Topological Properties of Carbon Nanocones

References

• A. G. Cano-Marquez, W. G. Schmidt, J. Ribeiro-Soares, L. G. Canado, W. N. Rodrigues, A. P. Santos, C. A. Furtado, P. Autreto, R. Paupitz, D. S. Galvão, et al., “Enhanced Mechanical Stability of Gold Nanotips through Carbon Nanocone Encapsulation,” Scientific Reports 5 (2015): 10408.
   PubMed Web of Science ®Google Scholar
• M. Ge and K. Sattler, “Observation of Fullerene Cones,” Chemical Physics Letters 220 (1994): 192–196.
   Web of Science ®Google Scholar
• J. A. Jaszczak, G. W. Robinson, S. Dimovski, and Y. Gogotsi, “Naturally Occurring Graphite Cones,” Carbon 41 (2003): 2085–2092.
   Web of Science ®Google Scholar
• A. Krishnan, E. Dujardin, M. M. J. Treacy, J. Hugdahl, S. Lynum, and T. W. Ebbesen, “Graphitic Cones and the Nucleation of Curved Carbon Surfaces,” Nature 388 (1997): 451–454.
   Web of Science ®Google Scholar
• S. N. Naess, A. Elgsaeter, G. Helgesen, and K. D. Knudsen, “Carbon Nanocones: Wall Structure and Morphology,” Science and Technology of Advanced Materials 10 (2009): 065002.
   PubMed Web of Science ®Google Scholar
• Y. Alizadeh and S. Klavžar, “Interpolation Method and Topological Indices: 2 Parametric Families of Graphs,” Match-Communications In Mathematical and in Computer Chemistry 69 (2013): 523–534.
   Web of Science ®Google Scholar
• A. G. Cano-Marquez et al., “Enhanced Mechanical Stability of Gold Nanotips,” 10408.
   Google Scholar
• J. C. Charlier and G. M. Rignanese, “Electronic Structure of Carbon Nanocones,” Physics Review Letters 86 (2001): 5970–5973.
   PubMed Web of Science ®Google Scholar
• R. Majidi and K. G. Tabrizi, “Study of Neon Adsorption on Carbon Nanocones Using Molecular Dynamics Simulation,” Physica B: Condensed Matter 405 (2010): 2144–2148.
   Web of Science ®Google Scholar
• J. W. Yan, K. M. Liew, and L. H. He, “Ultra-Sensitive Analysis of a Cantilevered Single-Walled Carbon Nanocone-Based Mass Detector,” Nanotechnology 24 (2013): 125–703.
   Web of Science ®Google Scholar
• Parsons Moss, “Interactions of Plutonium and Lanthanides with Ordered Mesoporous Materials” (PhD Thesis, University of California, Berkeley, 2014).
   Google Scholar
• Parsons Moss, L. K. Schwaiger, A. Hubaud, Y. J. Hu, H. Tuysuz, P. Yang, K. Balasubramanian, and H. Nitsche, “Plutonium Complexation by Phosphonate-Functionalized Mesoporous Silica,” United States, 2010. https://www.osti.gov/biblio/1016927/cite/.
   Google Scholar
• K. Balasubramanian, “Characteristic Polynomials of Organic Polymers and Periodic Structures,” Journal of Computational Chemistry 6 (1985): 656–661.
   Web of Science ®Google Scholar
• K. Balasubramanian, “Applications of Combinatorics and Graph Theory to Spectroscopy and Quantum Chemistry,” Chemical Reviews 85 (1985): 599–618.
   Web of Science ®Google Scholar
• K. Balasubramanian and X. Liu, “Computer Generation of Spectra of Graphs: Applications to C60 Clusters and Other Systems,” Journal of Computational Chemistry 9 (1988): 406–415.
   Web of Science ®Google Scholar
• K. Balasubramanian, “Matching Polynomials of Fullerene Clusters,” Chemical Physics Letters 201 (1993): 306–314.
   Web of Science ®Google Scholar
• K. Balasubramanian, “Laplacian Polynomials of Fullerenes (C20C40),” Chemical Physics Letters 224 (1994): 325–332.
   Web of Science ®Google Scholar
• K. Balasubramanian, “Laplacians of Fullerenes (C42C90),” Journal of Physical Chemistry 99 (1995): 6509–6518.
   Web of Science ®Google Scholar
• K. Balasubramanian, “Exhaustive Generation and Analytical Expressions of Matching Polynomials of Fullerenes C20C50,” Journal of Chemical Information and Modeling 34 (2010): 421–427.
