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On topological indices of honeycomb networks and graphene networks

Year 2018, Volume: 47 Issue: 1, 19 - 35, 01.02.2018

Shehnaz Akhter , Muhammad Imran , Wei Gao Mohammad Reza Farahani

Abstract

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.

Keywords

Topological indices atom-bond connectivity index geometric - arithmetic index honeycomb network graphene

References

  • 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).

Year 2018, Volume: 47 Issue: 1, 19 - 35, 01.02.2018

Shehnaz Akhter , Muhammad Imran , Wei Gao Mohammad Reza Farahani

Abstract

References

  • 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).
There are 30 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Shehnaz Akhter

Muhammad Imran

Wei Gao This is me

Mohammad Reza Farahani This is me

Publication Date February 1, 2018
Published in Issue Year 2018 Volume: 47 Issue: 1

Cite

APA Akhter, S., Imran, M., Gao, W., Farahani, M. R. (2018). On topological indices of honeycomb networks and graphene networks. Hacettepe Journal of Mathematics and Statistics, 47(1), 19-35.
AMA Akhter S, Imran M, Gao W, Farahani MR. On topological indices of honeycomb networks and graphene networks. Hacettepe Journal of Mathematics and Statistics. February 2018;47(1):19-35.
Chicago Akhter, Shehnaz, Muhammad Imran, Wei Gao, and Mohammad Reza Farahani. “On Topological Indices of Honeycomb Networks and Graphene Networks”. Hacettepe Journal of Mathematics and Statistics 47, no. 1 (February 2018): 19-35.
EndNote Akhter S, Imran M, Gao W, Farahani MR (February 1, 2018) On topological indices of honeycomb networks and graphene networks. Hacettepe Journal of Mathematics and Statistics 47 1 19–35.
IEEE S. Akhter, M. Imran, W. Gao, and M. R. Farahani, “On topological indices of honeycomb networks and graphene networks”, Hacettepe Journal of Mathematics and Statistics, vol. 47, no. 1, pp. 19–35, 2018.
ISNAD Akhter, Shehnaz et al. “On Topological Indices of Honeycomb Networks and Graphene Networks”. Hacettepe Journal of Mathematics and Statistics 47/1 (February 2018), 19-35.
JAMA Akhter S, Imran M, Gao W, Farahani MR. On topological indices of honeycomb networks and graphene networks. Hacettepe Journal of Mathematics and Statistics. 2018;47:19–35.
MLA Akhter, Shehnaz et al. “On Topological Indices of Honeycomb Networks and Graphene Networks”. Hacettepe Journal of Mathematics and Statistics, vol. 47, no. 1, 2018, pp. 19-35.
Vancouver Akhter S, Imran M, Gao W, Farahani MR. On topological indices of honeycomb networks and graphene networks. Hacettepe Journal of Mathematics and Statistics. 2018;47(1):19-35.

https://dergipark.org.tr/en/pub/hujms