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On topological properties of the line graphs of subdivision graphs of certain nanostructures

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  • Nadeem, Muhammad Faisal
  • Zafar, Sohail
  • Zahid, Zohaib

Abstract

In the study of QSAR/QSPR, topological indices such as Shultz index, generalized Randic index, Zagreb index, general sum-connectivity index, atom-bond connectivity (ABC) index and geometric–arithmetic (GA) index are exploited to estimate the bioactivity of chemical compounds. A topological index attaches a chemical structure with a numeric number. There are numerous applications of graph theory in this field of research. In this paper we computed generalized Randic, general Zagreb, general sum-connectivity, ABC, GA, ABC4 and GA5 indices of the line graphs of 2D-lattice, nanotube and nanotorus of TUC4C8[p, q] by using the concept of subdivision.

Suggested Citation

  • Nadeem, Muhammad Faisal & Zafar, Sohail & Zahid, Zohaib, 2016. "On topological properties of the line graphs of subdivision graphs of certain nanostructures," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 125-130.
    • Handle: RePEc:eee:apmaco:v:273:y:2016:i:c:p:125-130
    DOI: 10.1016/j.amc.2015.10.010
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    1. Nadeem, Muhammad Faisal & Zafar, Sohail & Zahid, Zohaib, 2015. "On certain topological indices of the line graph of subdivision graphs," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 790-794.
    2. Su, Guifu & Xu, Lan, 2015. "Topological indices of the line graph of subdivision graphs and their Schur-bounds," Applied Mathematics and Computation, Elsevier, vol. 253(C), pages 395-401.
    3. Tsang, Eric W. K., 2014. "Old and New," Management and Organization Review, Cambridge University Press, vol. 10(03), pages 390-390, November.
    4. Shi, Yongtang, 2015. "Note on two generalizations of the Randić index," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 1019-1025.
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    Cited by:

    1. Adnan Aslam & Muhammad Faisal Nadeem & Zohaib Zahid & Sohail Zafar & Wei Gao, 2019. "Computing Certain Topological Indices of the Line Graphs of Subdivision Graphs of Some Rooted Product Graphs," Mathematics, MDPI, vol. 7(5), pages 1-9, April.
    2. Shahid Imran & Muhammad Kamran Siddiqui & Muhammad Imran & Muhammad Faisal Nadeem, 2018. "Computing Topological Indices and Polynomials for Line Graphs," Mathematics, MDPI, vol. 6(8), pages 1-10, August.
    3. Kashif Elahi & Ali Ahmad & Roslan Hasni, 2018. "Construction Algorithm for Zero Divisor Graphs of Finite Commutative Rings and Their Vertex-Based Eccentric Topological Indices," Mathematics, MDPI, vol. 6(12), pages 1-9, December.
    4. Mohanappriya. G & Ijayalakshmi. D.V, 2017. "Edge Version Molecular Descriptors Of Polycyclic Aromatic Hydrocarbons," Acta Chemica Malaysia (ACMY), Zibeline International Publishing, vol. 1(2), pages 18-21, January.

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