Vertex-Degree Based Topological Indices of Graphene

References

• J. Devillers and A. Balaban, Topological Indices and Related Descriptors in QSAR and QSPR (Amsterdam: Gordon & Breach, 1999).
   Google Scholar
• L. Kier and L. Hall, Molecular Connectivity in Chemistry and Drug Research (New York: Academic Press, 1976).
   Google Scholar
• L. Kier and L. Hall, Molecular Connectivity in Structure–Activity Analysis (New York: Wiley, 1986).
   Google Scholar
• R. Todeschini and V. Consonni, Handbook of Molecular Descriptors (Weinheim: Wiley-VCH, 2000).
   Google Scholar
• R. Todeschini and V. Consonni, Molecular Descriptors for Chemoinformatics (Weinheim: Wiley-VCH, 2009).
   Google Scholar
• A. Ali, L. Zhong, and I. Gutman, “Harmonic Index and Its Generalizations: Extremal Results and Bounds,” MATCH Communications in Mathematical and in Computer Chemistry 81 (2019): 249–311.
   Web of Science ®Google Scholar
• B. Borovićanin, K. C. Das, B. Furtula, and I. Gutman, “Bounds for Zagreb Indices,” MATCH Communications in Mathematical and in Computer Chemistry 78 (2017): 17–100.
   Web of Science ®Google Scholar
• Y. Huang, B. Liu, and L. Gan, “Augmented Zagreb Index of Connected Graphs,” MATCH Communications in Mathematical and in Computer Chemistry 67 (2012): 483–94.
   Web of Science ®Google Scholar
• X. Ke, “Atom-Bond Connectivity Index of Benzenoid Systems and Fluoranthene Congeners,” Polycyclic Aromatic Compounds 32, no. 1 (2012): 27–35.
   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 (2008): 127–56.
   Web of Science ®Google Scholar
• Y. Ma, S. Cao, Y. Shi, I. Gutman, M. Dehmer, and B. Furtula, “From the Connectivity Index to Various Randić-Type Descriptors,” MATCH Communications in Mathematical and in Computer Chemistry 80 (2018): 85–106.
   Web of Science ®Google Scholar
• P. Wilczek, “New Geometric-Arithmetic Indices,” MATCH Communications in Mathematical and in Computer Chemistry 79 (2018): 5–54.
   Web of Science ®Google Scholar
• J. Rada and R. Cruz, “Vertex-Degree-Based Topological Indices over Graphs,” MATCH Communications in Mathematical and in Computer Chemistry 72 (2014): 603–16.
   Web of Science ®Google Scholar
• J. Rada and S. Bermudo, “Is Every Graph the Extremal Value of a Vertex-Degree-Based Topological Index?,” MATCH Communications in Mathematical and in Computer Chemistry 81 (2019): 315–23.
   Web of Science ®Google Scholar
• Y. Yao, M. Liu, K.C. Das, and Y. Ye, “Some Extremal Results for Vertex-Degree-Based Invariants,” MATCH Communications in Mathematical and in Computer Chemistry 81 (2019): 325–44.
   Web of Science ®Google Scholar
• I. Gutman, S.J. Cyvin, Introduction to the Theory of Benzenoid Hydrocarbons (Berlin: Springer-Verlag, 1989).
   Google Scholar
• J. Rada, O. Araujo, and I. Gutman, “Randic Index of Benzenoid Systems and Phenylenes,” Croatica Chemica Acta 74 (2001): 225–35.
   Web of Science ®Google Scholar
• P. Bondavalli, Graphene and Related Nanomaterials (Amsterdam: Elsevier, 2018).
   Google Scholar
• A. K. Geim and K. S. Novoselov, “The Rise of Graphene,” Nature Materials 6, no. 3 (2007): 183–91.
   PubMed Web of Science ®Google Scholar
• M. Katsnelson, Graphene. Carbon in Two Dimensions (Cambridge: Cambridge University Press, 2012).
   Google Scholar
• J. Warner, F. Schäffel, M. Rümmeli, and A. Bachmatiuk, Graphene. Fundamentals and emergent applications (Amsterdam: Elsevier, 2013).
   Google Scholar
• S. Akhter, M. Imran, W. Gao, and M. Farahani, “On Topological Indices of Honeycomb Networks and Graphene Networks,” Hacettepe Journal of Mathematics and Statistics 47, no. 1 (2018): 19–35.
