Computing Topological Indices for Molecules Structure of Polyphenylene via M-Polynomials

References

• G. Rucker, and C. Rucker, “On Topological Indices, Boiling Points, and Cycloalkanes,” Journal of Chemical Information and Modeling 39 (1999): 788–802.
   Google Scholar
• H. Zhang, and F. Zhang, “The Clar Covering Polynomial of Hexagonal Systems I,” Discrete Applied Mathematics 69, no. 1-2 (1996): 147–67.
   Web of Science ®Google Scholar
• I. Gutman, “Some Properties of the Wiener Polynomials,” Graph Theory Notes of New York 125 (1993): 13–8.
   Google Scholar
• H. Wiener, “Structural Determination of Paraffin Boiling Points,” Journal of the American Chemical Society 69, no. 1 (1947): 17–20.
   PubMed Web of Science ®Google Scholar
• F. Asif, Z. Zahid, and S. Zafar, “Leap Zagreb and Leap Hyper-Zagreb Indices of Jahangir and Jahangir Derived Graphs,” Engineering and Applied Science Letter 3, no. 2 (2020): 1–8.
   Google Scholar
• A. Shah, and S. A. U. B. Bokhary, “On Chromatic Polynomial of Certain Families of Dendrimer Graphs,” Open Journal of Mathematical Sciences 3, no. 1 (2019): 404–16.
   Google Scholar
• A. A. Dobrynin, R. Entringer, and I. Gutman, “Wiener Index of Trees: Theory and Applications,” Acta Applicandae Mathematicae 66, no. 3 (2001): 211–49.
   Web of Science ®Google Scholar
• S. Klavžar, and I. Gutman, “A Comparison of the Schultz Molecular Topological Index with the Wiener Index,” Journal of Chemical Information and Computer Sciences 36, no. 5 (1996): 1001–3.
   Google Scholar
• F. M. Brückler, T. Došlić, A. Graovac, and I. Gutman, “On a Class of Distance-Based Molecular Structure Descriptors,” Chemical Physics Letters 503, no. 4-6 (2011): 336–8.
   Web of Science ®Google Scholar
• J.-B. Liu, C. Wang, S. Wang, and B. Wei, “Zagreb Indices and Multiplicative Za- Greb Indices of Eulerian Graphs,” Bulletin of the Malaysian Mathematical Sciences Society 42, no. 1 (2019): 67–78.
   Web of Science ®Google Scholar
• J.-B. Liu, J. Zhao, and Z. X. Zhu, “On the Number of Spanning Trees and Normalized Laplacian of Linear Octagonal Quadrilateral Networks,” International Journal of Quantum Chemistry 119, no. 17 (2019): 25–35.
   Web of Science ®Google Scholar
• J.-B. Liu, J. Zhao, J. Min, and J. D. Cao, “On the Hosoya Index of Graphs Formed by a Fractal Graph,” Fractals-Complex Geometry Patterns and Scaling in Nature and Society 27, no. 08 (2019): 1950135.
   Web of Science ®Google Scholar
• J.-B. Liu, J. Zhao, and Z. Cai, “On the Generalized Adjacency, Laplacian and Signless Laplacian Spectra of the Weighted Edge Corona Networks,” Physica A 540 (2020): 12–30.
   Web of Science ®Google Scholar
• J.-B. Liu, J. Zhao, H. He, and Z. Shao, “Valency-Based Topological Descriptors and Structural Property of the Generalized Sierpinski Networks,” Journal of Statistical Physics 177, no. 6 (2019): 1131–47.
   Web of Science ®Google Scholar
• J.-B. Liu, Z-Y. Shi, Y.-H. Pan, J. Cao, M. Abdel-Aty, and U. Al-Juboori, “Computing the Laplacian Spectrum of Linear Octagonal-Quadrilateral Networks and Its Applications,” Polycyclic Aromatic Compounds 10 (2020): 23–43.
   Google Scholar
• E. Deutsch, and S. Klavar, “M-Polynomial and Degree-Based Topological Indices,” Iranian Journal of Mathematical Chemistry 6 (2015): 93–102.
   Web of Science ®Google Scholar
• M. Munir, W. Nazeer, S. Rafique, and S. M. Kang, “M-Polynomial and Related Topological Indices of Nanostar Dendrimers,” Symmetry 8, no. 9 (2016): 12–97.
