Skip to main content
SpringerLink
Log in

On topological properties of poly honeycomb networks

  • Published:
Periodica Mathematica Hungarica Aims and scope Submit manuscript

Abstract

Topological indices are numerical parameters of a graph which characterize its topology and are usually graph invariant. In QSAR/QSPR study, physico-chemical properties and topological indices such as the Randić, the atom-bond connectivity (ABC) and the geometric-arithmetic (GA) indices are used to predict the bioactivity of chemical compounds. Graph theory has found a considerable use in this area of research. In this paper, we study poly honeycomb networks which are generated by a honeycomb network of dimension n and derive analytical closed results for the general Randić index \(R_\alpha (G)\) for different values of \(\alpha \), for a David derived network \((\textit{DD}(n))\) of dimension n, a dominating David derived network \((\textit{DDD}(n))\) of dimension n as well as a regular triangulene silicate network of dimension n. We also compute the general first Zagreb, ABC, GA, \(\textit{ABC}_4\) and \(\textit{GA}_5\) indices for these poly honeycomb networks for the first time and give closed formulas of these degree based indices in case of poly honeycomb networks.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. M. Bača, J. Horváthová, M. Mokričová, A. Suhányiovč, On topological indices of fullerenes. Appl. Math. Comput. 251, 154–161 (2015)

    MathSciNet  MATH  Google Scholar 

  2. A.Q. Baig, M. Imran, H. Ali, Computing Omega, Sadhana and PI polynomials of benzoid carbon nanotubes. Optoelectron. Adv. Mater. Rapid Commun. 9, 248–255 (2015)

    Google Scholar 

  3. A.Q. Baig, M. Imran, H. Ali, On topological indices of poly oxide, poly silicate, DOX and DSL networks. Can. J. Chem. 93(7), 730–739 (2015)

    Article  Google Scholar 

  4. M. Deza, P.W. Fowler, A. Rassat, K.M. Rogers, Fullerenes as tiling of surfaces. J. Chem. Inf. Comput. Sci. 40, 550–558 (2000)

    Article  Google Scholar 

  5. M.V. Diudea, I. Gutman, J. Lorentz, Molecular Topology (Nova, Huntington, 2001)

    Google Scholar 

  6. E. Estrada, L. Torres, L. Rodríguez, I. Gutman, An atom-bond connectivity index: modelling the enthalpy of formation of alkanes, Indian. J. Chem. 37A, 849–855 (1998)

    Google Scholar 

  7. M. Ghorbani, M.A. Hosseinzadeh, Computing \(ABC_{4}\) index of nanostar dendrimers. Optoelectron. Adv. Mater. Rapid Commun. 4, 1419–1422 (2010)

    Google Scholar 

  8. A. Graovac, M. Ghorbani, M.A. Hosseinzadeh, Computing fifth geometric-arithmetic index for nanostar dendrimers. J. Math. Nanosci. 1, 33–42 (2011)

    Google Scholar 

  9. I. Gutman, O.E. Polansky, Mathematical Concepts in Organic Chemistry (Springer, New York, 1986)

    Book  MATH  Google Scholar 

  10. S. Hayat, M. Imran, Computation of certain topological indices of nanotubes. J. Comput. Theor. Nanosci. 12, 70–76 (2015)

    Article  Google Scholar 

  11. S. Hayat, M. Imran, Computation of certain topological indices of nanotubes covered by \(C_{5}\) and \(C_{7}\). J. Comput. Theor. Nanosci. 12(4), 533–541 (2014)

    Article  Google Scholar 

  12. S. Hayat, M. Imran, On degree based topological indices of certain nanotubes. J. Comput. Theor. Nanosci. 12(8), 1599–1605 (2015)

  13. S. Hayat, M. Imran, Computation of topological indices of certain networks. Appl. Math. Comput. 240, 213–228 (2014)

    MathSciNet  MATH  Google Scholar 

  14. A. Iranmanesh, M. Zeraatkar, Computing GA index for some nanotubes. Optoelectron. Adv. Mater. Rapid Commun. 4, 1852–1855 (2010)

    Google Scholar 

  15. W. Lin, J. Chen, Q. Chen, T. Gao, X. Lin, B. Cai, Fast computer search for trees with minimal ABC index based on tree degree sequences. MATCH Commun. Math. Comput. Chem. 72, 699–708 (2014)

    MathSciNet  Google Scholar 

  16. P.D. Manuel, M.I. Abd-El-Barr, I. Rajasingh, B. Rajan, An efficient representation of Benes networks and its applications. J. Discret. Algorithms 6, 11–19 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  17. J.L. Palacios, A resistive upper bound for the ABC index. MATCH Commun. Math. Comput. Chem. 72, 709–713 (2014)

    MathSciNet  Google Scholar 

  18. M. Randić, On characterization of molecular branching. J. Am. Chem. Soc. 97, 6609–6615 (1975)

    Article  Google Scholar 

  19. F. Simonraj, A. George, Embedding of poly honeycomb networks and the metric dimension of star of david network. GRAPH-HOC 4, 11–28 (2012)

    Article  Google Scholar 

  20. F. Simonraj, A. George, Topological properties of few poly oxide, poly silicate, DOX and DSL networks, Int. J. Future Comput. Commun. 2, 90–95 (2013)

    Article  Google Scholar 

  21. Star of David [online] available, http://en.wikipedia.org/wiki/Star of David

  22. D. Vukičević, B. Furtula, Topological index based on the ratios of geometrical and arithmetical means of end-vertex degrees of edges. J. Math. Chem. 46, 1369–1376 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  23. H. Wiener, Structural determination of paraffin boiling points. J. Am. Chem. Soc. 69, 17–20 (1947)

    Article  Google Scholar 

Download references

Acknowledgments

This research is supported by COMSATS Attock via Grant No. 16-51/CRGP/CIIT/ATK/14/654, by the Grant of Higher Education Commission of Pakistan via Ref. No. 20-367/NRPU/R&D/HEC/12/831 and by National University of Sciences and Technology, Islamabad, Pakistan.

Author information

Authors and Affiliations

  1. Department of Mathematics, School of Natural Sciences (SNS), National University of Sciences and Technology (NUST), Sector H-12, Islamabad, Pakistan

    Muhammad Imran

  2. Department of Mathematics, COMSATS Institute of Information Technology, Attock Campus, Pakistan

    Abdul Qudair Baig & Shafiq Ur Rehman

  3. Department of Mathematics, Government College University, Faisalabad, Pakistan

    Haidar Ali

Authors
  1. Muhammad Imran
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Abdul Qudair Baig
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Haidar Ali
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Shafiq Ur Rehman
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Muhammad Imran.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Imran, M., Baig, A.Q., Ali, H. et al. On topological properties of poly honeycomb networks. Period Math Hung 73, 100–119 (2016). https://doi.org/10.1007/s10998-016-0132-5

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10998-016-0132-5

Keywords

Mathematics Subject Classification

Search

Navigation