Topological Indices and Their Applications to Circumcised Donut Benzenoid Systems, Kekulenes and Drugs

References

• M. Bača, J. Horváthová, M. Mokrišová, A. Semaničová-Feňovčíková, and A. Suhányiová, “On Topological Indices of a Carbon Nanotube Network,” Canadian Journal of Chemistry 93 (2015): 1157–60.
   Web of Science ®Google Scholar
• J. R. Dias, “The Polyhex/Polypent Topological Paradigm: Regularities in the Isomer Numbers and Topological Properties of Select Subclasses of Benzenoid Hydrocarbons and Related Systems,” Chemical Society Reviews 39 (2010): 1913–24.
   PubMed Web of Science ®Google Scholar
• M. Eliasi, “Harary Index of Zigzag Polyhex Nanotorus,” Digest Journal of Nanomaterials and Biostructures 4 (2009): 757–62.
   Web of Science ®Google Scholar
• M. R. Farahani, “A New Version of Zagreb Index of Circumcoronene Series of Benzenoid,” Chemical Physics Research Journal 6 (2013): 27–33.
   Google Scholar
• W. Gao and M. R. Farahani, “Computing the Reverse Eccentric Connectivity Index for Certain Family of Nanocone and Fullerene Structures,” Journal of Nanotechnology 2016 (2016): 1–6.
   Web of Science ®Google Scholar
• M. Ghorbani and M. Ghazi, “Computing Some Topological Indices of Triangular Benzenoid,” Digest Journal of Nanomaterials and Biostructures 5 (2010): 1107–11.
   Web of Science ®Google Scholar
• M. Imran, A. Q. Baig, and H. Ali, “On Molecular Topological Properties of Hex-Derived Networks,” Journal of Chemometrics 30 (2016): 121–29.
   Web of Science ®Google Scholar
• W. Gao and W. Wang, “Second Atom-Bond Connectivity Index of Special Chemical Molecular Structures,” Journal of Chemistry 2014 (2014): 1–8.
   Web of Science ®Google Scholar
• W. Gao, W. F. Wang, and M. R. Farahani, “Topological Indices Study of Molecular Structure in Anticancer Drugs,” Journal of Chemistry 2016 (2016): 1–8.
   Web of Science ®Google Scholar
• J.-I. Aihara, M. Makino, T. Ishida, and J. R. Dias, “Analytical Study of Superaromaticity in Cycloarenes and Related Coronoid Hydrocarbons,” Journal of Physical Chemistry A 117 (2013): 4688–97.
   PubMed Web of Science ®Google Scholar
• A. T. Balaban, “Challenging Problems Involving Benzenoid Polycyclics and Related Systems,” Pure and Applied Chemistry 54, no. 5 (1982): 1075–96.
   Web of Science ®Google Scholar
• A. T. Balaban and F. Harary, “Chemical Graphs. V. Enumeration and Proposed Nomenclature of Benzenoid Cata-Condensed Polycyclic Aromatic Hydrocarbons,” Tetrahedron 24 (1968): 2505–16.
   Web of Science ®Google Scholar
• R. S. Chen, “Coronoid Systems with Perfect Matchings,” Discrete Applied Mathematics 64 (1996): 117–33.
   Web of Science ®Google Scholar
• R. S. Chen and F. J. Zhang, “Regular Coronoid Systems,” Discrete Applied Mathematics 74 (1997): 147–58.
   Web of Science ®Google Scholar
• R. S. Chen and F. J. Zhang, “Coronoid Systems with Fixed Bonds,” Journal of Molecular Structure 403 (1997): 237–43.
   Web of Science ®Google Scholar
• J. Cioslowski, “Additive Nodal Increments for Approximate Calculation of the Total π-Electron Energy of Benzenoid Hydrocarbons,” Theoretica Chimica Acta 68 (1985): 315–19.
   Google Scholar
• S. J. Cyvin, J. Brunvoll, and B. N. Cyvin, Coronoids and Coronoid-Like Systems (Berlin: Springer-Verlag, 1991).
   Google Scholar
• S. J. Cyvin, J. Brunvoll, B. R. N. Cyvin, J. L. Bergan, and E. Brendsdal, “The Simplest Coronoids: Hollow Hexagons,” Structural Chemistry 2 (1991): 555–66.
   Web of Science ®Google Scholar
• S. J. Cyvin, J. Brunvoll, B. N. Cyvin, R. S. Chen, and F. J. Zhang, Generation and Enumeration of Single Coronoid Isomers (Berlin: Springer, 1994).
   Google Scholar
• S. J. Cyvin and I. Gutman, Kekulé Structures in Benzenoid Hydrocarbons (Berlin: Springer, 1988).
   Google Scholar
• J. R. Dias, “A Periodic Table for Polycyclic Aromatic Hydrocarbons. Isomer Enumeration of Fused Polycyclic Aromatic Hydrocarbons,” Journal of Chemical Information and Computer Sciences 22 (1982): 15–22.
   Google Scholar
• J. R. Dias, Handbook of Polycyclic Hydrocarbons - Part A - Benzenoid Hydrocarbons (Amsterdam: Elsevier, 1987).
   Google Scholar
• J. R. Dias, “Structure and Electronic Characteristics of Coronoid Polycyclic Aromatic Hydrocarbons as Potential Models of Graphite Layers with Hole Defects,” The Journal of Physical Chemistry A 112 (2008): 12281–92.
   PubMed Web of Science ®Google Scholar
• I. Gutman and S. J. Cyvin, Introduction to the Theory of Benzenoid Hydrocarbons (Berlin: Springer-Verlag, 1989).
