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The Second Maximum Mostar Index of Unicyclic Graphs With Given Diameter

Author

Listed:
  • Muhammad Amer Qureshi
  • Asad Ullah
  • Parvez Ali
  • Emad E. Mahmoud
  • Melaku Berhe Belay

Abstract

Topological invariants are key tools for studying the physicochemical and thermodynamic properties of chemical compounds. Recently, a new bond-additive distance-based graph invariant called the Mostar index has been developed. It measures the importance of individual edges and the graph as a whole. It is denoted and defined as MoG=∑xy∈EGnxxy−nyxy. This invariant is helpful to characterize the structure of a given connected graph G. In this invariant, the quantity nxxy means the number of vertices closer to x than y. In the present study, first, we have considered the Mostar index of extremal unicyclic graphs of n vertices with given diameter. Second, we have determined all unicyclic graphs that contain the second maximum Mostar index.

Suggested Citation

  • Muhammad Amer Qureshi & Asad Ullah & Parvez Ali & Emad E. Mahmoud & Melaku Berhe Belay, 2026. "The Second Maximum Mostar Index of Unicyclic Graphs With Given Diameter," Journal of Mathematics, Hindawi, vol. 2026, pages 1-17, March.
    • Handle: RePEc:hin:jjmath:7269046
    DOI: 10.1155/jom/7269046
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