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Mostar index: Results and perspectives

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  • Ali, Akbar
  • Došlić, Tomislav

Abstract

The Mostar index is a recently introduced bond-additive distance-based graph invariant that measures the degree of peripherality of particular edges and of the graph as a whole. It attracted considerable attention, both in the context of complex networks and in more classical applications of chemical graph theory, where it turned out to be useful as a measure of the total surface area of octane isomers and as a tool for studying topological aspects of fullerene shapes. This paper aims to gather some known bounds and extremal results concerning the Mostar index. Also, it presents various modifications and generalizations of the aforementioned index and it outlines several possible directions of further research. Finally, some open problems and conjectures are listed.

Suggested Citation

  • Ali, Akbar & Došlić, Tomislav, 2021. "Mostar index: Results and perspectives," Applied Mathematics and Computation, Elsevier, vol. 404(C).
    • Handle: RePEc:eee:apmaco:v:404:y:2021:i:c:s0096300321003350
    DOI: 10.1016/j.amc.2021.126245
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    References listed on IDEAS

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    1. 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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    Cited by:

    1. Martin Knor & Niko Tratnik, 2023. "A New Alternative to Szeged, Mostar, and PI Polynomials—The SMP Polynomials," Mathematics, MDPI, vol. 11(4), pages 1-15, February.
    2. Brezovnik, Simon & Dehmer, Matthias & Tratnik, Niko & Žigert Pleteršek, Petra, 2023. "Szeged and Mostar root-indices of graphs," Applied Mathematics and Computation, Elsevier, vol. 442(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.

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    1. Liu, Guorong & Deng, Kecai, 2023. "The maximum Mostar indices of unicyclic graphs with given diameter," Applied Mathematics and Computation, Elsevier, vol. 439(C).
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    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.

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