Generic placeholder image

Current Organic Chemistry

Author(s): Muhammad Mudassar Hassan*

DOI: 10.2174/0113852728271631231121061349

DownloadDownload PDF Flyer Cite As
Connection Number-based Multiplicative Zagreb Indices of Chemical Structures

Page: [1873 - 1881] Pages: 9

  • * (Excluding Mailing and Handling)

Explore Articles
About Journal
For Authors
For Editors
For Reviewers

Abstract

A topological index is a quantitative measure of molecular structure and connection. It also estimates the toxicological, structural, biological, and physicochemical characteristics of a chemical molecule. The use of nano-structured graphs in the study of chemistry is very extensive. Melem, one of the most significant tri−s−triazine compounds, is a nucleophilic reagent that may be employed in reactions with derivatives of phthalic acid. Materials with borophene nanostructures are also exploited in cross-disciplinary research. In comparison to carbon hexagonal nanotubes, boron triangular nanotubes are thought to be a superior conductor. The goal of computing the multiplicative Zagreb connection indices for Chemical graphs is to understand the complexity, connectedness, and chemical activity of molecules. Information is useful in a number of applications, including drug design, chemical synthesis, and property prediction. In this paper, we compute the first, second, third, fourth, and fifth multiplicative Zagreb connection indices (ZCIs) of the melem chain MC(s), the borophene chain B36(s), and the boron triangular sheet BTS(m,s).

