On topological indices of honeycomb networks and graphene networks

In QSAR/QSPR study, topological indices such as the Shultz index, generalized Randic index,Zagreb index, general sum-connectivity index, atom-bond connectivity ($ABC$) index and geometric-arithmetic ($GA$) index exploited to estimate the bioactivity of chemical compounds. In this paper, we compute first general Zagreb index, general Randic connectivity index, general sum-connectivity index, $ABC$, $GA$, $ABC_4$ and $GA_5$ indices of the line graphs of subdivision graphs of honeycomb networks and graphene.

___

  • S.; Akhter, M.; Imran, “On degree based topological descriptors of strong product graphs", Can. J. Chem., 94(6), 559–565(2016).
  • A.; Ali, Z.; Raza, A. A.; Bhatti, “Extremal pentagonal chains with respect to bond incident degree indices", Can. J. Chem., 94(10), 870–876(2016).
  • A.; Ali, A. A.; Bhatti, Z.; Raza, “Topological study of tree-like polyphenylene systems, spiro hexagonal systems and polyphenylene dendrimer nanostars", Quantum Matter, 5(4), 534–538(2016).
  • A.; Ali, Z.; Raza, A. A.; Bhatti, “Bond incident degree (BID) indices, nanostructures", Optoelectronics Adv. Materials-Rapid Commun, 10, 1-2(2016).
  • A.; Ali, Z.; Raza, A. A.; Bhatti, “Bond Incident Degree (BID) Indices of Polyomino Chains: A Unified Approach", Appl. Math. Comput., 287(9), 28–37(2016).
  • A.; Ali, Z.; Raza, A. A.; Bhatti, “On the Augmented Zagreb Index", Kuwait Journal of Science, 43(2), 123–138(2016).
  • A.; Ali, A. A.; Bhatti, Z.; Raza, “The augmented Zagreb index, vertex connectivity and matching number of graphs", Bull. Iranian Math. Soc. 42(2), 417–425(2016).
  • M.; Baca, J.; Horvathova, M.; Mokrisova and A.; Suhanyiova, “On topological indices of fullerenes", Appl. Math. Comput., 251, 154–161(2015).
  • 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).
  • M.; Ghorbani and M. A.; Hosseinzadeh, “Computing ABC4 index of nanostar dendrimers", Optoelectron. Adv. Mater.-Rapid Commun., 4(9), 1419–1422(2010).
  • A.; Graovac, M.; Ghorbani and M. A.; Hosseinzadeh, “Computing fifth geometricarithmetic index for nanostar dendrimers", J. Math. Nanosci., 1(1), 33–42(2011).
  • S.; Hayat and M.; Imran, “Computation of certain topological indices of nanotubes covered by C5 and C7", J. Comput. Theor. Nanosci., 12(4), 533–541(2015).
  • S.; Hayat and M.; Imran, “On some degree based topological indices of certain nanotubes", J. Comput. Theor. Nanosci., 12(8), 1599–1605(2015).
  • S.; Hayat and M.; Imran, “Computation of certain topological indices of nanotubes", J. Comput. Theor. Nanosci., 12(1), 70–76(2015).
  • M.; Imran and S.; Hayat, “Computation of topological indices of certain networks", Appl. Math. Comput., 240, 213–228(2014).
  • M.; Imran, S.; Hayat and M. Y. H.; Malik, “On topological indices of certain interconnection networks", Appl. Math. Comput., 244, 936–951(2014).
  • X.; Li and H.; Zhao, “Trees with the first three smallest and largest generalized topological indices", MATCH Commun. Math. Comput. Chem., 50, 57–62(2004).
  • M. F.; Nadeem, S.; Zafar and Z.; Zahid, “On certain topological indices of the line graph of subdivision graphs", Appl. Math. Comput., 271, 790–794(2015).
  • M. F.; Nadeem, S.; Zafar and Z.; Zahid, “On topological properties of the line graphs of subdivision graphs of certain nanostructures", Appl. Math. Comput., 273, 125–130(2016).
  • Z.; Raza, “The edge version of geometric arithmetic index of polyomino chains of 8-cycles and arbitrary carbon nanocones", J. Comput. Theor. Nanosci., 13, 1–5(2016).
  • Z.; Raza, A. A.; Bhatti, A.; Ali, “More on Comparison Between First Geometric-Arithmetic Index and Atom-Bond Connectivity Index", Miskolc Mathematical Notes, 17(1), 561– 570(2016).
  • M.; Randic, “On characterization of molecular branching", J. Am. Chem. Soc., 97, 6609– 6615(1975).
  • B.; Rajan, A.; William, C.; Grigorious and S.; Stephen, “On certain topological indices of silicate, honeycomb and hexagonal networks", J. Comp. Math. Sci., 5, 530–535(2012).
  • P. S.; Ranjini, V.; Lokesha and I. N.; Cangl, “On the Zagreb indices of the line graphs of the subdivision graphs", Appl. Math. Comput., 18, 699–702(2011).
  • P. S.; Ranjini, V.; Lokesha and M. A.; Rajan, “On the Shultz index of the subdivision graphs", Adv. Stud. Contemp. Math., 21(3), 279–290(2011).
  • G.; Su and L.; Xu, “Topological indices of the line graph of subdivision graphs and their Schur-bounds", Appl. Math. Comput., 253, 395–401(2015).
  • G.; Sridhara, M. R.; Rajesh Kanna and R. S.; Indumathi, “Computation of Topological Indices of Graphene" J. Nanomaterials, (2015).
  • D.; Vukicevic and B.; Furtula, “Topological index based on the ratios of geometrical and arithmetical mmeans of end-vertex degrees of edges" J. Math. Chem., 46, 1369–1376(2009).
  • B.; Zhou and N.; Trinajstic, “On a novel connectivity index", J. Math. Chem., 46, 1252– 1270(2009).
  • B.; Zhou and N.; Trinajstic, “On general sum-connectivity index", J. Math. Chem., 47, 210–218(2010).