   Web of Science ®Google Scholar
• J. R. Dias, “Handbook of Polycyclic Hydrocarbons. Part A: Benzenoid Hydrocarbons,” United States, 1987. https://www.osti.gov/biblio/6042790.
   Google Scholar
• A. Iranmanesh, Y. Alizadeh, and S. Mirzaie, “Computing Wiener Polynomial, Wiener Index and Hyper Wiener Index of C80 Fullerene by GAP Program,” Fullerenes Nanotubes and Carbon Nanostructures 17 (2009): 560–566.
   Web of Science ®Google Scholar
• D. M. Joiţa and L. Jäntschi, “Extending the Characteristic Polynomial for Characterization of C20 Fullerene Congeners,” Mathematics 5 (2017): 84.
   Web of Science ®Google Scholar
• F. H. Kaatz and A. Bultheel, “Statistical Properties of Carbon Nanostructures,” Journal of Mathematical Chemistry 51 (2013): 1211–1220.
   Web of Science ®Google Scholar
• M. Manoharan, M. Balakrishnarajan, P. Venuvanalingam, and K. Balasubramanian, “Topological Resonance Energy Predictions of the Stability of Fullerene Clusters,” Chemical Physics Letters 222 (1994): 95–100.
   Web of Science ®Google Scholar
• M. A. Malik, S. Hayat, and M. Imran, “On the Anti-Kekule Number of Nanotubes and Nanocones,” Journal of Computational and Theoretical Nanoscience 12, no. 10 (2015): 3125–3129.
   Google Scholar
• R. Ramaraj and K. Balasubramanian, “Computer Generation of Matching Polynimials of Chemical Graphs and Lattices,” Journal of Computational Chemistry 6 (1985): 122–141.
   Web of Science ®Google Scholar
• A. A. Rezaei, “Tiling Fullerene Surface with Heptagon and Octagon,” Fullerenes Nanotubes and Carbon Nanostructures 23 (2015): 1033–1036.
   Web of Science ®Google Scholar
• A. A. Rezaei, “Tiling Fullerene Surfaces, Distance, Symmetry, and Topology in Carbon Nanomaterials,” Carbon Materials: Chemistry and Physics (2016): 437–446.
   Google Scholar
• H. Terrones, “Curved Graphite and Its Mathematical Transformations,” Journal of Mathematical Chemistry 15 (1994): 143–156.
   Web of Science ®Google Scholar
• M. A. Alipour and A. R. Ashrafi, “A Numerical Method for Computing the Wiener Index of One-Heptagonal Carbon Nanocone,” Journal of Computational and Theoretical Nanoscience 6 (2009): 1204–1207.
   Google Scholar
• M. A. Alipour and A. R. Ashrafi, “Computer Calculation of the Wiener Index of One-Pentagonal Carbon Nanocone,” Digest Journal of Nanomaterials and Biostructures 4 (2009): 16.
   Web of Science ®Google Scholar
• A. R. Ashrafi and Z. M. Abadi, “On Wiener Index of One-Heptagonal Nanocone,” Current Nanoscience 8 (2012): 180–185.
   Web of Science ®Google Scholar
• A. R. Ashrafi and F. G. Nezhaad, “The Edge Szeged Index of Onepentagonal Carbon Nanocones,” Journal of Nanoscience and Nanotechnology 4 (2008): 35–38.
   Google Scholar
• A. R. Ashrafi and F. G. Nezhaad, “The PI and Edge Szeged Indices of One-Heptagonal Carbon Nanocones,” Current Nanoscience 5 (2009): 51–53.
   Web of Science ®Google Scholar
• A. R. Ashrafi and F. G. Nezhaad, “The PI and Edge Szeged Indices of CNC3[n] and CNC4[n] Carbon Nanocones,” Optoelectronics and Advanced Materials: Rapid Communications 4 (2010): 531–533.
   Web of Science ®Google Scholar
• A. R. Ashrafi and H. Saati, “PI and Szeged Indices of One-Pentagonal Carbon Nanocones,” Journal of Computational and Theoretical Nanoscience 4 (2007): 761–763.
   Google Scholar
• A. Ilić, M. V. Diudea, F. G. Nezhad, and A. R. Ashrafi, Topological Indices in Nanocones, Novel Molecular Structure Descriptors Theory and Applications I. (Kragujevac: Univ. Kragujevac, 2010).
   Google Scholar
• M. Khalifeh, H. Yousefi-Azari, and A. Ashrafi, “Another Aspect of Graph Invariants Depending on the Path Metric and an Application in Nanoscience,” Computers & Mathematics with Applications 60 (2010): 2460–2468.
