160
Views
0
CrossRef citations to date
0
Altmetric
Research Articles

The Weighted Mostar Invariants of Phthalocyanines, Triazine-Based and Nanostar Dendrimers

ORCID Icon, , &
Pages 772-789 | Received 21 Apr 2021, Accepted 06 Dec 2021, Published online: 30 Dec 2021

References

  • W. Gao, H. Wu, M. K. Siddiqui, and A. Q. Baig, “Study of Biological Networks Using Graph Theory,” Saudi Journal of Biological Sciences 25, no. 6 (2018): 1212–9.
  • W. Wu, C. Zhang, W. Lin, Q. Chen, X. Guo, Y. Qian, and L. Zhang, “Quantitative Structure-Property Relationship (QSPR) Modeling of Drug-Loaded Polymeric Micelles via Genetic Function Approximation,” PLoS One 10, no. 3 (2015): e0119575–129.
  • S. Akhter, and M. Imran, “On Molecular Topological Properties of Benzenoid Structures,” Canadian Journal of Chemistry 94, no. 8 (2016): 687–98.
  • S. Akhter, M. Imran, M. R. Farahan, and I. Javaid, “On Topological Properties of Hexagonal and Silicate Networks,” Hacettepe Journal of Mathematics and Statistics 48, no. 3 (2017): 1–13.
  • S. Akhter, M. Imran, W. Gao, and M. R. Farahani, “On Topological Indices of Honeycomb Networks and Graphene Networks,” Hacettepe Journal of Mathematics and Statistics 47, no. 1 (2018): 19–35.
  • S. Akhter, M. Imran, and Z. Iqbal, “Mostar Indices of SiO2 Nanostructures and Melem Chain Nanostructures,” International Journal of Quantum Chemistry 121 (2021): e26520.
  • S. Akhter, Z. Iqbal, A. Aslam, and W. Gao, “Mostar Index of Graph Operations,” International Journal of Quantum Chemistry 121 (2021): e26674.
  • W. Gao, S. Akhter, Z. Iqbal, M. Qasim, and A. Aslam, “The Topological Aspects of Phthalocyanines and Porphyrins Dendrimers,” IEEE Access 8 (2020): 168631–49.
  • W. Gao, Z. Iqbal, S. Akhter, M. Ishaq, and A. Aslam, “On Irregularity Descriptors of Derived Graphs,” AIMS Mathematics 5, no. 5 (2020): 4085–107.
  • M. Imran, S. Akhter, and Z. Iqbal, “On the Eccentric Connectivity Polynomial of F-Sum of Connected Graphs,” Complexity 2020 (2020): 1–9.
  • M. Imran, S. Akhter, and Z. Iqbal, “Edge Mostar Index of Chemical Structures and Nanostructures Using Graph Operations,” International Journal of Quantum Chemistry 120, no. 15 (2020): e26259.
  • H. Yang, M. Imran, S. Akhter, Z. Iqbal, and M. K. Siddiqui, “On Distance-Based Topological Descriptors of Subdivision Vertex-Edge Join of Three Graphs,” IEEE Access 7 (2019): 143381–91.
  • X. Zhang, X. Wu, S. Akhter, M. K. Jamil, J. B. Liu, and M. R. Farahani, “Edge-Version Atom-Bond Connectivity and Geometric Arithmetic Indices of Generalized Bridge Molecular Graphs,” Symmetry 10, no. 12 (2018): 751.
  • F. Vogtle, E. W. Buhleier, and W. Wehner, “Cascade and Nonskid-Chain-like Syntheses of Molecular Cavity Topologies,” Synthesis 1978, no. 2 (1978): 155–8.
  • M. V. Diudea, and G. Katona, “Molecular Topology of Dendrimers,” ChemInform 30, no. 50 (2010): no–201.
  • D. A. Tomalia, H. Baker, J. Dewald, M. Hall, G. Kallos, S. Martin, J. Roeck, J. Ryder, and P. Smith, “A New Class of Polymers: Starburst-Dendritic Macromolecules,” Polymer Journal 17, no. 1 (1985): 117–32.
  • K. Naka, Y. Tanaka, and Y. Chujo, “Effect of Anionic Starburst Dendrimers on the Crystallization of CaCO3 in Aqueous Solution, Size Control of Spherical Vaterite Particles,” Langmuir 18, no. 9 (2002): 3655–8.
  • E. Abbasi, S. Aval, F. Akbarzadeh, A. Milani, M. Nasrabadi, H. T. Joo, S. W. Hanifehpour, Y. Nejati-Koshki, and K. Pashaei-Asl, “Dendrimers: Synthesis, Applications and Properties,” Nanoscale Research Letters 9, no. 1 (2014): 247–56.
  • R. Suresh, C. Singh, and P. Rewar, “Dendrimers as Carriers and Its Application in Therapy,” International Journal of Analytical, Pharmaceutical and Biomedical Sciences 4, no. 3 (2015): 15–23.
  • Z. Zhao, S. Lou, Y. Hu, J. Zhu, and C. Zhang, “A Nano-in-Nano Polymer-Dendrimer Nanoparticle-Based Nanosystem for Controlled Multidrug Delivery,” Molecular Pharmaceutics 14, no. 8 (2017): 2697–710.
  • H. Wiener, “Structural Determination of Paraffin Boiling Points,” Journal of the American Chemical Society 69, no. 1 (1947): 17–20.
