Valizadeh Harzand, F., Mousavi Nejad, S.N., Babapoor, A., Mousavi, S.M., Hashemi, S.A., Gholami, A., Chiang, W.-H., Buonomenna, M.G. & Lai, C.W. Recent Advances in Metal-Organic Framework (MOF) Asymmetric Membranes/Composites for Biomedical Applications, Symmetry (2023).Yassue-Cordeiro, P. H. et al. 1 – Chitosan-based nanocomposites for drug delivery. In Inamuddin (eds Asiri, A. M. & Mohammad, A.) 1–26 (Woodhead Publishing, 2018).
Google Scholar
Salahpour-Anarjan, F., Nezhad-Mokhtari, P. & Akbarzadeh, A. Chapter 3—Smart drug delivery systems. In Modeling and Control of Drug Delivery Systems (Azar, A.T. Ed.). 29–44 (Academic Press, 2021).de Farias, R.F. 1—Oxides and phosphates. In Interface Science and Technology (de Farias, R.F. Ed.). 1–2 (Elsevier, 2023).Gutman, I., Monsalve, J. & Rada, J. A relation between a vertex-degree-based topological index and its energy. Linear Algebra Appl. 636, 134–142 (2022).Article
MathSciNet
Google Scholar
Randic, M. Characterization of molecular branching. J. Am. Chem. Soc. 97, 6609–6615 (1975).Article
CAS
Google Scholar
Wiener, H. Structural Determination of Paraffin Boiling Points. J. Am. Chem. Soc. 69, 17–20 (1947).Article
CAS
PubMed
Google Scholar
Darafsheh, M. R. Computation of topological indices of some graphs. Acta Appl. Math. 110, 1225–1235 (2010).Article
MathSciNet
Google Scholar
Ayache, A. & Alameri, A. Topological indices of the mk-graph. J. Assoc. Arab Univ. Basic Appl. Sci. 24, 283–291 (2017).
Google Scholar
Gao, W., Chen, Y. & Wang, W. The topological variable computation for a special type of cycloalkanes. J. Chem. 2017, 6534758 (2017).Article
Google Scholar
Ullah, A., Jabeen, S., Zaman, S., Hamraz, A. & Meherban, S. Predictive potential of K-Banhatti and Zagreb type molecular descriptors in structure–property relationship analysis of some novel drug molecules. J. Chin. Chem. Soc. 71, 250–276 (2024).Article
CAS
Google Scholar
Ullah, A., Bano, Z. & Zaman, S. Computational aspects of two important biochemical networks with respect to some novel molecular descriptors. J. Biomol. Struct. Dyn. 42, 791–805 (2024).Article
CAS
PubMed
Google Scholar
Zaman, S., Yaqoob, H.S.A., Ullah, A. & Sheikh, M. QSPR analysis of some novel drugs used in blood cancer treatment via degree based topological indices and regression models. Polycycl. Arom. Compds. 1–17. https://doi.org/10.1080/10406638.2023.2217990 (2023).Zaman, S., Ullah, A. & Shafaqat, A. Structural modeling and topological characterization of three kinds of dendrimer networks. Eur. Phys. J. E Soft Matter 46, 36 (2023).Article
CAS
PubMed
Google Scholar
Zaman, S. et al. Three-dimensional structural modelling and characterization of sodalite material network concerning the irregularity topological indices. J. Math. 2023, 1–9 (2023).Article
MathSciNet
Google Scholar
Zaman, S., Jalani, M., Ullah, A., Ali, M. & Shahzadi, T. On the topological descriptors and structural analysis of cerium oxide nanostructures. Chem. Pap. 77, 2917–2922 (2023).Article
CAS
Google Scholar
Zaman, S., Jalani, M., Ullah, A., Ahmad, W. & Saeedi, G. Mathematical analysis and molecular descriptors of two novel metal–organic models with chemical applications. Sci. Rep. 13, 5314 (2023).Article
ADS
CAS
PubMed
PubMed Central
Google Scholar
Ullah, A., Zaman, S., Hussain, A., Jabeen, A. & Belay, M. B. Derivation of mathematical closed form expressions for certain irregular topological indices of 2D nanotubes. Sci. Rep. 13, 11187 (2023).Article
ADS
CAS
PubMed
PubMed Central
Google Scholar
