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Szeged and Mostar root-indices of graphs

Author

Listed:
  • Brezovnik, Simon
  • Dehmer, Matthias
  • Tratnik, Niko
  • Žigert Pleteršek, Petra

Abstract

Various distance-based root-indices of graphs are introduced and studied in the present article. They are obtained as unique positive roots of modified graph polynomials. In particular, we consider the Szeged polynomial, the weighted-product Szeged polynomial, the weighted-plus Szeged polynomial, and the Mostar polynomial. We derive closed formulas of these polynomials for some basic families of graphs. Consequently, we provide closed formulas for some root-indices and examine the convergence of sequences of certain root-indices. Moreover, some general properties of studied root-indices are stated. Finally, numerical results related to discrimination power, correlations, structure sensitivity, and abruptness of root-indices are calculated, interpreted, and compared to already known similar descriptors.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:442:y:2023:i:c:s0096300322008049
    DOI: 10.1016/j.amc.2022.127736
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    References listed on IDEAS

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    1. Dehmer, Matthias & Emmert-Streib, Frank & Mowshowitz, Abbe & Ilić, Aleksandar & Chen, Zengqiang & Yu, Guihai & Feng, Lihua & Ghorbani, Modjtaba & Varmuza, Kurt & Tao, Jin, 2020. "Relations and bounds for the zeros of graph polynomials using vertex orbits," Applied Mathematics and Computation, Elsevier, vol. 380(C).
    2. Ali, Akbar & Došlić, Tomislav, 2021. "Mostar index: Results and perspectives," Applied Mathematics and Computation, Elsevier, vol. 404(C).
    3. Matthias Dehmer & Laurin A J Mueller & Armin Graber, 2010. "New Polynomial-Based Molecular Descriptors with Low Degeneracy," PLOS ONE, Public Library of Science, vol. 5(7), pages 1-6, July.
    4. Dehmer, M. & Moosbrugger, M. & Shi, Y., 2015. "Encoding structural information uniquely with polynomial-based descriptors by employing the Randić matrix," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 164-168.
    5. Matthias Dehmer & Aleksandar Ilić, 2012. "Location of Zeros of Wiener and Distance Polynomials," PLOS ONE, Public Library of Science, vol. 7(3), pages 1-12, March.
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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.

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