On Analysis of Topological Aspects of Entropy Measures for Polyphenylene Structure

References

• O. C. Havare, and A. K. Havare, “Computation of the Forgotten Topological Index and co-Index for Carbon Base Nanomaterial,” Polycyclic Aromatic Compounds 10 (2020): 1–20.
   Google Scholar
• K. Shiino, J. Miyake, and K. Miyatake, “Highly Stable Polyphenylene Ionomer Membranes from Dichlorobiphenyls,” Chemical Communications (Cambridge, England) 55, no. 49 (2019): 7073–6.
   PubMed Web of Science ®Google Scholar
• M. H. Muhammad, X. L. Chen, Y. Liu, T. Shi, Y. Peng, L. Qu, and B. Yu, “Recyclable Cu@C3N4-Catalyzed Hydroxylation of Aryl Boronic Acids in Water under Visible Light: synthesis of Phenols under Ambient Conditions and Room Temperature,” ACS Sustainable Chemistry & Engineering 8, no. 7 (2020): 2682–7.
   Web of Science ®Google Scholar
• Y.-M. Chu, K. Julietraja, P. Venugopal, M. K. Siddiqui, and S. Prabhu, “Degree- and Irregularity-Based Molecular Descriptors for Benzenoid Systems,” The European Physical Journal Plus 136, no. 1 (2021): 1–17.
   Web of Science ®Google Scholar
• D. Zhao, M. H. Muhammad, M. K. Siddiqui, M. Nasir, M. F. Nadeem, and M. F. Hanif, “Computation and Analysis of Topological Co-Indices for Metal-Organic Compound,” Current Organic Synthesis 18, no. 8 (2021): 750–60.
   PubMed Web of Science ®Google Scholar
• X.-L. Wang, M. K. Siddiqui, S. A. K. Kirmani, S. Manzoor, S. Ahmad, and M. Dhlamini, “On Topological Analysis of Entropy Measures for Silicon Carbides Networks,” Complexity 2021 (2021): 1–26.
   Web of Science ®Google Scholar
• M. K. Siddiqui, M. Imran, and A. Ahmad, “On Zagreb Indices, Zagreb Polynomials of Some Nanostar Dendrimers,” Journal of Applied Mathematics and Computing 280 (2016): 132–9.
   Web of Science ®Google Scholar
• M. K. Siddiqui, M. Naeem, N. A. Rahman, and M. Imran, “Computing Topological Indicesof Certain Networks,” Journal of Optoelectronics and Advanced Materials 18, no. 9 (2016): 884–92.
   Web of Science ®Google Scholar
• K. Anand, and G. Bianconi, “Entropy Measures for Networks: Toward an Information Theory of Complex Topologies,” Physical Review E 80, no. 4 (2009): 45–55.
   Web of Science ®Google Scholar
• M. Dehmer, and A. Mowshowitz, “A History of Graph Entropy Measures,” Information Sciences 181, no. 1 (2011): 57–78.
   Web of Science ®Google Scholar
• S. Manzoor, M. K. Siddiqui, and S. Ahmad, “On Entropy Measures of Molecular Graphs Using Topological Indices,” Arabian Journal of Chemistry 13, no. 8 (2020): 6285–98.
   Web of Science ®Google Scholar
• C. E. Shannon, “A Mathematical Theory of Communication,” Bell System Technical Journal 27, no. 3 (1948): 379–423.
   Google Scholar
• S. Cao, and M. Dehmer, “Degree-Based Entropies of Networks Revisited,” Journal of Applied Mathematics and Computing 261 (2015): 141–7.
   Google Scholar
• M. Imran, S. Manzoor, M. K. Siddiqui, S. Ahmad, and M. H. Muhammad, “On Physical Analysis of Synthesis Strategies and Entropy Measures of Dendrimers,” Arabian Journal of Chemistry 15, no. 2 (2022): 103574. ID = 103574
   Web of Science ®Google Scholar
• S. Manzoor, M. K. Siddiqui, and S. Ahmad, “On Computation of Entropy Measures for Phthalocyanines and Porphyrins Dendrimers,” International Journal of Quantum Chemistry 122, no. 5 (2022): 1–26. article id = e26854.
   Web of Science ®Google Scholar
• N. Rashevsky, “Life, Information Theory, and Topology,” The Bulletin of Mathematical Biophysics 17, no. 3 (1955): 229–35.
   Google Scholar
• W. K. Lee, R. C. W. Phan, B. M. Goi, L. Chen, X. Zhang, and N. N. Xiong, “Parallel and High Speed Hashing in Gpu for Telemedicine Applications,” IEEE Access 6 (2018): 37991–8002.
   Web of Science ®Google Scholar
• B. Furtula, A. Graovac, and D. Vukicevic, “Augmented Zagreb Index,” Journal of Mathematical Chemistry 48, no. 2 (2010): 370–80.
   Web of Science ®Google Scholar
• X. Shi, H. U. I. Yang, Z. Xu, X. Zhang, and M. R. Farahani, “An Independent Component Analysis Classification for Complex Power Quality Disturbances with Sparse Auto Encoder Features,” IEEE Access 7 (2019): 20961–6.
   Web of Science ®Google Scholar
• Z. Chen, M. Dehmer, and Y. Shi, “A Note on Distance Based Graph Entropies,” Entropy 16, no. 10 (2014): 5416–27.
   Web of Science ®Google Scholar
• M. Randi, c’, “On Characterization of Molecular Branching,” Journal of the American Chemical Society 97, no. 23 (1975): 6609–15.