Ullah, A., Zaman, S., Hamraz, A. & Muzammal, M. On the construction of some bioconjugate networks and their structural modeling via irregularity topological indices. Eur. Phys. J. E 46, 72 (2023).Article
CAS
PubMed
Google Scholar
Ullah Shamsudin, A., Zaman, S. & Hamraz, A. Zagreb connection topological descriptors and structural property of the triangular chain structures. Phys. Scr. 98, 025009 (2023).Article
ADS
Google Scholar
Hakeem, A., Ullah, A. & Zaman, S. Computation of some important degree-based topological indices for γ- graphyne and Zigzag graphyne nanoribbon. Mol. Phys. 121, e2211403 (2023).Article
ADS
Google Scholar
Zaman, S., Jalani, M., Ullah, A., Saeedi, G. & Guardo, E. Structural analysis and topological characterization of Sudoku nanosheet. J. Math. 2022, 1–10 (2022).Article
MathSciNet
Google Scholar
Ullah, A., Shamsudin, S., Zaman, A., Hamraz, G. & Saeedi, J. O. Caceres, network-based modeling of the molecular topology of Fuchsine acid dye with respect to some irregular molecular descriptors. J. Chem. 2022, 1–8 (2022).Article
Google Scholar
Ullah, A., Zeb, A. & Zaman, S. A new perspective on the modeling and topological characterization of H-naphtalenic nanosheets with applications. J. Mol. Model. 28, 211 (2022).Article
CAS
PubMed
PubMed Central
Google Scholar
Ullah, A., Qasim, M., Zaman, S. & Khan, A. Computational and comparative aspects of two carbon nanosheets with respect to some novel topological indices. Ain Shams Eng. J. 13, 101672 (2022).Article
Google Scholar
Zhang, X., Aslam, A., Saeed, S., Razzaque, A. & Kanwal, S. Investigation for metallic crystals through chemical invariants, QSPR and fuzzy-TOPSIS. J. Biomol. Struct. Dyn. 1, 1. https://doi.org/10.1080/07391102.2023.2209656 (2023).Article
CAS
Google Scholar
Zhong, J.-F., Rauf, A., Naeem, M., Rahman, J. & Aslam, A. Quantitative structure-property relationships (QSPR) of valency based topological indices with Covid-19 drugs and application. J. Arab. J. Chem. 14, 103240 (2021).Article
CAS
Google Scholar
Iqbal, Z., Ishaq, M., Aslam, A., Aamir, M. & Gao, W. The measure of irregularities of nanosheets. Open Phys. 18, 419–431 (2020).Article
CAS
Google Scholar
Khabyah, A. A., Zaman, S., Koam, A. N. A., Ahmad, A. & Ullah, A. Minimum Zagreb eccentricity indices of two-mode network with applications in boiling point and benzenoid hydrocarbons. Mathematics 10, 4 (2022).Article
Google Scholar
Ullah, A., Shaheen, M., Khan, A., Khan, M. & Iqbal, K. Evaluation of topology-dependent growth rate equations of three-dimensional grains using realistic microstructure simulations. Mater. Res. Exp. 6, 026523 (2018).Article
Google Scholar
Ullah, A. et al. Simulations of grain growth in realistic 3D polycrystalline microstructures and the MacPherson–Srolovitz equation. Mater. Res. Exp. 4, 066502 (2017).Article
Google Scholar
Asad, U. et al. Neighborhood topological effect on grain topology-size relationship in three-dimensional polycrystalline microstructures. Chin. Sci. Bull. 58, 3704–3708 (2013).Article
Google Scholar
Gutman, I. & Trinajstić, N. Graph theory and molecular orbitals. Total φ-electron energy of alternant hydrocarbons. Chem. Phys. Lett. 17, 535–538 (1972).Article
ADS
CAS
Google Scholar
Das, K. C. Atom-bond connectivity index of graphs. Discrete Appl. Math. 158, 1181–1188 (2010).Article
MathSciNet
Google Scholar
Ghorbani, M. & Hosseinzadeh, M. A. Computing ABC4 index of nanostar dendrimers. Optoelectron. Adv. Mater. Rapid Commun. 4, 1419–1422 (2010).CAS
Google Scholar
Alaeiyan, M., Farahani, M. R. & Jamil, M. K. Computation of the fifth geometric-arithmetic index for polycyclic aromatic hydrocarbons PAHk, applied mathematics and nonlinear. Sciences 1, 283–290 (2016).
