M-Polynomial and Degree-Based Topological Indices of Polyhex Nanotubes

The discovery of new nanomaterials adds new dimensions to industry, electronics, and pharmaceutical and biological therapeutics. In this article, we first find closed forms of M-polynomials of polyhex nanotubes. We also compute closed forms of various degree-based topological indices of these tubes. These indices are numerical tendencies that often depict quantitative structural activity/property/toxicity relationships and correlate certain physico-chemical properties, such as boiling point, stability, and strain energy, of respective nanomaterial. To conclude, we plot surfaces associated to M-polynomials and characterize some facts about these tubes.

[1]  Xueliang Li,et al.  A Survey on the Randic Index , 2008 .

[2]  Shin Min Kang,et al.  Some Invariants of Circulant Graphs , 2016, Symmetry.

[3]  Hanyuan Deng,et al.  A unified linear-programming modeling of some topological indices , 2015, J. Comb. Optim..

[4]  Emeric Deutsch,et al.  M-Polynomial and Degree-Based Topological Indices , 2014, 1407.1592.

[5]  M. Farahani.  Some connectivity indices and zagreb index of polyhex nanotubes. , 2012, Acta chimica Slovenica.

[6]  Hanyuan Deng,et al.  A general modeling of some vertex-degree based topological indices in benzenoid systems and phenylenes , 2011, Comput. Math. Appl..

[7]  Kathryn Fraughnaugh,et al.  Introduction to graph theory , 1973, Mathematical Gazette.

[8]  Jianxiu Hao,et al.  Theorems about Zagreb Indices and Modified Zagreb Indices , 2011 .

[9]  Franka Miriam Bruckler,et al.  On a class of distance-based molecular structure descriptors , 2011 .

[10]  Shin Min Kang,et al.  M-Polynomial and Related Topological Indices of Nanostar Dendrimers , 2016, Symmetry.

[11]  Shin Min Kang,et al.  M-Polynomials and Topological Indices of Titania Nanotubes , 2016, Symmetry.

[12]  Ali Iranmanesh,et al.  Computing Ga index for some nanotubes , 2010 .

[13]  Sandi Klavzar,et al.  A Comparison of the Schultz Molecular Topological Index with the Wiener Index , 1996, J. Chem. Inf. Comput. Sci..

[14]  I. Gutman,et al.  Graph theory and molecular orbitals. Total φ-electron energy of alternant hydrocarbons , 1972 .

[15]  Qing Hua Wang,et al.  Flat panel display prototype using gated carbon nanotube field emitters , 2001 .

[16]  Kevin A. Cavicchi,et al.  Tailor-Made Fluorinated Copolymer/Clay Nanocomposite by Cationic RAFT Assisted Pickering Miniemulsion Polymerization. , 2015, Langmuir : the ACS journal of surfaces and colloids.

[17]  Bryan D. Vogt,et al.  Unidirectional Alignment of Block Copolymer Films Induced by Expansion of a Permeable Elastomer during Solvent Vapor Annealing , 2014 .

[18]  H. Wiener.  Structural determination of paraffin boiling points. , 1947, Journal of the American Chemical Society.

[19]  Dun‐Yen Kang,et al.  Defective Single‐Walled Aluminosilicate Nanotubes: Structural Stability and Mechanical Properties , 2016 .

[20]  Heping Zhang,et al.  The Clar Covering Polynomial of Hexagonal Systems I , 1996, Discret. Appl. Math..

[21]  Gerta Rücker,et al.  On Topological Indices, Boiling Points, and Cycloalkanes , 1999, J. Chem. Inf. Comput. Sci..

[22]  Robert Weiss,et al.  Supramolecular Multiblock Polystyrene–Polyisobutylene Copolymers via Ionic Interactions , 2014 .

[23]  Heping Zhang,et al.  The Clar covering polynomial of hexagonal systems III , 2000, Discret. Math..