   Google Scholar
• I. Gutman and O. E. Polansky, Mathematical Concepts in Organic Chemistry (Berlin: Springer-Verlag, 1986).
   Google Scholar
• N. Ohkami, “Graph-Theoretical Analysis of the Sextet Polynomial. Proof of the Correspondence Between the Sextet Patterns and Kekulé Patterns,” Journal of Mathematical Chemistry 5 (1990): 23–42.
   Web of Science ®Google Scholar
• D. Djoković, “Distance Preserving Subgraphs of Hypercubes,” Journal of Combinatorial Theory, Series B 14 (1973): 263–7.
   Google Scholar
• X. Ke, “The Number of Normal Components of Essentially Disconnected Coronoid Systems,” Polycyclic Aromatic Compounds 36 (2015): 89–105.
   Web of Science ®Google Scholar
• H. Miyoshi, S. Nobusue, A. Shimizu, and Y. Tobe, “Non-Alternant Non-Benzenoid Kekulenes: The Birth of a New Kekulene Family,” Chemical Society Reviews 44 (2015): 6560–77.
   PubMed Web of Science ®Google Scholar
• H. Wenchen and H. Wenjie, Peak-valley Path Method on Benzenoid and Coronoid Systems (Berlin: Springer-Verlag, 1990).
   Google Scholar
• H. Zhang and S. Xu, “None of the Coronoid Systems Can be Isometrically Embedded into a Hypercube,” Discrete Applied Mathematics 156 (2008): 2817–22.
   Web of Science ®Google Scholar
• P. Winkler, “Isometric Embeddings in Products of Complete Graphs,” Discrete Applied Mathematics 7 (1984): 221–5.
   Web of Science ®Google Scholar
• B. Gute, G. Grunwald, and S. C. Basak, “Prediction of the Dermal and Penetration of Polycyclic Aromatics: A Hierachical QSAR Approach,” SAR and QSAR in Environmental Research 10 (1999): 1–15.
   PubMed Web of Science ®Google Scholar
• V. N. Viswanadhan, G. A. Mueller, S. C. Basak, and J. N. Weinstein, “Comparison of a Neural Net-Based QSAR Algorithm (PCANN) with Hologram-and Multiple Linear Regression-Based QSAR Approaches: Application to 1,4-Dihydropyridine-Based Calcium Channel Antagonists,” Journal of Chemical Information and Computer Sciences 41, no. 3 (2001): 505–11.
   PubMedGoogle Scholar
• M. Arockiaraj, J. Clement, and K. Balasubramanian, “Analytical Expressions for Topological Properties of Polycyclic Benzenoid Networks,” Journal of Chemometrics 30 (2016): 682–97.
   Web of Science ®Google Scholar
• H. Wiener, “Structural Determination of Paraffin Boiling Points,” Journal of the American Chemical Society 69 (1947): 17–20.
   PubMed Web of Science ®Google Scholar
• I. Gutman, “A Formula for the Wiener Number of Trees and Its Extension to Graphs Containing Cycles,” Graph Theory Notes New York 27 (1994): 9–15.
   Google Scholar
• I. Gutman and A. R. Ashrafi, “The Edge Version of the Szeged Index,” Croatica Chemica Acta 81 (2008): 263–6.
   Web of Science ®Google Scholar
• M. H. Khalifeh, H. Yousefi-Azari, A. R. Ashrafi, and I. Gutman, “The Edge Szeged Index of Product Graphs,” Croatica Chemica Acta 81, no. 2 (2008): 277–81.
   Web of Science ®Google Scholar
• A. Mahmiani, O. Khormali, A. Iranmanesh, and M. Yousefidaz, “The New Version of Szeged Index,” Optoelectronics and Advanced Materials - Rapid Communications 5 (2010): 2182–4.
   Web of Science ®Google Scholar
• P. V. Khadikar, S. Karmarkar, and V. K. Agrawal, “A Novel PI Index and Its Applications to QSPR/QSAR Studies,” Journal of Chemical Information and Modeling 41 (2001): 934–49.
   Google Scholar
• H. P. Schultz, “Topological Organic Chemistry. 1. Graph Theory and Topological Indices of Alkanes,” Journal of Chemical Information and Computer Sciences 29, no. 3 (1989): 227–8.
   Google Scholar
• S. Klavžar and M. J. Nadjafi-Arani, “Wiener Index in Weighted Graphs via Unification of Θ*-Classes,” European Journal of Combinatorics 36 (2014): 71–76.
   Web of Science ®Google Scholar
• M. Črepnjak and N. Tratnik, “The Szeged Index and the Wiener Index of Partial Cubes with Applications to Chemical Graphs,” Applied Mathematics and Computation 309 (2017): 324–33.
   Web of Science ®Google Scholar
• N. Tratnik, “The Edge-Szeged Index and the PI Index of Benzenoid Systems in Linear Time,” MATCH Communications in Mathematical and in Computer Chemistry 77 (2017): 393–406.
   Web of Science ®Google Scholar
• S. Klavžar, P. Manuel, M.J. Nadjafi-Arani, R.S. Rajan, C. Grigorious, and S. Stephen, “Average Distance in Interconnection Networks via Reduction Theorems for Vertex-Weighted Graphs,” The Computer Journal 59 (2016): 1900–10.
   Web of Science ®Google Scholar
• H. A. Staab and F. Diederich, “Cycloarenes, a New Class of Aromatic Compounds, I. Synthesis of Kekulene,” Chemische Berichte 116 (1983): 3487–503.
   Google Scholar
• S. Klavžar and I. Gutman, “Wiener Number of Vertex-Weighted Graphs and a Chemical Application,” Discrete Applied Mathematics 80 (1997): 73–81.
   Web of Science ®Google Scholar