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On topological properties of poly honeycomb networks

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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.

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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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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

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  1. Muhammad Imran
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  2. Abdul Qudair Baig
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  3. Haidar Ali
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  4. Shafiq Ur Rehman
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Correspondence to Muhammad Imran.

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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

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