   Web of Science ®Google Scholar
• M. Berhe and C. Wang, “Computation of Certain Topological Coindices of Graphene Sheet and C4C8(S) nanotubes and Nanotorus,” Applied Mathematics and Nonlinear Sciences 4, no. 2 (2019): 455–68.
   Google Scholar
• W. Gao, M. Siddiqui, M. Imran, M. Jamil, and M. Farahani, “Forgotten Topological Index of Chemical Structure in Drugs,” Saudi Pharmaceutical Journal: SPJ: The Official Publication of the Saudi Pharmaceutical Society 24, no. 3 (2016): 258–64.
   PubMed Web of Science ®Google Scholar
• R. Jagadeesh, M.R. Rajesh Kanna, and R.S. Indumathi, “Some Results on Topological Indices of Graphene,” Nanomaterials and Nanotechnology 6 (2016): 184798041667962–6.
   Web of Science ®Google Scholar
• R. Kumar, S. Nandappa, and M.R. Kanna, “Redefined Zagreb, Randi ć, Harmonic and GA Indices of Graphene,” International Journal of Mathematical Analysis 11, no. 10 (2017): 493–502.
   Google Scholar
• Y. Kwun, A. Virk, M. Rafaqat, M. Rehman, and W. Nazeer, “Some Reversed Degree-Based Topological Indices for Graphene,” Journal of Discrete Mathematical Sciences and Cryptography 22, no. 7 (2019): 1305–14.
   Web of Science ®Google Scholar
• S. Mondal, N. De, and A. Pa, “Topological Properties of Graphene Using Some Novel Neighborhood Degree-Based Topological Indices,” International Journal of Mathematics for Industry 11, no. 01 (2019): 1950006–14.
   Google Scholar
• H. L. Parashivamurthy, M. R. Rajesh Kanna, and R. Jagadeesh, “Some Topological Indices and Their Polynomials of Graphene,” Oriental Journal of Chemistry 35, no. 5 (2019): 1514–8.
   Web of Science ®Google Scholar
• P. Puttaswamy, and V. Mathad, “Some Topological Indices of Fluorographene,” Journal of Mathematical Nanoscience 6, no. 1–2 (2016): 1–16.
   Google Scholar
• Prosanta Sarkar, Nilanjan De, and Anita Pal, “The Generalized Zagreb Index of Some Carbon Structures,” Acta Chemica Iasi 26, no. 1 (2018): 91–104.
   Web of Science ®Google Scholar
• V.S. Shigehalli and R. Kanabur, “Computation of New Degree-Based Topological Indices of Graphene,” Journal of Mathematics 2016, no. 2016 (2016): 1–6.
   Google Scholar
• V. Shigehalli and R. Kanabur, “Computing Some Degree-Based Topological Indices of Graphene,” Indonesian Journal of Electrical Engineering and Informatics 5 (2017): 155–61.
   Google Scholar
• G. Sridhara, M.R. Rajesh Kanna, and R.S. Indumathi, “Computation of Topological Indices of Graphene,” Journal of Nanomaterials 2015 (2015): 1–8.
   Web of Science ®Google Scholar
• I. Gutman and N. Trinajstić, “Graph Theory and Molecular Orbitals. Total π-Electron Energy of Alternant Hydrocarbons,” Chemical Physics Letters 17, no. 4 (1972): 535–8.
   Web of Science ®Google Scholar
• M. Randić, “On Characterization of Molecular Branching,” Journal of the American Chemical Society 97 (1975): 6609–15.
   Web of Science ®Google Scholar
• L. Zhong, “The Harmonic Index for Graphs,” Applied Mathematics Letters 25, no. 3 (2012): 561–6.
   Web of Science ®Google Scholar
• D. Vukičević and B. Furtula, “Topological Index Based on the Ratios of Geometrical and Arithmetical Means of End-Vertex Degrees of Edges,” Journal of Mathematical Chemistry 46, no. 4 (2009): 1369–76.
   Web of Science ®Google Scholar
• B. Zhou and N. Trinajstić, “On a Novel Connectivity Index,” Journal of Mathematical Chemistry 46, no. 4 (2009): 1252–70.
   Web of Science ®Google Scholar
• E. Estrada, L. Torres, L. Rodríguez, and I. Gutman, “An Atom-Bond Connectivity Index: Modelling the Enthalpy of Formation of Alkanes,” Indian Journal of Chemistry 37A (1998): 849–55.
   Google Scholar
• B. Furtula, A. Graovac, and D. Vukičević, “Augmented Zagreb Index,” Journal of Mathematical Chemistry 48, no. 2 (2010): 370–80.
   Web of Science ®Google Scholar