Google Scholar
Husin, N. H., Hasni, R. & Du, Z. On extremum geometric-arithmetic indices of (molecular) trees. Match 78, 375–386 (2017).MathSciNet
Google Scholar
Graovac, A., Ghorbani, M. & Hosseinzadeh, M. A. Computing fifth geometric-arithmetic index for nanostar dendrimers. J. Math. Nanosci. 1, 33–42 (2011).
Google Scholar
Hayat, S. Distance-based graphical indices for predicting thermodynamic properties of benzenoid hydrocarbons with applications. Comput. Mater. Sci. 230, 112492 (2023).Article
CAS
Google Scholar
Hayat, S., Khan, S., Khan, A. & Imran, M. Distance-based topological descriptors for measuring the π-electronic energy of benzenoid hydrocarbons with applications to carbon nanotubes. Math. Methods Appl. Sci. (2020).Liu, J. B., Gu, J. J. & Wang, K. The expected values for the Gutman index, Schultz index, and some Sombor indices of a random cyclooctane chain. Int. J. Quantum Chem 123, e27022 (2022).Article
Google Scholar
Liu, J.-B., Zhao, J., Min, J. & Cao, J. The Hosoya index of graphs formed by a fractal graph. J. Fractals 27, 1950135 (2019).Article
ADS
Google Scholar
Arockiaraj, M., Klavzar, S., Clement, J., Mushtaq, S. & Balasubramanian, K. Edge distance-based topological indices of strength-weighted graphs and their application to coronoid systems, carbon nanocones and SiO(2) nanostructures. Mol. Inform. 38, e1900039 (2019).Article
PubMed
Google Scholar
Zaman, S., Kamboh, A., Ullah, A. & Liu, J.-B. Development of some novel resistance distance based topological indices for certain special types of graph networks. Phys. Scr. 98, 125250 (2023).Article
ADS
Google Scholar
Hayat, S., Khan, M. A., Khan, A., Jamil, H. & Malik, M. Y. H. Extremal hyper-Zagreb index of trees of given segments with applications to regression modeling in QSPR studies. Alex. Eng. J. 80, 259–268 (2023).Article
Google Scholar
Hayat, S. & Asmat, F. Sharp bounds on the generalized multiplicative first Zagreb index of graphs with application to QSPR modeling. Mathematics (2023).Hayat, S., Arif, A., Zada, L., Khan, A. & Zhong, Y. Mathematical properties of a novel graph-theoretic irregularity index with potential applicability in QSPR modeling. Mathematics (2022).Liu, J.-B., Ali, H., Shafiq, M. K., Dustigeer, G. & Ali, P. On topological properties of planar octahedron networks. Polycycl. Arom. Compds. 43, 755–771 (2023).Article
CAS
Google Scholar
Raza, Z., Arockiaraj, M., Maaran, A., Kavitha, S. R. J. & Balasubramanian, K. Topological entropy characterization, NMR and ESR spectral patterns of coronene-based transition metal organic frameworks. ACS Omega 8, 13371–13383 (2023).Article
CAS
PubMed
PubMed Central
Google Scholar
Paul, D., Arockiaraj, M., Jacob, K. & Clement, J. Multiplicative versus scalar multiplicative degree based descriptors in QSAR/QSPR studies and their comparative analysis in entropy measures. Eur. Phys. J. Plus 138, 323 (2023).Article
Google Scholar
Arockiaraj, M. et al. Novel molecular hybrid geometric-harmonic-Zagreb degree based descriptors and their efficacy in QSPR studies of polycyclic aromatic hydrocarbons. SAR QSAR Environ. Res. 34, 569–589 (2023).Article
CAS
PubMed
Google Scholar
Mondal, S., De, N. & Pal, A. Topological indices of some chemical structures applied for the treatment of COVID-19 patients. J. Polycycl. Arom. Compds. 42, 1220–1234 (2022).Article
CAS
Google Scholar
Mondal, S., De, N. & Pal, A. On neighborhood Zagreb index of product graphs. J. Mol. Struct. 1223, 129210 (2021).Article
CAS
PubMed
Google Scholar