   Web of Science ®Google Scholar
• I. Gutman, B. Ruscic, N. Trinajsti, and C. F. Wilcox, Jr, “Graph Theory and Molecular Orbitals. XII. Acyclic Polyenes,” The Journal of Chemical Physics 62, no. 9 (1975): 3399–405.
   Web of Science ®Google Scholar
• I. Gutman, and K. C. Das, “The First Zagreb Index 30 Years after,” MATCH Communications in Mathematical and in Computer Chemistry 50 (2004): 83–92.
   Google Scholar
• G. H. Shirdel, H. RezaPour, and A. M. Sayadi, “The Hyper Zagreb Index of Graph Operations,” Iranian Journal of Mathematical Chemistry 4, no. 2 (2013): 213–20.
   Google Scholar
• B. Furtula, and I. Gutman, “A Forgotten Topological Index,” Journal of Mathematical Chemistry 53, no. 4 (2015): 1184–90.
   Web of Science ®Google Scholar
• P. Xu, M. Azeem, M. M. Izhar, S. M. Shah, M. A. Binyamin, and A. Aslam, “On Topological Descriptors of Certain Metal-Organic Frameworks,” Journal of Chemistry 2020 (2020): 1–12.
   Web of Science ®Google Scholar
• A. T. Balaban, “Highly Discriminating Distance-Based Topological Index,” Chemical Physics Letters 89, no. 5 (1982): 399–404.
   Web of Science ®Google Scholar
• A. T. Balaban, and L. V. Quintas, “The Smallest Graphs, Trees, and 4-Trees with Degenerate Topological Index,” Journal of Mathematical Chemistry 14 (1983): 213–33.
   Google Scholar
• M. Azeem, A. Aslam, Z. Iqbal, M. A. Binyamin, and W. Gao, “Topological Aspects of 2D Structures of trans-Pd(NH2)S Lattice and a Metal-Organic Superlattice,” Arabian Journal of Chemistry 14, no. 3 (2021): 102963.
   Web of Science ®Google Scholar
• M. Y. H. Malik, S. Hayat, S. Khan, and M. A. Binyamin, “Predictive Potential of Spectrum-Based Topological Descriptors for Measuring the pi-Electronic Energy of Benzenoid Hydrocarbons with Applications to Boron Triangular and Boron Nanotubes,” Mathematical Methods in the Applied Science 15 (2021): 1–22.
   Google Scholar
• V. Rohart, L. L. Lebel, and M. Dube, “Influence of Freeze/Thaw Cycling on the Mechanical Performance of Resistance-Welded Carbon Fibre/Polyphenylene Sulphide Composite Joints,” Journal of Reinforced Plastics and Composites 39, no. 21–22 (2020): 837–51.
   Web of Science ®Google Scholar
• J. B. Liu, J. Zhao, J. Min, and J. Cao, “The Hosoya Index of Graphs Formed by a Fractal Graph,” Fractals 27, no. 08 (2019): 1950135.
   Web of Science ®Google Scholar
• C. Zhu, J. Zhang, J. Xu, X. Yin, J. Wu, S. Chen, Z. Zhu, L. Wang, and H. Wang, “Facile Fabrication of Cellulose/Polyphenylene Sulfide Composite Separator for Lithium-Ion Batteries,” Carbohydrate Polymers 248 (2020): 116753.
   PubMed Web of Science ®Google Scholar
• M. A. Rashid, S. Ahmad, M. K. Siddiqui, S. Manzoor, and M. Dhlamini, “An Analysis of Eccentricity-Based Invariants for Biochemical Hypernetworks,” Complexity 2021 (2021): 1–14.
   Google Scholar
• Z. He, H. Ren, J. Li, T. Huang, S. Zhang, and P. Liu, “Optimization of Structure and Properties of Polyphenylene Sulfide Porous Membrane by Controlling the Process of Thermally Induced Phase Separation,” Polymer International 69, no. 9 (2020): 813–21.
   Web of Science ®Google Scholar
• Z. Shao, M. K. Siddiqui, and M. H. Muhammad, “Computing Zagreb Indices and Zagreb Polynomials for Symmetrical Nanotubes,” Symmetry 10, no. 7 (2018): 244–60.
   Google Scholar
• J. B. Liu, J. Zhao, H. He, and Z. Shao, “Valency-Based Topological Descriptors and Structural Property of the Generalized Sierpiski Networks,” Journal of Statistical Physics 177, no. 6 (2019): 1131–47.
   Web of Science ®Google Scholar
• J. B. Liu, C. Wang, S. Wang, and B. Wei, “Zagreb Indices and Multiplicative Zagreb Indices of Eulerian Graphs,” Bulletin of the Malaysian Mathematical Sciences Society 42, no. 1 (2019): 67–78.
   Web of Science ®Google Scholar
• G. V. Rajasekharaiah, and U. P. Murthy, “Hyper-Zagreb Indices of Graphs and Its Applications,” Journal of Algebra Combinatorics Discrete Structures and Applications 8, no. 1 (2021): 9–22.
   Google Scholar
• D. Janezic, A. Milicevic, S. Nikolic, N. Trinajstic, and D. Vukicevic, “Zagreb Indices: extension to Weighted Graphs Representing Molecules Containing Heteroatoms,” Croatica Chemica Acta 80, no. 3–4 (2007): 541–5.
   Web of Science ®Google Scholar