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Location of Zeros of Wiener and Distance Polynomials

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  • Matthias Dehmer
  • Aleksandar Ilić

Abstract

The geometry of polynomials explores geometrical relationships between the zeros and the coefficients of a polynomial. A classical problem in this theory is to locate the zeros of a given polynomial by determining disks in the complex plane in which all its zeros are situated. In this paper, we infer bounds for general polynomials and apply classical and new results to graph polynomials namely Wiener and distance polynomials whose zeros have not been yet investigated. Also, we examine the quality of such bounds by considering four graph classes and interpret the results.

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  • 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.
    • Handle: RePEc:plo:pone00:0028328
    DOI: 10.1371/journal.pone.0028328
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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).
    2. Ghorbani, Modjtaba & Hakimi-Nezhaad, Mardjan & Dehmer, Matthias, 2022. "Novel results on partial hosoya polynomials: An application in chemistry," Applied Mathematics and Computation, Elsevier, vol. 433(C).

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