Graphical Abstract

[1]
Assad, A.A. Leonhard Euler: A brief appreciation. Networks. Int. J., 2007, 49(3), 190-198.
[2]
Trinajstić N.; Klein, D.J.; Randić M. On some solved and unsolved problems of chemical graph theory. Int. J. Quantum Chem., 1986, 30(S20), 699-742.
[http://dx.doi.org/10.1002/qua.560300762]
[3]
Balaban, A.T. Topological indices based on topological distances in molecular graphs. Pure Appl. Chem., 1983, 55(2), 199-206.
[http://dx.doi.org/10.1351/pac198855020199]
[4]
Kiang, Y.S. Partition technique and molecular graph theory. Int. J. Quantum Chem., 1981, 20(S15), 293-304.
[http://dx.doi.org/10.1002/qua.560200832]
[5]
Zaman, S.; Jalani, M.; Ullah, A.; Ali, M.; Shahzadi, T. On the topological descriptors and structural analysis of cerium oxide nanostructures. Chem. Zvesti, 2023, 77(5), 2917-2922.
[http://dx.doi.org/10.1007/s11696-023-02675-w]
[6]
Xu, K.; Zheng, Z.Ch.; Das, K. Extremal t‐apex trees with respect to matching energy. Complexity, 2016, 21(5), 238-247.
[http://dx.doi.org/10.1002/cplx.21651]
[7]
Ali, H.; Baig, A.Q.; Shafiq, M.K. On topological properties of boron triangular sheet BTS (m, n), borophene chain B36 (n) and melem chain MC (n) nanostruc-tures. J. Math Nanosci., 2017, 7(1), 39-60.
[8]
Wang, X.; Zhang, Q.; Guo, D.; Zhao, X. A survey of continuous subgraph matching for dynamic graphs. Knowl. Inf. Syst., 2023, 65(3), 945-989.
[http://dx.doi.org/10.1007/s10115-022-01753-x]
[9]
Jia, P.; Pei, J.; Wang, G.; Pan, X.; Zhu, Y.; Wu, Y.; Ouyang, L. The roles of computer-aided drug synthesis in drug development. Green Synth. Catal., 2022, 3(1), 11-24.
[http://dx.doi.org/10.1016/j.gresc.2021.11.007]
[10]
Dorahy, G.; Chen, J.Z.; Balle, T. Computer-aided drug design towards new psychotropic and neurological drugs. Molecules, 2023, 28(3), 1324.
[http://dx.doi.org/10.3390/molecules28031324] [PMID: 36770990]
[11]
Rantanen, J.; Khinast, J. The future of pharmaceutical manufacturing sciences. J. Pharm. Sci., 2015, 104(11), 3612-3638.
[12]
Yang, Z.; Yuan, K.; Meng, J.; Hu, M. Electric field tuned anisotropic to isotropic thermal transport transition in monolayer borophene without altering its atomic structure. Nanoscale, 2020, 12(37), 19178-19190.
[http://dx.doi.org/10.1039/D0NR03273E] [PMID: 32926048]
[13]
Shang, J.; Ma, Y.; Gu, Y.; Kou, L. Two dimensional boron nanosheets: Synthesis, properties and applications. Phys. Chem. Chem. Phys., 2018, 20(46), 28964-28978.
[http://dx.doi.org/10.1039/C8CP04850A] [PMID: 30426985]
[14]
Huang, F.; Li, X.; Qin, Z.; Magnant, C.; Ozeki, K. On two conjectures about the proper connection number of graphs. Discrete Math., 2017, 340(9), 2217-2222.
[http://dx.doi.org/10.1016/j.disc.2017.04.022]
[15]
Fatima, N.; Bhatti, A.A.; Ali, A.; Gao, W. Zagreb connection indices of two dendrimer nanostars. Acta Chemica Iasi, 2019, 27(1), 1-14.
[http://dx.doi.org/10.2478/achi-2019-0001]
[16]
Du, Z.; Ali, A. Trinajstić N. Alkanes with the first three maximal/minimal modified first Zagreb connection indices. Mol. Inform., 2019, 38(4)1800116
[http://dx.doi.org/10.1002/minf.201800116] [PMID: 30614630]
[17]
Liu, J.B.; Wang, C.; Wang, S.; Wei, B. Zagreb indices and multiplicative zagreb indices of eulerian graphs. Bull. Malays. Math. Sci. Soc., 2019, 42(1), 67-78.
[http://dx.doi.org/10.1007/s40840-017-0463-2]
[18]
Noureen, S.; Bhatti, A.A.; Ali, A. Extremal trees for the modified first Zagreb connection index with fixed number of segments or vertices of degree 2. J. Taibah Univ. Sci., 2020, 14(1), 31-37.
[http://dx.doi.org/10.1080/16583655.2019.1699227]
[19]
Raza, Z.; Bataineh, M.S.; Sukaiti, M.E. On the zagreb connection indices of hex and honeycomb networks. J. Intell. Fuzzy Syst., 2021, 40(3), 4107-4114.
[http://dx.doi.org/10.3233/JIFS-200659]
[20]
Hussain, A.; Numan, M.; Naz, N.; Butt, S.I.; Aslam, A.; Fahad, A. On topological indices for new classes of benes network. J. Math., 2021, 2021, 1-7.
[http://dx.doi.org/10.1155/2021/6690053]
[21]
Hasan, A.; Qasmi, M.H.; Alsinai, A.; Alaeiyan, M.; Farahani, M.R.; Cancan, M. Distance and degree based topological polynomial and indices of X-level wheel graph. J. Prime Res. Math., 2021, 17(2), 39-50.
[22]
Fahad, A.; Aslam, A.; Qureshi, M.I.; Jamil, M.K.; Jaleel, A. Zagreb connection indices of some classes of networks. Biointerface Res. Appl. Chem., 2021, 11(3), 10074-10081.
[23]
Sattar, A.; Javaid, M.; Bonyah, E. Computing connection-based topological indices of dendrimers. J. Chem.,, 2022.
[24]
Raza, Z. Zagreb connection indices for some benzenoid systems. Polycycl. Aromat. Compd., 2022, 42(4), 1814-1827.
[http://dx.doi.org/10.1080/10406638.2020.1809469]
[25]
Ahmed, H.; Alsinai, A.; Khan, A.; Othman, H.A. The eccentric Zagreb indices for the subdivision of some graphs and their applications. Appl. Math. Inf. Sci., 2022, 16(3), 467-472.
[http://dx.doi.org/10.18576/amis/160308]
[26]
Alsinai, A.; Rehman, H.M.; Manzoor, Y.; Cancan, M. Taş, Z.; Farahani, M.R. Sharp upper bounds on forgotten and SK indices of cactus graph. J. Discrete Math. Sci. Cryptogr., , 2022, 1-22.
