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The Upper Bound of the Edge Mostar Index with Respect to Bicyclic Graphs

Author

Listed:
  • Hui Wang

    (School of Mathematics, Lanzhou Jiaotong University, Lanzhou 730070, China)

  • Mengmeng Liu

    (School of Mathematics, Lanzhou Jiaotong University, Lanzhou 730070, China)

Abstract

Let G be a connected graph; the edge Mostar index M o e ( G ) of G is defined as M o e ( G ) = ∑ e = u v ∈ E ( G ) | m u ( e ) − m v ( e ) | , where m u ( e ) and m v ( e ) denote the number of edges in G that are closer to vertex u than to vertex v and the number of edges that are closer to vertex v than to vertex u , respectively. In this paper, we determine the upper bound of the edge Mostar index for all bicyclic graphs and identify the extremal graphs that achieve this bound.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:11:p:2506-:d:1159065
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    References listed on IDEAS

    as
    1. Ali Ghalavand & Ali Reza Ashrafi & Mardjan Hakimi-Nezhaad & Ismail Naci Cangul, 2021. "On Mostar and Edge Mostar Indices of Graphs," Journal of Mathematics, Hindawi, vol. 2021, pages 1-14, April.
    2. Ali, Akbar & Došlić, Tomislav, 2021. "Mostar index: Results and perspectives," Applied Mathematics and Computation, Elsevier, vol. 404(C).
    3. Tepeh, Aleksandra, 2019. "Extremal bicyclic graphs with respect to Mostar index," Applied Mathematics and Computation, Elsevier, vol. 355(C), pages 319-324.
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