   Google Scholar
• M. Munir, W. Nazeer, S. Rafique, A. R. Nizami, and S. M. Kang, “M-Polynomial and Degree-Based Topological Indices of Titania Nanotubes,” Symmetry 8, no. 11 (2016): 117–8.
   Google Scholar
• Y. Kwun, M. Munir, W. Nazeer, S. Rafique, and S. M. Kang, “M-Polynomial and Degree-Based Topological Indices of V-Phenalinic Nanotubes and Nanotori,” Sci. Rep. 7 (2017): 23–36.
   PubMed Web of Science ®Google Scholar
• M. Munir, W. Nazeer, S. Rafique, A. R. Nizami, and S. M. Kang, “Some Computational Aspects of Triangular Boron Nanotubes,” Symmetry 9, no. 1 (2017): 6–15.
   Google Scholar
• M. Randic, “On Characterization of Molecular Branching,” Journal of the American Chemical Society 97, no. 23 (1975): 6609–15.
   Web of Science ®Google Scholar
• H. Yang, M. A. Rashid, S. Ahmad, S. S. Khan, and M. K. Siddiqui, “On Molecular Descriptors of Face-Centred Cubic Lattice,” Processes 7, no. 5 (2019): 280–15.
   Web of Science ®Google Scholar
• X. Li, and I. Gutman, Mathematical Aspects of Randic-Type Molecular Structure Descriptors; Mathematical Chemistry Monographs, No. 1 (Kragujevac, Serbia: University of Kragujevac, 2006).
   Google Scholar
• I. Gutman, and B. Furtula, eds. Recent Results in the Theory of Randic Index (Kragujevac, Serbia: University of Kragujevac, 2008).
   Google Scholar
• M. Randic, “The Connectivity Index 25 Years after,” Journal of Molecular Graphics and Modelling 20 (2001): 19–35.
   PubMed Web of Science ®Google Scholar
• X. Li, and Y. Shi, “A Survey on the Randic Index,” MATCH Communications in Mathematical and in Computer Chemistry 59 (2008): 127–56.
   Web of Science ®Google Scholar
• M. Nadeem, S. Ahmad, M. K. Siddiqui, and M. Naeem, “Topological Descriptor of 2-Dimensional Silicon Carbons and Their Applications,” Open Chemistry 17, no. 1 (2019): 1473–82.
   Web of Science ®Google Scholar
• S. Nikolic, G. Kovacevic, A. Milicevic, and N. Trinajstic, “The Zagreb Indices 30 Years after,” Croatica Chemica Acta 76 (2003): 113–24.
   Web of Science ®Google Scholar
• I. Gutman, and K. C. Das, “The First Zagreb Indices 30 Years after,” MATCH Communications in Mathematical and in Computer Chemistry 50 (2004): 83–92.
   Google Scholar
• N. Trinajstic, S. Nikolic, and A. Milicevic, “Gutman on Zagreb Indices,” Kemija u Industriji 59 (2010): 577–89.
   Google Scholar
• K. C. Das, and I. Gutman, “Some Properties of the Second Zagreb Index,” MATCH Communications in Mathematical and in Computer Chemistry 52 (2004): 103–12.
   Google Scholar
• G. Hong, Z. Gu, H. M. Awais, M. Javaid, and M. K. Siddiqui, “Degree-Based Topological Invariants of Metal-Organic Networks,” IEEE Access 8, no. 1 (2020): 68288–300.
   Web of Science ®Google Scholar
• M. K. Siddiqui, M. Imran, and M. Saeed, “Topological Properties of Face-Centred Cubic Lattice,” Hacettepe Journal of Mathematics and Statistics 49, no. 1 (2019): 1–207.
   Web of Science ®Google Scholar
• H. Deng, J. Yang, and F. Xia, “A General Modeling of Some Vertex-Degree Based Topological Indices in Benzenoid Systems and Phenylenes,” Computers & Mathematics with Applications 61, no. 10 (2011): 3017–23.
   Web of Science ®Google Scholar
• Y. Li, Z. Zhou, P. Shen, and Z. Chen, “Two-Dimensional Polyphenylene: Experimentally Available Porous Graphene as a Hydrogen Purification Membrane,” Chemical Communications 46, no. 21 (2010): 3672–4.
   PubMed Web of Science ®Google Scholar