  • I. Gutman, and N. Trinajstić, “Graph Theory and Molecular Orbitals. Total Electron Energy of Alternant Hydrocarbons,” Chemical Physics Letters 17, no. 4 (1972): 535–8.
  • M. O. Albertson, “The Irregularity of a Graph,” Ars Comb 46 (1997): 219–25.
  • I. Gutman, “A Formula for the Wiener Number of Trees and Its Extension to Graphs Containing Cycles,” Graph Theory, Notes New York 27, no. 9 (1994): 9–15.
  • P. V. Khadikar, S. Karmarkar, and V. K. Agrawal, “A Novel PI Index and Its Applications to QSPR/QSAR Studies,” Journal of Chemical Information and Computer Sciences 41, no. 4 (2001): 934–49.
  • S. Klavzar, S. Li, and H. Zhang, “On the Difference between the (Revised) Szeged Index and the Wiener Index of Cacti,” Discrete Applied Mathematics 247 (2018): 77–89.
  • T. Pisanski, and M. Randić, “Use of the Szeged Index and the Revised Szeged Index for Measuring Network Bipartivity,” Discrete Applied Mathematics 158, no. 17 (2010): 1936–44.
  • S. Li, and H. Zhang, “Proofs of Three Conjectures on the Quotients of the (Revised) Szeged Index and the Wiener Index and beyond,” Discrete Mathematics 340, no. 3 (2017): 311–24.
  • T. Doslić, I. Martinjak, R. Skrekovski, S. T. Spuzević, and I. Zubac, “Mostar Index,” Journal of Mathematical Chemistry 56, no. 10 (2018): 2995–3013.
  • K. Deng, and S. Li, “Extremal Catacondensed Benzenoids with Respect to the Mostar Index,” Journal of Mathematical Chemistry 58, no. 7 (2020): 1437–65.
  • R. V. Solé, and S. Valverde, “Information Theory of Complex Networks: On Evolution and Architectural Constraints,” In Complex Networks. Lecture Notes in Physics, ed. Ben-Naim E., Frauenfelder H., Toroczkai Z. (vol. 650, 2014). Berlin, Heidelberg: Springer. doi:10.1007/978-3-540-44485-5_9
  • N. Tratnik, “Computing the Mostar Index in Networks with Applications to Molecular Graphs,” Iranian J. Math. Chem. 12, no. 1 (2021): 1–18.
  • M. Arockiaraj, J. Clement, and N. Tratnik, “Mostar Indices of Carbon Nanostructures and Circumscribed Donut Benzenoid Systems,” International Journal of Quantum Chemistry 119, no. 24 (2019): e26043.
  • S. Klavzar, I. Gutman, and B. Mohar, “Labeling of Benzenoid Systems Which Reflects the Vertex-Distance Relations,” Journal of Chemical Information and Computer Sciences 35, no. 3 (1995): 590–3.
  • M. R. Farahani, “Computing Edge-PI Index and Vertex PI Index of Circumcoronene Series of Benzenoid Hk by Use of Cut Method,” International Journal of Mathematical Modeling and Applied Computing 1, no. 6 (2013): 41–50.
  • K. M. Kadish, K. M. Smith, R. Guilard, The Porphyrin Hand-book (San Diego, CA: Academic, 2003), 15–20.
  • K. M. Kadish, K. M. Smith, R. Guilard, Handbook of PorphyrinScience (Singapore, World Scientific, 2012), 1–25.
  • J. J. Cid, J. H. Yum, S. R. Jang, M. K. Nazeeruddin, E. Martínez-Ferrero, E. Palomares, J. Ko, M. Grätzel, and T. Torres, “Molecular Cosensitization for Efficient Panchromatic Dye-Sensitized Solar Cells,” Angewandte Chemie 119, no. 44 (2007): 8510–4.
  • I. López-Duarte, M. Wang, R. Humphry-Baker, M. Ince, M. V. Martínez-Díaz, M. K. Nazeeruddin, T. Torres, and M. Grátzel, “Molecular Engineering of Zinc Phthalocyanines with Phosphinic Acid Anchoring Groups,” Angewandte Chemie 124, no. 8 (2012) : 1931–4.
  • M. E. Ragoussi, J. J. Cid, J. H. Yum, G. D. L. Torre, D. D. Censo, M. Grátzel, M. K. Nazeeruddin, and T. Torres, “Carboxyethynyl Anchoring Ligands: A Means to Improving the Efficiency of Phthalocyanine-Sensitized Solar Cells,” Angewandte Chemie (International ed. in English) 51, no. 18 (2012): 4375–8.
  • F. Setaro, R. Ruiz-González, S. Nonell, U. Hahn, and T. Torres, “Synthesis, Photophysical Studies and 1O2 Generation of Ruthenium Phthalocyanine Dendrimers,” Journal of Porphyrins and Phthalocyanines 20 (2016): 378–87.
  • D. Gajjar, D. Wadia, and R. Patel, “Development, Characterization of Hydroxyl Terminated Dendritic Macromolecules as Prospective Drug Carriers,” American Journal of Polymer Science and Engineering 3 (2015): 73–89.
  • M. V. Diudea, G. Katona, “Molecular Topology of Dendrimers,” in Advances in Dendritic Macromolecules, ed. G. A. Newkome (vol. 4, 1999), 135–201.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.