On Bond Incident Degree Indices of Random Spiro Chains

References

• I. Gutman, and N. Trinajstić, “Graph Theory and Molecular Orbitals. Total φ-Electron Energy of Alternant Hydrocarbons,” Chemical Physics Letters 17, no. 4 (1972): 535–8.
   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, no. 1 (2004): 83–92.
   Google Scholar
• J. Devillers, and A. Balaban, Topological Indices and Related Descriptors in QSAR and QSPR (Singapore: Gordon and Breach, 1999).
   Google Scholar
• N. H. A. M. Saidi, M. N. Husin, and N. B. Ismail, “On the Topological Indices of the Line Graphs of Polyhenylene Dendrimer,” AIP Conference Proceedings 2365, no. 1 (2021): 060001.
   Google Scholar
• N. H. A. M. Saidi, M. N. Husin, and N. B. Ismail, “Zagreb Indices and Zagreb Coindices of the Line Graphs of the Subdivision Graphs,” Journal of Discrete Mathematical Sciences and Cryptography 23, no. 6 (2020): 1253–67.
   Web of Science ®Google Scholar
• M. N. Husin, R. Hasni, and M. Imran, “More Results on Computation of Topological Indices of Certain Networks,” International Journal of Networking and Virtual Organisations 17, no. 1 (2017): 46–63.
   Google Scholar
• I. Gutman, E. Milovanović, and I. Milovanović, “Beyond the Zagreb Indices,” AKCE International Journal of Graphs and Combinatorics 17, no. 1 (2020): 74–85.
   Web of Science ®Google Scholar
• A. Ali, B. Furtula, I. Gutman, and D. Vukicevic, “Augmented Zagreb Index: Extremal Results and Bounds,” MATCH Communications in Mathematical and in Computer Chemistry 85, no. 2 (2021): 211–44.
   Web of Science ®Google Scholar
• M. Randić, “Characterization of Molecular Branching,” Journal of the American Chemical Society 97, no. 23 (1975): 6609–15.
   Web of Science ®Google Scholar
• X. Li, and Y. Shi, “A Survey on the Randić Index,” MATCH Communications in Mathematical and in Computer Chemistry 59, no. 1 (2008): 127–56.
   Web of Science ®Google Scholar
• M. Shanmukha, A. Usha, M. Siddiqui, S. Fufa, and B. Praveen, “Degree-Based Molecular Descriptors of Guar Gum and Its Chemical Derivatives,” Journal of Chemistry 2022 (2022): 1–14.
   Web of Science ®Google Scholar
• J. Zhang, and B. Wu, “Randić Index of a Line Graph,” Axioms 11, no. 5 (2022): 210.
   Web of Science ®Google Scholar
• I. Gutman, “Geometric Approach to Degree-Based Topological Indices: Sombor Indices,” MATCH Communications in Mathematical and in Computer Chemistry 86, no. 1 (2021): 11–6.
   Web of Science ®Google Scholar
• H. Deng, Z. Tang, and R. Wu, “Molecular Trees with Extremal Values of Sombor Indices,” International Journal of Quantum Chemistry 121, no. 11 (2021): 26622.
   Web of Science ®Google Scholar
• H. Liu, I. Gutman, L. You, and Y. Huang, “Sombor Index: Review of Extremal Results and Bounds,” Journal of Mathematical Chemistry 60, no. 5 (2022): 771–98.
   Web of Science ®Google Scholar
• Y. Shang, “Sombor Index and Degree-Related Properties of Simplicial Networks,” Applied Mathematics and Computation 419 (2022): 126881.
   Web of Science ®Google Scholar
• V. Kulli, “Nirmala Index,” International Journal of Mathematics Trends and Technology 67, no. 3 (2021): 8–12.
   Google Scholar
• V. Kulli, B. Chaluvaraju, and T. Asha, “Computation of Nirmala Indices of Some Chemical Networks,” Journal of Ultra Scientist of Physical Sciences Section A 33, no. 4 (2021): 30–41.
   Google Scholar
• I. Gutman, and V. Kulli, “Nirmala Energy,” Open Journal of Discrete Applied Mathematics 4, no. 2 (2021): 11–6.
