The Second Maximum Mostar Index of Unicyclic Graphs With Given Diameter

Muhammad Amer Qureshi, Asad Ullah, Parvez Ali, Emad E. Mahmoud and Melaku Berhe Belay

Journal of Mathematics, 2026, vol. 2026, 1-17

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.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:7269046

DOI: 10.1155/jom/7269046

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