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Periodica Mathematica Hungarica

, Volume 73, Issue 1, pp 100–119 | Cite as

On topological properties of poly honeycomb networks

  • Muhammad ImranEmail author
  • Abdul Qudair Baig
  • Haidar Ali
  • Shafiq Ur Rehman
Article

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.

Keywords

General Randić index Atom-bond connectivity (\(\textit{ABC}\)) index Geometric-arithmetic (\(\textit{GA}\)) index David derived networks Regular triangulene silicate network 

Mathematics Subject Classification

05C12 05C90 

Notes

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.

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2016

Authors and Affiliations

  • Muhammad Imran
    • 1
    Email author
  • Abdul Qudair Baig
    • 2
  • Haidar Ali
    • 3
  • Shafiq Ur Rehman
    • 2
  1. 1.Department of Mathematics, School of Natural Sciences (SNS)National University of Sciences and Technology (NUST)IslamabadPakistan
  2. 2.Department of MathematicsCOMSATS Institute of Information TechnologyAttock CampusPakistan
  3. 3.Department of MathematicsGovernment College UniversityFaisalabadPakistan

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