   Web of Science ®Google Scholar
• M. Khalifeh, H. Yousefi-Azari, and A. Ashrafi, “A Method for Computing the Wiener Index of One-Pentagonal Carbon Nanocones,” Current Nanoscience 6 (2010): 155–157.
   Web of Science ®Google Scholar
• F. Koorepazan-Moftakhar, A. R. Ashrafi, O. Ori, and M. V. Putz, “Topological Invariants of Nanocones and Fullerenes,” Current Organic Chemistry 19 (2015): 240–248.
   Web of Science ®Google Scholar
• 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): 896–897.
   Web of Science ®Google Scholar
• M. Alaeiyan, J. Asadpour, and R. Mojarad. “A Numerical Method for MEC Polynomial and MEC Index of One-Pentagonal Carbon Nanocones,” Fullerenes Nanotubes and Carbon Nanostructures 21 (2013): 825–835.
   Web of Science ®Google Scholar
• W. Gao, M. K. Jamil, W. Nazeer, and M. Amin, “Degree-Based Multiplicative Atom-Bond Connectivity Index of Nanostructures,” IAENG International Journal of Applied Mathematics 47 (2017): 388–397.
   Google Scholar
• W. Gao and W. F. Wang, “The Fifth Geometric-Arithmetic Index of Bridge Graph and Carbon Nanocones,” Journal of Difference Equations and Applications 23 (2016): 100–109.
   Web of Science ®Google Scholar
• W. Gharibi, A. Ahmad, and M. K. Siddiqui, “On Zagreb Indices, Zagreb Polynomials of Nanocone and Nanotubes,” Journal of Computational and Theoretical Nanoscience 13 (2016): 5086–5092.
   Google Scholar
• Y. Huo, J. B. Liu, Z. Zahid, S. Zafar, M. R. Farahani, and M. F. Nadeem, “On Certain Topological Indices of the Line Graph of CNCk[n] Nanocones,” Journal of Computational and Theoretical Nanoscience 13 (2016): 4318–4322.
   Google Scholar
• A. Khaksar, M. Ghorbani, and H. R. Maimani, “On Atom Bond Connectivity and GA Indices of Nanocones,” Optoelectronics and Advanced Materials: Rapid Communications 4 (2010): 1868–1870.
   Google Scholar
• Z. Raza, “The Edge Version of Geometric Arithmetic Index of Polyomino Chains of 8 Cycles and Arbitrary Carbon Nanocones,” Journal of Computational and Theoretical Nanoscience 13 (2016): 8455–8459.
   Google Scholar
• Alizadeh and Klavžar, “Interpolation Method and Topological Indices,” 523–534.
   Google Scholar
• M. R. Darafsheh, M. H. Khalifeh, and H. Jolany, “The Hyper-Wiener Index of One-Pentagonal Carbon Nanocone,” Current Nanoscience 9 (2013): 16.
   Web of Science ®Google Scholar
• S. Ediz, “The Ediz Eccentric Connectivity Index of One Pentagonal Carbon Nanocones,” Fullerenes Nanotubes and Carbon Nanostructures 21 (2013): 113–116.
   Web of Science ®Google Scholar
• M. Ghorbani and M. Jalali, “The Vertex PI, Szeged and Omega Polynomials of Carbon Nanocones CNC4[n],” Match-Communications in Mathematical and in Computer Chemistry 62 (2009): 353–362.
   Web of Science ®Google Scholar
• S. Hayat, A. Khan, F. Yousafzai, M. Imran, and M. U. Rehman, “On Spectrum Related Topological Descriptors of Carbon Nanocones,” Optoelectronics and Advanced Materials: Rapid Communications 9 (2015): 798–802.
   Web of Science ®Google Scholar
• M. F. Nadeem, S. Zafar, and Z. Zahid, “Some Topological Indices of L(S(CNCk[n])),” Punjab University Journal of Mathematics 49 (2017): 13–17.
   Web of Science ®Google Scholar
• A. Nejati and A. Mehdi, “On Reverse Eccentric Connectivity Index of One Tetragonal Carbon Nanocones,” Journal of Computational and Theoretical Nanoscience 1 (2014): 1000115.
   Google Scholar
• H. Saati, “Topological Index of Some Carbon Nanotubes and the Symmetry Group for Nanotubes and Unit Cells in Solids,” Journal of Mathematical Sciences 211 (2015): 58–126.
