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Relations and bounds for the zeros of graph polynomials using vertex orbits

Author

Listed:
  • Dehmer, Matthias
  • Emmert-Streib, Frank
  • Mowshowitz, Abbe
  • Ilić, Aleksandar
  • Chen, Zengqiang
  • Yu, Guihai
  • Feng, Lihua
  • Ghorbani, Modjtaba
  • Varmuza, Kurt
  • Tao, Jin

Abstract

In this paper, we prove bounds for the unique, positive zero of OG★(z):=1−OG(z), where OG(z) is the so-called orbit polynomial [1]. The orbit polynomial is based on the multiplicity and cardinalities of the vertex orbits of a graph. In [1], we have shown that the unique, positive zero δ ≤ 1 of OG★(z) can serve as a meaningful measure of graph symmetry. In this paper, we study special graph classes with a specified number of orbits and obtain bounds on the value of δ.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:380:y:2020:i:c:s0096300320302083
    DOI: 10.1016/j.amc.2020.125239
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. 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).

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