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The Szeged index and the Wiener index of partial cubes with applications to chemical graphs

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  • Črepnjak, Matevž
  • Tratnik, Niko

Abstract

In this paper, we study the Szeged index of partial cubes and hence generalize the result proved by Chepoi and Klavžar, who calculated this index for benzenoid systems. It is proved that the problem of calculating the Szeged index of a partial cube can be reduced to the problem of calculating the Szeged indices of weighted quotient graphs with respect to a partition coarser than Θ-partition. Similar result for the Wiener index was recently proved by Klavžar and Nadjafi-Arani. Furthermore, we show that such quotient graphs of partial cubes are again partial cubes. Since the results can be used to efficiently calculate the Wiener index and the Szeged index for specific families of chemical graphs, we consider C4C8 systems and show that the two indices of these graphs can be computed in linear time.

Suggested Citation

  • Črepnjak, Matevž & Tratnik, Niko, 2017. "The Szeged index and the Wiener index of partial cubes with applications to chemical graphs," Applied Mathematics and Computation, Elsevier, vol. 309(C), pages 324-333.
    • Handle: RePEc:eee:apmaco:v:309:y:2017:i:c:p:324-333
    DOI: 10.1016/j.amc.2017.04.011
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    References listed on IDEAS

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    1. Lei, Hui & Yang, Hua, 2015. "Bounds for the Sum-Balaban index and (revised) Szeged index of regular graphs," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 1259-1266.
    2. Knor, Martin & Škrekovski, Riste & Tepeh, Aleksandra, 2015. "An inequality between the edge-Wiener index and the Wiener index of a graph," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 714-721.
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    Cited by:

    1. Tratnik, Niko, 2018. "On the Steiner hyper-Wiener index of a graph," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 360-371.
    2. Klavžar, Sandi & Azubha Jemilet, D. & Rajasingh, Indra & Manuel, Paul & Parthiban, N., 2018. "General Transmission Lemma and Wiener complexity of triangular grids," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 115-122.
    3. Brezovnik, Simon & Tratnik, Niko & Žigert Pleteršek, Petra, 2020. "Resonance graphs of catacondensed even ring systems," Applied Mathematics and Computation, Elsevier, vol. 374(C).
    4. Alizadeh, Yaser & Klavžar, Sandi, 2018. "On graphs whose Wiener complexity equals their order and on Wiener index of asymmetric graphs," Applied Mathematics and Computation, Elsevier, vol. 328(C), pages 113-118.
    5. Sharon, Jane Olive & Rajalaxmi, T.M. & Klavžar, Sandi & Rajan, R. Sundara & Rajasingh, Indra, 2021. "Transmission in H-naphtalenic nanosheet," Applied Mathematics and Computation, Elsevier, vol. 406(C).
    6. Ji, Shengjin & Liu, Mengmeng & Wu, Jianliang, 2018. "A lower bound of revised Szeged index of bicyclic graphs," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 480-487.

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