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Extremal bicyclic graphs with respect to Mostar index

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  • Tepeh, Aleksandra

Abstract

For an edge uv of a graph G, nu denotes the number of vertices of G closer to u than to v, and similarly nv is the number of vertices closer to v than to u. The Mostar index of a graph G is defined as the sum of absolute differences between nu and nv over all edges uv of G. In the paper we prove a recent conjecture of Došlić et al. (2018) on a characterization of bicyclic graphs with given number of vertices, for which extremal values of Mostar index are attained.

Suggested Citation

  • Tepeh, Aleksandra, 2019. "Extremal bicyclic graphs with respect to Mostar index," Applied Mathematics and Computation, Elsevier, vol. 355(C), pages 319-324.
    • Handle: RePEc:eee:apmaco:v:355:y:2019:i:c:p:319-324
    DOI: 10.1016/j.amc.2019.03.014
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    Cited by:

    1. Buyantogtokh, Lkhagva & Azjargal, Enkhbayar & Horoldagva, Batmend & Dorjsembe, Shiikhar & Adiyanyam, Damchaa, 2021. "On the maximum size of stepwise irregular graphs," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    2. Deng, Kecai & Li, Shuchao, 2021. "On the extremal values for the Mostar index of trees with given degree sequence," Applied Mathematics and Computation, Elsevier, vol. 390(C).
    3. Liu, Guorong & Deng, Kecai, 2023. "The maximum Mostar indices of unicyclic graphs with given diameter," Applied Mathematics and Computation, Elsevier, vol. 439(C).
    4. Hui Wang & Mengmeng Liu, 2023. "The Upper Bound of the Edge Mostar Index with Respect to Bicyclic Graphs," Mathematics, MDPI, vol. 11(11), pages 1-8, May.
    5. Ali, Akbar & Došlić, Tomislav, 2021. "Mostar index: Results and perspectives," Applied Mathematics and Computation, Elsevier, vol. 404(C).

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