New Bounds for the Estrada Index of Phenylenes

References

• M. Saheli, H. Saati, and A. R. Ashrafi, “The Eccentric Connectivity Index of One Pentagonal Carbon Nanocones,” Optoelectronics and Advanced Materials – Rapid Communications 4 (2010): 896–7.
   Web of Science ®Google Scholar
• V. R. Kulli, Multiplicative Connectivity Indices of Nanostructures (Rīgā: LAP LAMBERT Academic Publishing, 2018).
   Google Scholar
• N. Trinajstić, Chemical Graph Theory (Boca Raton, FL: CRC Press, 1992).
   Google Scholar
• C. Wang, S. Wang, and B. Wei, “Cacti with Extremal PI Index,” Transactions on Combinatorics 5, no. 4 (2016): 1–8.
   Web of Science ®Google Scholar
• G. W. Milne, “Mathematics as a Basis for Chemistry,” Journal of Chemical Information and Computer Sciences 37, no. 4 (1997): 639–44.
   PubMedGoogle Scholar
• E. Estrada, “Characterization of 3D Molecular Structure,” Chemical Physics Letters 319, no. 5–6 (2000): 713–8.
   Web of Science ®Google Scholar
• E. Estrada, “Characterization of the Folding Degree of Proteins,” Bioinformatics (Oxford, England) 18, no. 5 (2002): 697–704.
   PubMed Web of Science ®Google Scholar
• E. Estrada, and J. A. Rodríguez-Velázquez, “Subgraph Centrality in Complex Networks,”Physical Review E 71, no. 5 (2005): 159–69.
   Web of Science ®Google Scholar
• E. Estrada, and J. A. Rodríguez-Velázquez, “Spectral Measures of Bipartivity in Complex Networks,” Physical Review E 72, no. 4 (2005): 223–45.
   Web of Science ®Google Scholar
• I. Gutman, O. E. Polansky, Mathematical Concepts in Organic Chemistry (Berlin: Springer, 1986).
   Google Scholar
• G. Bauer, and G. Bolch, “Analytical Approach to Discrete Optimization of Queuing Networks,” Computer and Communications 13, no. 8 (1990): 494–502.
   Web of Science ®Google Scholar
• M. Krishnamoorth, and B. Krishnamirthy, “Fault Diameter of Interconnection Networks,” Computers & Mathematics with Applications 13 (1987): 577–82.
   Web of Science ®Google Scholar
• B. Mohar, “Isoperimetric Numbers of Graphs,” Journal of Combinatorial Theory B 47, no. 3 (1989): 274–91.
   Web of Science ®Google Scholar
• M. Fiedler, “Algebraic Connectivity of Graphs,” Czechoslovak Mathematical Journal 23 (1973): 298–305.
   Web of Science ®Google Scholar
• J. A. De la Peña, I. Gutman, and J. Rada, “Estimating the Estrada Index,” Linear Algebra and its Applications 427, no. 1 (2007): 70–6.
   Web of Science ®Google Scholar
• J. Wu, M. Barahona, Y. J. Tan, and H. Z. Deng, “Natural Connectivity of Complex Networks,” Chinese Physics Letters 27 (2010): 55–65.
   Web of Science ®Google Scholar
• I. Gutman, S. J. Cyvin, Introduction to the Theory of Benzenoid Hydrocarbons (Berlin: Springer, 1989).
   Google Scholar
• J. Wu, M. Barahona, Y. J. Tan, and H. Z. Deng, “Robustness of Random Graphs Based on Natural Connectivity,” arXiv:1009.3430 (2010).
   Google Scholar
• Y. Shang, “Perturbation Results for the Estrada Index in Weighted Networks,” Journal of Physics A: Mathematical and Theoretical 44, no. 7 (2011): 075003–89.
   Web of Science ®Google Scholar
• Y. Shang, “Biased Edge Failure in Scale-Free Networks Based on Natural Connectivity,” Indian Journal of Physics 86, no. 6 (2012): 485–8.
   Web of Science ®Google Scholar
• S. Yi-Lun, “Local Natural Connectivity in Complex Networks,” Chinese Physics Letters 28 (2011): 68–79.
   Web of Science ®Google Scholar
• I. Gutman, B. Furtula, V. Marković, and B. Glišić, “Alkanes with Greatest Estrada Index,” Zeitschrift für Naturforschung 62 (2007): 495–8.
   Google Scholar
• I. Gutman, and S. Radenković, “Estrada Index of Benzenoid Hydrocarbons,” Zeitschrift für Naturforschung 62 (2007): 254–8.
   Google Scholar
• I. Gutman, S. Radenković, A. Graovac, and D. Plavsić, “Monte Carlo Approach to Estrada Index,” Chemical Physics Letters 446, no. 1–3 (2007): 233–6.
   Web of Science ®Google Scholar
• N. J. Rad, A. Jahanbani, and D. A. Mojdeh, “Tetracyclic Graphs with Maximal Estrada Index,” Discrete Mathematics, Algorithms and Applications 09, no. 03 (2017): 1750041–185.