   Google Scholar
• L. Zhu and W. Gao, “Modified Eccentric Connectivity Index and Polynomial of Tetragonal Carbon Nanocones CNC4[n],” Advances in Analysis 2 (2017): 30–34. doi:10.22606/aan.2017.11005.
   Google Scholar
• Q.-X. Zhang, S. J. Xu, and H. Y. Chen, “The Hosoya Polynomial of One-Pentagonal Carbon Nanocone,” Fullerenes Nanotubes and Carbon Nanostructures 22 (2014): 866–873.
   Web of Science ®Google Scholar
• Balasubramanian, “Characteristic Polynomials of Organic Polymers,” 656–661.
   Google Scholar
• Balasubramanian, “Applications of Combinatorics and Graph Theory,” 599–618.
   Google Scholar
• Balasubramanian and Liu, “Computer Generation of Spectra of Graphs,” 406–415.
   Google Scholar
• Balasubramanian, “Matching Polynomials of Fullerene Clusters,” 306–314.
   Google Scholar
• Balasubramanian, “Laplacian Polynomials of Fullerenes (C20C40),” 325–332.
   Google Scholar
• Balasubramanian, “Laplacians of Fullerenes (C42C90),” 6509–6518.
   Google Scholar
• Balasubramanian, “Exhaustive Generation and Analytical Expressions,” 421–427.
   Google Scholar
• K. Balasubramanian, “Graph-Theoretical Characterization of Fullerene Cages,” Polycyclic Aromatic Compounds 3 (2006): 247–259.
   Google Scholar
• A. Balaban, D. Klein, and X. Liu, “Graphitic Cones,” Carbon 32 (1994): 357–359.
   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
• M. Arockiaraj, J. Clement, and K. Balasubramanian, “Analytical Expressions for Topological Properties of Polycyclic Benzenoid Networks,” Journal of Chemometrics 30 (2016): 682–697.
   Web of Science ®Google Scholar
• M. Arockiaraj, J. Clement, and A. J. Shalini, “Variants of Szeged Index in Certain Chemical Nanosheets,” Canadian Journal of Chemistry 94 (2016): 608–619.
   Web of Science ®Google Scholar
• S. C. Basak, K. Balasubramanian, B. D. Gute, D. Mills, A. Gorczynska, and S. Roszak, “Prediction of Cellular Toxicity of Halocarbons from Computed Chemodescriptors: A Hierarchical QSAR Approach,” Journal of Chemical Information and Modeling 43 (2003): 1103–1109.
   Google Scholar
• S. C. Basak, G. D. Grunwald, B. D. Gute, K. Balasubramanian, and D. Opitz, “Use of Statistical and Neural Net Approaches in Predicting Toxicity of Chemicals,” Journal of Chemical Information and Modeling 40 (2000): 885–890.
   Google Scholar
• S. C. Basak, D. Mills, M. M. Mumtaz, and K. Balasubramanian, “Use of Topological Indices in Predicting Aryl Hydrocarbon Receptor Binding Potency of Dibenzofurans: A Hierarchical QSAR Approach,” Indian Journal of Chemistry A 42A (2003): 1385–1391.
   Google Scholar
• J. Devillers and A. T. Balaban (Eds.), Topological Indices and Related Descriptors in QSAR and QSPR (Amsterdam: Gordon and Breach, 1999).
   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): 115.
   Web of Science ®Google Scholar
• S. Hayat, “Computing Distance-Based Topological Descriptors of Complex Chemical Networks: New Theoretical Techniques,” Chemical Physics Letters 688 (2017): 51–58.
   Web of Science ®Google Scholar
• S. Hayat and M. Imran, “On Topological Properties of Nanocones CNCk[n],” Studia Universitatis Babes-Bolyai Chemia 59, no. 4 (2014): 113–128.
   Web of Science ®Google Scholar
• M. Arockiaraj, J. Clement, and K. Balasubramanian, “Topological Indices and Their Applications to Circumcised Donut Benzenoid Systems, Kekulenes and Drugs,” Polycyclic Aromatic Compounds (2018). doi:10.1080/10406638.2017.1411958
   Web of Science ®Google Scholar
• M. Randić, “Novel Molecular Description for Structure-Property Studies,” Chemical Physics Letters 211 (1993): 478–483.
   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): 915.
   Google Scholar
• I. Gutman and A. R. Ashrafi, “The Edge Version of the Szeged Index,” Croatica Chemica Acta 81 (2008): 263–266.