Zaman, S. & Ullah, A. Kemeny’s constant and global mean first passage time of random walks on octagonal cell network. Math. Methods Appl. Sci. 46, 9177–9186 (2023).Article
ADS
MathSciNet
Google Scholar
Zaman, S., Mustafa, M., Ullah, A. & Siddiqui, M. K. Study of mean-first-passage time and Kemeny’s constant of a random walk by normalized Laplacian matrices of a penta-chain network. Eur. Phys. J. Plus 138, 770 (2023).Article
Google Scholar
Yu, X., Zaman, S., Ullah, A., Saeedi, G. & Zhang, X. Matrix analysis of hexagonal model and its applications in global mean-first-passage time of random walks. IEEE Access 11, 10045–10052 (2023).Article
Google Scholar
Yan, T., Kosar, Z., Aslam, A., Zaman, S. & Ullah, A. Spectral techniques and mathematical aspects of K4 chain graph. Phys. Scr. 98, 045222 (2023).Article
ADS
Google Scholar
Kosar, Z., Zaman, S., Ali, W. & Ullah, A. The number of spanning trees in a K5 chain graph. Phys. Scr. (2023).Sattar, A., Javaid, M. & Bonyah, E. Connection-based multiplicative Zagreb indices of dendrimer nanostars. J. Math. 2021, 2107623 (2021).Article
MathSciNet
Google Scholar
Ali, U., Javaid, M. & Alanazi, A.M. Computing analysis of connection-based indices and coindices for product of molecular networks. Symmetry (2020).Usman, M. & Javaid, M. Connection-based Zagreb indices of polycyclic aromatic hydrocarbons structures. Curr. Org. Synth. https://doi.org/10.2174/1570179421666230823141758 (2023).Article
PubMed
Google Scholar
Raza, Z. Zagreb connection indices for some benzenoid systems. Polycycl. Arom. Compds. 42, 1814–1827 (2022).Article
CAS
Google Scholar
Nikolić, S., Kovačević, G., Miličević, A. & Trinajstić, N. The Zagreb indices 30 years after. Croat. Chem. Acta 76, 113–124 (2003).
Google Scholar
Das, K. C., Mondal, S. & Raza, Z. On Zagreb connection indices. Eur. Phys. J. Plus 137, 1242 (2022).Article
Google Scholar
Javaid, M. & Sattar, A. On topological indices of zinc-based metal organic frameworks. Main Group Met. Chem. 45, 74–85 (2022).Article
CAS
Google Scholar
Sattar, A. & Javaid, M. Topological aspects of metal–organic frameworks: Zinc silicate and oxide networks. Comput. Theor. Chem. 1222, 114056 (2023).Article
CAS
Google Scholar
Sattar, A. & Javaid, M. Topological aspects of metal organic frameworks: Zinc silicate and oxide networks. Comput. Theor. Chem. 1222, 114056 (2023).Article
CAS
Google Scholar
Rajpoot, A. & Selvaganesh, L. Potential application of novel AL-indices as molecular descriptors. J. Mol. Graph. Model. 118, 108353 (2023).Article
CAS
PubMed
Google Scholar
Randić, M. & Trinajstić, N. In search for graph invariants of chemical interes. J. Mol. Struct. 300, 551–571 (1993).Article
ADS
Google Scholar
Mondal, S., Dey, A., De, N. & Pal, A. QSPR analysis of some novel neighbourhood degree-based topological descriptors. Complex Intell. Syst. 7, 977–996 (2021).Article
Google Scholar
Randic, M., Guo, X., Oxley, T., Krishnapriyan, H. & Naylor, L. Wiener matrix invariants. J. Chem. Inf. Comput. Sci. 34, 361–367 (2002).Article
Google Scholar
Calvin, W.R. Handbook of Chemistry and Physics. A Ready-Reference Book of Chemical and Physical Data. 66th Ed. (CRC Press, 1986).Shigehalli, V. S. & Dsouza, A. M. Quantitative structure property relationship (QSPR) analysis of general Randić index. J. Algebr. Stat. 13, 1957–1967 (2022).
Google Scholar
Ullah, A., Jamal, M. & Zaman, S. Shamsudin, connection based novel AL topological descriptors and structural property of the zinc oxide metal organic frameworks. Phys. Scr. 99, 055202 (2024).Article
ADS
Google Scholar