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Research Articles

An Efficient Technique to Construct Certain Counting Polynomials and Related Topological Indices for 2D-Planar Graphs

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Pages 4328-4342 | Received 12 Dec 2020, Accepted 05 Feb 2021, Published online: 11 Mar 2021

References

  • A. R. Ashrafi, M. Jalali, M. Ghorbani, and M. V. Diudea, “Computing PI and Omega Polynomials of an Infinite Family of Fullerenes,” Match 60, no. 3 (2008): 905–16.
  • M. V. Diudea, B. Pârv, E. C. Kirby, B. Pârv, and E. C. Kirby, “Azulenic Tori,” MATCH Communications in Mathematical and in Computer Chemistry 47 (2003): 53–70.
  • H. Hosoya, “On Some Counting Polynomials in Chemistry,” Discrete Applied Mathematics 19, no. 1–3 (1988): 239–57.
  • P. Khadikar, S. Joshi, A. Bajaj, and D. Mandloi, “Correlations between the Benzene Character of Acenes or Helicenes and Simple Molecular Descriptors,” Bioorganic & Medicinal Chemistry Letters 14, no. 5 (2004): 1187–91.
  • M. Nadeem, A. Yousaf, and A. Razaq, “On Sequences of Molecular Descriptors Related to Some Counting Polynomials of a Benzenoid Graph,” Utilitas Mathematica 114 (2020): 167–71.
  • M. V. Diudea, “Omega Polynomial,” Carpathian Journal of Mathematics 22 (2006): 43–7.
  • M. V. Diudea, “Omega Polynomial in All R[8] Lattices,” Iranian Journal of Mathematical Chemistry 1, no. 1 (2010): 69–77.
  • Z. Raza, M. Essa, and K. Sukaiti, “M-Polynomial and Degree Based Topological Indices of Some Nanostructures,” Symmetry 12, no. 5 (2020): 831.
  • A. Rajpoot, and L. Selvaganesh, “Extension of m-Polynomial and Degree Based Topological Indices for Nanotube,” TWMS Journal of Applied and Engineering Mathematics 11 (2021): 268–79.
  • Z. Raza, “Zagreb Connection Indices for Some Benzenoid Systems,” Polycyclic Aromatic Compounds 8 (2020): 1–14. doi:10.1080/10406638.2020.1809469
  • J.-B. Liu, Z. Raza, and M. Javaid, “Zagreb Connection Numbers for Cellular Neural Networks,” Discrete Dynamics in Nature and Society 2020 (2020): 1–8. doi:10.1155/2020/8038304
  • A. Kanwal, A. Aslam, Z. Raza, N. Iqbal, and B. K. Kometa, “On the Variable Sum Exdeg Index and Cut Edges of Graphs,” Communications in Combinatorics and Optimization 6, no. 2 (2021): 249–57.
  • Z. Shao, H. Jiang, and Z. Raza, “Inequalities among Topological Descriptors,” Kragujevac Journal of Mathematics 47, no. 5 (2023): 661–72.
  • Z. Raza, and A. Ali, “Bounds on the Zagreb Indices for Molecular (n,m) ‐Graphs,” International Journal of Quantum Chemistry 120, no. 18 (2020): 1–10. doi:10.1002/qua.26333
  • Z. Raza, “The Expected Values of Arithmetic Bond Connectivity and Geometric Indices in Random Phenylene Chains,” Heliyon 6, no. 7 (2020): e04479. doi:10.1016/j.heliyon.2020.e04479
  • M. Imran, A. Q. Baig, S. U. Rehman, H. Ali, and R. Hasni, “Computing Topological Polynomials of Mesh-Derived Networks,” Discrete Mathematics, Algorithms and Applications 10, no. 06 (2018): 1850077. doi:10.1142/S1793830918500775
  • M. Ghorbani, “Computing Vertex PI, Omega and Sadhana Polynomials of F 12(2n + 1) Fullerenes,” Iranian Journal of Mathematical Chemistry 1 (2010): 105–10.
  • M. Ghorbani, M. Ghazi, and S. Shakeraneh, “Computing Omega and Sadhana Polynomials of an Infinite Class of Fullerenes F4x3n,” Optoelectronics and Advanced Materials, Rapid Communications 4, no. 6 (2010): 893–5.
  • M. Ghorbani, and M. Jalali, “Omega and Sadhana Polynomials of an Infinite Family of Fullerenes,” Digest Journal of Nanomaterials and Biostructures 4, no. 1 (2009): 177–82.
  • A. R. Ashrafi, M. Ghorbani, and M. Jalali, “The Vertex PI and Szeged Indices of an Infinite Family of Fullerenes,”Journal of Theoretical and Computational Chemistry 7, no. 2 (2008): 221–31.
  • M. Ghorbani, and M. Ghazi, “Computing Omega and Pi Polynomials of Graphs,” Digest Journal of Nanomaterials Biostructures 5, no. 4 (2010): 843–9.
  • C. Delorme, O. Favaron, and D. Rautenbach, “On the Randic Index,” Discrete Mathematics 257, no. 1 (2002). doi:10.1016/S0012-365X(02)00256-X
  • M. Ahmad, M. Javaid, M. Saeed, and C. Y. Jung, “Valency-Based Molecular Descriptors of Bakelite Network BNmn,” Open Chemistry 17, no. 1 (2019): 663–70.
  • M. Imran, W. Gao Sabeel-e-Hafi, and M. Reza Farahani, “On Topological Properties of Sierpinski Networks,” Chaos, Solitons & Fractals 98 (2017): 199–204.
  • P. Khadikar, “On a Novel Structural de-Scriptor pi,” National Academy Science Letters 23, no. 7–8 (2000): 113–8.
  • M. Nadeem, A. Yousaf, H. Alolaiyan, and A. Razaq, “Certain Polynomials and Related Topological Indices for the Series of Benzenoid Graphs,” Scientific Reports 9, no. 1 (2019): 1–5.
  • S. L. Joice, J. Quadras, S. S. Surya, and A. Shanthakumari, “PI Index of Mesh Structured Chemicals,” Communications in Computer and Information Science 253, no. 3 (2011): 400–9.
  • D. J. Klein, Y. Yang, and D. Ye, “HOMO–LUMO Gaps for Sub-Graphenic and Sub-Buckytubic Species,” Proceedings of the Royal Society Series A 471, no. 2 (2015): 183. doi:10.1098/rspa.2015.0183
  • P. E. John, P. V. Khadikar, and J. Singh, “A Method of Computing the PI Index of Benzenoid Hydrocarbons Using Orthogonal Cuts,” Journal of Mathematical Chemistry 42, no. 1 (2007): 37–45.

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