M-Polynomials And Topological Indices Of Zigzag And Rhombic Benzenoid Systems

Abstract M-polynomial of different molecular structures helps to calculate many topological indices. This polynomial is a new idea and its beauty is the wealth of information it contains about the closed forms of degree-based topological indices of molecular graph G of the structure. It is a well-known fact that topological indices play significant role in determining properties of the chemical compound [1, 2, 3, 4]. In this article, we computed the closed form of M-polynomial of zigzag and rhombic benzenoid systemsbecause of their extensive usages in industry. Moreover we give graphs of M-polynomials and their relations with the parameters of structures.

[1]  The General Connectivity Indices of Benzenoid Syste , 2010 .

[2]  Wei Gao,et al.  Computing Sanskruti Index of Titania Nanotubes , 2017 .

[3]  Glasnik Matematički ON THE EDGE DEGREES OF TREES , 2009 .

[4]  Wei Gao,et al.  On the edge-version atom-bond connectivity and geometric arithmetic indices of certain graph operations , 2017, Appl. Math. Comput..

[5]  Ante Graovac,et al.  Augmented Zagreb index , 2010 .

[6]  Béla Bollobás,et al.  Graphs of Extremal Weights , 1998, Ars Comb..

[7]  The General Sum-Connectivity Indices of Benzenoid Systems and Phenylenes , 2011 .

[8]  D. Vukicevic On the edge degrees of trees , 2009 .

[9]  Shin Min Kang,et al.  Some Topological Invariants of the Möbius Ladder , 2016 .

[10]  Shin Min Kang,et al.  M-Polynomial and Degree-Based Topological Indices of Polyhex Nanotubes , 2016, Symmetry.

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

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

[13]  S. Kang,et al.  Some Topological Invariants of the Möbius Ladders , 2017 .

[14]  I. Gutman,et al.  Wiener Index of Trees: Theory and Applications , 2001 .

[15]  S. Unger Molecular Connectivity in Structure–activity Analysis , 1987 .

[16]  Yufei Huang,et al.  Augmented Zagreb Index of Connected Graphs , 2012 .

[17]  Molecular description of copper(II) oxide , 2017 .

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

[19]  M. Javaid,et al.  $M$-POLYNOMIALS AND TOPOLOGICAL INDICES OF SILICATE AND OXIDE NETWORKS , 2017 .

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

[21]  Wei Gao,et al.  The first multiplication atom-bond connectivity index of molecular structures in drugs , 2017, Saudi pharmaceutical journal : SPJ : the official publication of the Saudi Pharmaceutical Society.

[22]  Hafiz Mutee ur Rehman,et al.  Computing topological indices of Hex Board and its line graph , 2017 .

[23]  Shin Min Kang,et al.  Some Computational Aspects of Triangular Boron Nanotubes , 2016 .

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

[25]  Young Chel Kwun,et al.  M-Polynomials and topological indices of V-Phenylenic Nanotubes and Nanotori , 2017, Scientific Reports.

[26]  Shin Min Kang,et al.  Some Computational Aspects of Boron Triangular Nanotubes , 2017, Symmetry.

[27]  I. Gutman Degree-Based Topological Indices , 2013 .

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

[29]  Sonja Nikolic,et al.  The Vertex-Connectivity Index Revisited , 1998, J. Chem. Inf. Comput. Sci..

[30]  Ivan Gutman,et al.  Molecular graphs with minimal and maximal Randić indices , 2002 .

[31]  A. W.,et al.  Journal of chemical information and computer sciences. , 1995, Environmental science & technology.

[32]  Sohail Zafar,et al.  The Generalized Zagreb Index of Capra-Designed Planar Benzenoid Series $Ca_k(C_6)$ , 2017 .