   Web of Science ®Google Scholar
• N. J. Rad, A. Jahanbani, and R. Hasni, “Pentacyclic Graphs with Maximal Estrada Index,” Ars Combinatoria 133 (2017): 133–45.
   Web of Science ®Google Scholar
• N. J. Rad, A. Jahanbani, and I. Gutman, “Zagreb Energy and Zagreb Estrada Index of Graphs,” MATCH Communications in Mathematical and in Computer Chemistry 79 (2018): 371–86.
   Web of Science ®Google Scholar
• J. Rodr iguez, “A note on new bounds for the Estrada Index,” Linear Algebra and its Applications 580 (2019): 121–127.
   Web of Science ®Google Scholar
• F. Harary, Graph Theory (Reading, Addison-Wesley, 1969).
   Google Scholar
• A. T. Balaban, Chemical Applications of Graph Theory (London, Academic Press, 1976).
   Google Scholar
• N. Trinajstić, Chemical Graph Theory (Boca Raton, FL: CRC Press, 1983); 2nd ed. (1992) 32–33.
   Google Scholar
• F. Toda, and P. Garratt, “Four-Membered Ring Compounds Containing Bis(methylene)cyclobutene or Tetrakis(methylene)cyclobutene Moietiess Benzocyclobutadiene, Benzodicyclobutadiene, Biphenylene, and Related Compounds,” Chemical Reviews 92, no. 8 (1992): 1685–707.
   Web of Science ®Google Scholar
• K. P. C. Vollhardt, and D. L. Mohler, “The phenylenes: Synthesis, Properties and Reactivity,” Advances in Strain in Organic Chemistry 5 (1996): 121–60.
   Google Scholar
• R. Faust, E. D. Glendening, A. Streitwieser, K. P. C. Vollhardt, and F. Weinhold, “Ab Initio Study of - and π-Effects in Benzenes Fused to Four-Membered Rings: Rehybridization, Delocalization, and Antiaromaticity,” Journal of the American Chemical Society 114, no. 21 (1992): 8263–8.
   Web of Science ®Google Scholar
• E. D. Glendening, R. Faust, A. Streitwieser, K. P. C. Vollhardt, and F. Weinhold, “The Role of Delocalization in Benzene,” Journal of the American Chemical Society 115, no. 23 (1993): 10952–7.
   Web of Science ®Google Scholar
• S. Marković, and I. Gutman, “Spectral Moments of the Edge Adjacency Matrix in Molecular Graphs. Benzenoid Hydrocarbons,” Journal of Chemical Information and Computer Sciences 39, no. 2 (1999): 289–93.
   Google Scholar
• S. Marković, Z. Marković, and R. I. McCrindle, “Spectral Moments of Phenylenes,” Journal of Chemical Information and Computer Sciences 41, no. 1 (2001): 112–9.
   PubMedGoogle Scholar
• D. H. Rouvray, In Chemical Applications of Graph Theory, ed. A. T. Balaban (London: Academic Press, 1976), 180–181.
   Google Scholar
• E. Estrada, “Edge Adjacency Relationships and a Novel Topological Index Related to Molecular Volume,” Journal of Chemical Information and Modeling 35, no. 1 (1995): 31–3.
   Web of Science ®Google Scholar
• E. Estrada, “Edge Adjacency Relationships in Molecular Graphs Containing Heteroatoms: A New Topological Index Related to Molar Volume,” Journal of Chemical Information and Modeling 35, no. 4 (1995): 701–7.
   Web of Science ®Google Scholar
• J. K. Burdett, and S. Lee, “Moments and the Energies of Solids,” Journal of the American Chemical Society 107, no. 11 (1985): 3050–63.
   Web of Science ®Google Scholar
• S. Lee, “Second-Moment Scaling and Covalent Crystal Structures,”Accounts of Chemical Research 24, no. 8 (1991): 249–54.
   Web of Science ®Google Scholar
• S. Marković, and A. Stajković, “The Evaluation of Spectral Moments for Molecular Graphs of Phenylenes,” Theoretical Chemistry Accounts 96, no. 4 (1997): 256–60.
   Web of Science ®Google Scholar
• S. Marković, “Tenth Spectral Moment for Molecular Graphs of Phenylenes,” Journal of Chemical Information and Computer Sciences 39, no. 4 (1999): 654–8.
   Google Scholar
• G. G. Hall, “The Evaluation of Moments for Polycyclic Hydrocarbons,” Theoretica Chimica Acta 70, no. 5 (1986): 323–32.
   Google Scholar
• L. Türker, “An Upper Bound for Total π-Electron Energy of Alternant Hydrocarbons,” MATCH Communications in Mathematical and in Computer Chemistry 16 (1984): 83–94.
   Google Scholar
• Y. Jiang, A. Tang, and R. Hoffmann, “Evaluation of Moments and their Application in Hückel Molecular Orbital Theory,” Theoretica Chimica Acta 66, no. 3–4 (1984): 183–92.
   Google Scholar