   Google Scholar
• V. Kulli, and I. Gutman, “On Some Mathematical Properties of Nirmala Index,” Annals of Pure and Applied Mathematics 23, no. 2 (2021): 93–9.
   Google Scholar
• I. Gutman, V. Kulli, and I. Redzepovic, “Nirmala Index of Kragujevac Trees,” International Journal of Mathematics Trends and Technology 67, no. 6 (2021): 44–9.
   Google Scholar
• Q. Feng, and Z. Hu, “Asymptotic Normality of the Zagreb Index of Random b-Ary Recursive Trees,” Dal’nevostochnyi Matematicheskii Zhurnal 15, no. 1 (2015): 91–101.
   Google Scholar
• R. Kazemi, “Gordon-Scantlebury and Platt Indices of Random Plane-Oriented Recursive Trees,” Mathematics Interdisciplinary Research 6, no. 1 (2021): 1–10.
   Google Scholar
• S. Li, L. Shi, and W. Gao, “Topological Indices Computing on Random Chain Structures,” International Journal of Quantum Chemistry 121, no. 8 (2021): 26589.
   Web of Science ®Google Scholar
• Z. Raza, and M. Imran, “Expected Values of Some Molecular Descriptors in Random Cyclooctane Chains,” Symmetry 13, no. 11 (2021): 2197.
   Google Scholar
• Z. Raza, “The Expected Values of Some Indices in Random Phenylene Chains,” The European Physical Journal Plus 136, no. 1 (2021): 1–15.
   Web of Science ®Google Scholar
• X. Fang, L. You, and H. Liu, “The Expected Values of Sombor Indices in Random Hexagonal Chains, Phenylene Chains and Sombor Indices of Some Chemical Graphs,” International Journal of Quantum Chemistry 121, no. 17 (2021): 26740.
   Web of Science ®Google Scholar
• S. Wei, X. Ke, and G. Hao, “Comparing the Excepted Values of Atom-Bond Connectivity and Geometric–Arithmetic Indices in Random Spiro Chains,” Journal of Inequalities and Applications 2018, no. 1 (2018): 1–11.
   PubMedGoogle Scholar
• H. Deng, “Wiener Indices of Spiro and Polyphenyl Hexagonal Chains,” Mathematical and Computer Modelling 55, no. 3–4 (2012): 634–44.
   Google Scholar
• Q. Li, Q. Yang, H. Yin, and S. Yang, “Analysis of by-Products from Improved Ullmann Reaction Using TOFMS and GCTOFMS,” Journal of University of Science and Technology of China 34 (2004): 335–41.
   Google Scholar
• S. Tepavcevic, A. Wroble, M. Bissen, D. Wallace, Y. Choi, and L. Hanley, “Photoemission Studies of Polythiophene and Polyphenyl Films Produced via Surface Polymerization by Ion-Assisted Deposition,” The Journal of Physical Chemistry B 109, no. 15 (2005): 7134–40.
   PubMed Web of Science ®Google Scholar
• P. Hall, and C. Heyde, Martingale Limit Theory and Its Application (New York, NY: Academic Press, 2014).
   Google Scholar
• T. Severini, Elements of Distribution Theory (New York, NY: Cambridge University Press, 2012).
   Google Scholar
• T. Došlić, T. Réti, and D. Vukičević, “On the Vertex Degree Indices of Connected Graphs,” Chemical Physics Letters 512, no. 4–6 (2011): 283–6.
   Web of Science ®Google Scholar
• A. Jahanbani, “The First Zagreb and Randić Indices in Random Spiro Chains,” Polycyclic Aromatic Compounds 42, no. 4 (2022): 1851–60.
   Web of Science ®Google Scholar
• W. Zhang, L. You, H. Liu, and Y. Huang, “The Expected Values and Variances for Sombor Indices in a General Random Chain,” Applied Mathematics and Computation 411 (2021): 126521.
   Web of Science ®Google Scholar
• Z. Raza, “The Harmonic and Second Zagreb Indices in Random Polyphenyl and Spiro Chains,” Polycyclic Aromatic Compounds 42, no. 3 (2022): 671–80.
   Web of Science ®Google Scholar