   Web of Science ®Google Scholar
• M. H. Khalifeh, H. YousefiAzari, A. R. Ashrafi, and I. Gutman, “The Edge Szeged Index of Product Graphs,” Croatica Chemica Acta 81, no. 2 (2008): 277–281.
   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): 2182–2184.
   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 Computer Science 41 (2001): 934–949.
   PubMedGoogle Scholar
• H. P. Schultz, “Topological Organic Chemistry. 1. Graph Theory and Topological Indices of Alkanes,” Journal of Chemical Information Computer Science 29, no. 3 (1989): 227–228.
   Google Scholar
• Arockiaraj et al., “Topological Indices and Their Applications,” doi:10.1080/10406638.2017.1411958
   Google Scholar
• Ibid.
   Google Scholar
• S. Klavžar, “On the Canonical Metric Representation, Average Distance, and Partial Hamming Graphs,” European Journal of Combinatorics 27 (2006): 68–73.
   Web of Science ®Google Scholar
• S. Klavžar and M. NadjafiArani, “Cut Method: Update on Recent Developments and Equivalence of Independent Approaches,” Current Organic Chemistry 19 (2015): 348–358.
   Web of Science ®Google Scholar
• S. Klavžar and M. J. NadjafiArani, “Partition Distance in Graphs,” Journal of Mathematical Chemistry 56 (2017): 69–80.
   Web of Science ®Google Scholar
• D. Djoković, “Distance Preserving Subgraphs of Hypercubes,” Journal of Combinatorial Theory, Series B 14 (1973): 263–267.
   Google Scholar
• P. Winkler, “Isometric Embeddings in Products of Complete Graphs,” Discrete Applied Mathematics 7 (1984): 221–225.
   Web of Science ®Google Scholar
• Arockiaraj et al., “Topological Indices and Their Applications,” doi:10.1080/10406638.2017.1411958
   Google Scholar
• Ilić et al., Topological Indices in Nanocones.
   Google Scholar
• Ibid.
   Google Scholar
• Ibid.
   Google Scholar
• Ibid.
   Google Scholar
• Khalifeh et al., “Another Aspect of Graph Invariants,” 2460–2468.
   Google Scholar
• Khalifeh et al., “A Method for Computing the Wiener Index,” 155–157.
   Google Scholar
• Ashrafi and Nezhaad, “The Edge Szeged Index,” 35–38.
   Google Scholar
• S. Klavžar, I. Gutman, and A. Rajapakse, “Wiener Numbers of Pericondensed Benzenoid Hydrocarbons,” Croatica Chemica Acta 70, no. 4 (1997): 979–999.
   Web of Science ®Google Scholar
• W. C. Shiu and P. C. B. Lam, “The Wiener Number of the Hexagonal Net,” Discrete Applied Mathematics 73 (1997): 101–111.
   Web of Science ®Google Scholar
• I. Gutman and S. Klavžar, “An Algorithm for the Calculation of Szeged Index of Benzenoid Hydrocarbons,” Journal of Chemical Information and Modeling 35 (1995): 1011–1014.
   Web of Science ®Google Scholar
• M. R. Farahani, “The Application of Cut Method to Computing the Edge Version of Szeged Index of Molecular Graphs,” Pacific Journal of Applied Mathematics 6 (2014): 249–258.
   Google Scholar
• Arockiaraj et al., “Analytical Expressions for Topological Properties,” 682–697.
   Google Scholar
• Ibid.
   Google Scholar
• M. R. Farahani, “Computing Edge-PI Index and Vertex-PI Index of Circumcoronene Series of Benzenoid Hk by Use of Cut Method,” International Journal of Mathematical Modeling and Applied Computing 1, no. 6 (2013): 26–35.
   Google Scholar
• A. Ilić, S. Klavžar, and D. Stevanović, “Calculating the Degree Distance of Partial Hamming Graphs,” Match-Communications In Mathematical and in Computer Chemistry 63 (2010): 411–424.
   Web of Science ®Google Scholar
• Arockiaraj et al., “Analytical Expressions for Topological Properties,” 682–697.
   Google Scholar
• Ashrafi and Abadi, “On Wiener Index,” 180–185.
   Google Scholar
• Ashrafi and Nezhaad, “The PI and Edge Szeged Indices,” 51–53.
   Google Scholar
• Ibid.
   Google Scholar
• P. V. Khadikar, P. P. Kale, N. V. Deshpande, S. Karmarkar, and V. K. Agrawal, “Novel PI Indices of Hexagonal Chains,” Journal of Mathematical Chemistry 29 (2001): 143–150.
   Web of Science ®Google Scholar