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On the Szeged and Wiener complexities in graphs

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  • Ghorbani, Modjtaba
  • Vaziri, Zahra

Abstract

When characterizing networks structurally, the discriminating ability of a topological index is crucial. This relates to investigate its discrimination power (also called uniqueness or degeneracy) that indicates how meaningful the given measure can distinguish nonisomorphic networks. Assume G is a connected graph. The Szeged complexity (or briefly Sz-complexity) of a graph G is the number of different portions in the Szeged index formula. Also, the Wiener complexity (or briefly W-complexity) can be defined similarly. In the current work, we study graphs with small Sz-complexity. We characterize trees with Sz-complexity two and bicyclic graphs with Sz-complexity one. In this way, first we introduce some graphs with Sz-complexity one. For instance, we investigate Θ-graph and two categories of k-cyclic graphs. Besides, we classify bicyclic graphs with Sz-complexity equal to the number of edge-orbits. Finally, we determine W-complexity of these graphs.

Suggested Citation

  • Ghorbani, Modjtaba & Vaziri, Zahra, 2024. "On the Szeged and Wiener complexities in graphs," Applied Mathematics and Computation, Elsevier, vol. 470(C).
    • Handle: RePEc:eee:apmaco:v:470:y:2024:i:c:s0096300324000043
    DOI: 10.1016/j.amc.2024.128532
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    References listed on IDEAS

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    1. Yang, Xiuwen & Wang, Ligong, 2020. "Extremal Laplacian energy of directed trees, unicyclic digraphs and bicyclic digraphs," Applied Mathematics and Computation, Elsevier, vol. 366(C).
    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. 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.
    4. Ghorbani, Modjtaba & Vaziri, Zahra, 2023. "Graphs with small distance-based complexities," Applied Mathematics and Computation, Elsevier, vol. 457(C).
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