[http://dx.doi.org/10.1080/09720529.2022.2027605]
[27]
Alsinai, A.; Saleh, A.; Ahmed, H.; Mishra, L.N.; Soner, N.D. On fourth leap Zagreb index of graphs. Discrete Math. Algorithms Appl., 2023, 15(2)2250077
[http://dx.doi.org/10.1142/S179383092250077X]
[28]
Chen, D.; Liu, J.; Wu, J.; Wei, G.W.; Pan, F.; Yau, S.T. Path topology in molecular and materials sciences. J. Phys. Chem. Lett., 2023, 14(4), 954-964.
[http://dx.doi.org/10.1021/acs.jpclett.2c03706] [PMID: 36688834]
[29]
Hassan, M.M.; Jabeen, S.; Ali, H.; Ali, P. Connection-based modified Zagreb indices of Boron triangular sheet BTS(m,n). Mol. Phys., 2023, •••e2226242
[http://dx.doi.org/10.1080/00268976.2023.2226242]
[30]
Saplinova, T.; Lehnert, C.; Böhme, U.; Wagler, J.; Kroke, E. Melem- and melamine-derived iminophosphoranes. New J. Chem., 2010, 34(9), 1893-1908.
[http://dx.doi.org/10.1039/b9nj00621d]
[31]
Mannix, A.J.; Zhang, Z.; Guisinger, N.P.; Yakobson, B.I.; Hersam, M.C. Borophene as a prototype for synthetic 2D materials development. Nat. Nanotechnol., 2018, 13(6), 444-450.
[http://dx.doi.org/10.1038/s41565-018-0157-4] [PMID: 29875501]
[32]
Wang, Y.; Park, Y.; Qiu, L.; Mitchell, I.; Ding, F. Borophene with large holes. J. Phys. Chem. Lett., 2020, 11(15), 6235-6241.
[http://dx.doi.org/10.1021/acs.jpclett.0c01359] [PMID: 32640798]
[33]
Hussain, S.; Afzal, F.; Afzal, D.; Cancan, M.; Ediz, S.; Farahani, M.R. Analyzing the boron triangular nanotube through topological indices via M -polynomial. J. Discrete Math. Sci. Cryptogr., 2021, 24(2), 415-426.
[http://dx.doi.org/10.1080/09720529.2021.1882158]
[34]
Rodríguez, J.M.; Sánchez, J.L.; Sigarreta, J.M. CMMSE-on the first general Zagreb index. J. Math. Chem., 2018, 56(7), 1849-1864.
[http://dx.doi.org/10.1007/s10910-017-0816-y]
[35]
Khalifeh, M.H.; Yousefi-Azari, H.; Ashrafi, A.R. The first and second Zagreb indices of some graph operations. Discrete Appl. Math., 2009, 157(4), 804-811.
[http://dx.doi.org/10.1016/j.dam.2008.06.015]
[36]
Iranmanesh, A.; Hosseinzadeh, M.A.; Gutman, I. On multiplicative Zagreb indices of graphs. Iranian J. Math. Chem., 2012, 3(2), 145-154.
[37]
Ali, A. Trinajstić N. A novel/old modification of the first Zagreb index. Mol. Inform., 2018, 37(6-7)1800008
[http://dx.doi.org/10.1002/minf.201800008] [PMID: 29536645]
[38]
Ali, U.; Javaid, M.; Kashif, A. Modified Zagreb connection indices of the T-sum graphs. Main Group Met. Chem., 2020, 43(1), 43-55.
[http://dx.doi.org/10.1515/mgmc-2020-0005]
[39]
Ranjini, P.S.; Lokesha, V.; Usha, A. Relation between phenylene and hexagonal squeeze using harmonic index. Int. J. Graph Theory., 2013, 1(4), 116-121.
[40]
Zhong, L. The harmonic index for graphs. Appl. Math. Lett., 2012, 25(3), 561-566.
[http://dx.doi.org/10.1016/j.aml.2011.09.059]
[41]
Gutman, I. Trinajstić N. Graph theory and molecular orbitals. Total φ-electron energy of alternant hydrocarbons. Chem. Phys. Lett., 1972, 17(4), 535-538.
[http://dx.doi.org/10.1016/0009-2614(72)85099-1]
[42]
Gutman, I.; Russic, B.; Trinajstic, N.; Wilcox, C.F., Jr Graph theory and molecular orbitals. XII. Acyclic polyenes. J. Chem. Phys., 1975, 62(9), 3399-3405.
[http://dx.doi.org/10.1063/1.430994]
[43]
Gutman, I. Degree-based topological indices. Croat. Chem. Acta, 2013, 86(4), 351-361.
[http://dx.doi.org/10.5562/cca2294]
[44]
Xu, X. Relationships between harmonic index and other topological indices. Appl. Math. Sci., 2012, 6(41), 2013-2018.
[45]
Ye, A.; Qureshi, M.I.; Fahad, A.; Aslam, A.; Jamil, M.K.; Zafar, A.; Irfan, R. Zagreb connection number index of nanotubes and regular hexagonal lattice. Open Chem., 2019, 17(1), 75-80.
[http://dx.doi.org/10.1515/chem-2019-0007]
[46]
Qureshi, M.I.; Fahad, A.; Jamil, M.K.; Ahmad, S. Zagreb connection index of drugs related chemical structures. Biointerface Res. Appl. Chem., 2021, 11(1), 11920-11930.
[47]
Haoer, R.S.; Mohammed, M.A.; Selvarasan, T.; Chidambaram, N.; Devadoss, N. Multiplicative leap Zagreb indices of T-thorny graphs. Eur. Chem. Commun., 2020, 2(8), 841-846.
[48]
Sattar, A.; Javaid, M.; Bonyah, E. Connection-based multiplicative Zagreb indices of dendrimer nanostars. J. Math., 2021, 2021, 1-14.
[http://dx.doi.org/10.1155/2021/2107623]
[49]
Sattar, A.; Javaid, M.; Alam, M.N. On the studies of dendrimers via connection-based molecular descriptors. Math. Probl. Eng., 2022, 2022, 1-13.
[http://dx.doi.org/10.1155/2022/1053484]
[50]
Javaid, M.; Ali, U.; Siddiqui, K. Novel connection based Zagreb indices of several wheel-related graphs. Comput. J. Combinator. Math., 2021, 1(1), 1-28.
[51]
Ali, U.; Javaid, M. Zagreb connection indices of disjunction and symmetric difference operations on graphs. J. Prime Res. Math., 2020, 16(2), 1-15.
[52]
Ali, U. Upper bounds of Zagreb connection indices of tensor and strong product on graphs. Punjab Univ. J. Math., 2020, 52(4), 89-100.
[53]
Usman, M.; Javaid, M. Connection-based multiplicative zagreb indices of polycyclic aromatic hydrocarbon structures. Appl. Math. Sci., 2022, 1(2), 36-56.