, Rehman MA. Reverse Zagreb and reverse hyper-Zagreb indices for silicon carbide Si2C3I [r, s] and Si2C3II [r, s]. Eng Appl Sci Letter. 2018;1(2): 37-50.
Virk AUR. Multiplicative shingali and kanabour indices for bismuth tri-iodide. J Prime Res Math. 2020;16(2):80-88.
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