On topological properties of hexagonal andsilicate networks

On topological properties of hexagonal andsilicate networks

Topological indices are the numerical quantities associated to a simple and finite graphswhich represent its structure. There are certain types of topological indices such as degreebased topological indices, distance based topological indices and counting related topo-logical indices etc. The degree based topological indices are exploited to estimate thebioactivity of chemical compounds. In this paper, we compute first general Zagreb index,general Randi ́cconnectivity index, general sum-connectivity index, atom-bond connectiv-ity index, geometric-arithmetic index,ABC4index andGA5index of the line graphs ofsilicate networks, chain silicate networks and hexagonal networks by using the subdivisionmethod.Mathematics Subject Classification (2010).05C90

___

  • [1]S. Akhter and M. Imran,On degree based topological descriptors of strong productgraphs, Can. J. Chem.94(6), 559–565, 2016.
  • [2]A.Q. Baig, M. Imran and H. Ali,Computing Omega, Sadhana and PI polynomialsof benzoid carbon nanotubes, Optoelectron. Adv. Mater.-Rapid Commun.9, 248–255,2015.
  • [3]A.Q. Baig, M. Imran, H. Ali and S.U. Rehman,Computing topological polynomialof certain nanostructures, Optoelectron. Adv. Mater.-Rapid Commun.17, 877–8832015.
  • [4]M. Bača, J. Horváthová, M. Mokrišová and A. Suhányiová,On topological indices offullerenes, Appl. Math. Comput.251, 154–161, 2015.
  • [5]E. Estrada, L. Torres, L. Rodriguez and I. Gutman,An atom-bond connectivity index:modelling the enthalpy of formation of alkanes, Ind. J. Chem.37A, 849–855, 1998.
  • [6]M. Ghorbani and M.A. Hosseinzadeh,ComputingABC4index of nanostar den-drimers, Optoelectron. Adv. Mater.-Rapid Commun.4(9), 1419–1422, 2010.
  • [7]A. Graovac, M. Ghorbani and M.A. Hosseinzadeh,Computing fifth geometric-arithmetic index for nanostar dendrimers, J. Math. Nanosci.1(1), 33–42, 2011.
  • [8]S. Hayat and M. Imran,Computation of topological indices of certain networks, Appl.Math. Comput.240, 213–228, 2014.
  • [9]S. Hayat and M. Imran,Computation of certain topological indices of nanotubes cov-ered byC5andC7, J. Comput. Theor. Nanosci.12(4), 533–541, 2015.
  • [10]S. Hayat and M. Imran,On some degree based topological indices of certain nanotubes,J. Comput. Theor. Nanosci.12(8), 1599–1605, 2015.
  • [11]M. Imran, S. Hayat and M.Y.H. Malik,On topological indices of certain interconnec-tion networks, Appl. Math. Comput.244, 936–951, 2014.
  • [12]X. Li and H. Zhao,Trees with the first three smallest and largest generalized topologicalindices, MATCH Commun. Math. Comput. Chem.50, 57–62, 2004.
  • [13]L.N. Lester and J. Sandor,Computer graphics on hexagonal grid, J. Computer Graph-ics,8, 401–409, 1984.
  • [14]B. Lučić, N. Trinajstić and B. Zhou,Comparison between the sum-connectivity indexand product-connectivity index for benzenoid hydrocarbons, Chem. Phys. Lett.475,146–148, 2009.
  • [15]M.F. Nadeem, S. Zafar and Z. Zahid,On certain topological indices of the line graphof subdivision graphs, Appl. Math. Comput.271, 790–794, 2015.
  • [16]M.F. Nadeem, S. Zafarb and Z. Zahid,On topological properties of the line graphsof subdivision graphs of certain nanostructures, Appl. Math. Comput.273, 125–130,2016.
  • [17]M. Randić,On characterization of molecular branching, J. Am. Chem. Soc.97, 6609–6615, 1975.
  • [18]P.S. Ranjini, V. Lokesha and I.N. Cangl,On the Zagreb indices of the line graphs ofthe subdivision graphs, Appl. Math. Comput.18, 699–702, 2011.
  • [19]P.S. Ranjini, V. Lokesha and M.A. Rajan,On the Shultz index of the subdivisiongraphs, Adv. Stud. Contemp. Math.21(3), 279–290, 2011.
  • [20]T. Shirai,Spectrum of Infinite Regular Line Graphs, Trans. Amer. Math. Soc.352(1), 115–132, 1999.
  • [21]G. Su and L. Xu,Topological indices of the line graph of subdivision graphs and theirSchur-bounds, Appl. Math. Comput.253, 395–401, 2015.
  • [22]G. Sridhara, M.R. Rajesh Kanna and R.S. Indumathi,Computation of topologicalindices of Graphene, J. Nanomaterials, 2015.
  • [23]D. Vukičević and B. Furtula,Topological index based on the ratios of geometrical andarithmetical mmeans of end-vertex degrees of edges, J. Math. Chem.46, 1369–1376,2009.
  • [24]H. Wiener,Structural determination of the paraffin boiling points, J. Am. Chem. Soc.69, 17–20, 1947.
  • [25]B. Zhou and N. Trinajstić,On a novel connectivity index, J. Math. Chem.46, 1252–1270, 2009.
  • [26]B. Zhou and N. Trinajstić,On general sum-connectivity index, J. Math. Chem.47,210–218, 2010.