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Graphs with small distance-based complexities

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  • Ghorbani, Modjtaba
  • Vaziri, Zahra

Abstract

Suppose G is a connected graph. The Wiener complexity (or briefly W-complexity) CW(G) is the number of different contributions to Wiener index in its summation formula. Also, the Szeged complexity (or briefly Sz-complexity) CSz(G) can be defined similarly. The main goal of the current work is to investigate graphs with small complexity. We classify all unicycle graphs, all distance-balanced graphs, and all regular graphs of diameter 2 with Sz-complexity one. In this way, the Sz-complexity and W-complexity of several families of graphs are determined.

Suggested Citation

  • Ghorbani, Modjtaba & Vaziri, Zahra, 2023. "Graphs with small distance-based complexities," Applied Mathematics and Computation, Elsevier, vol. 457(C).
    • Handle: RePEc:eee:apmaco:v:457:y:2023:i:c:s0096300323003570
    DOI: 10.1016/j.amc.2023.128188
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    Cited by:

    1. Ghorbani, Modjtaba & Vaziri, Zahra, 2024. "On the Szeged and Wiener complexities in graphs," Applied Mathematics and Computation, Elsevier, vol. 470(C).

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