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Discrimination power of graph measures based on complex zeros of the partial Hosoya polynomial

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  • Dehmer, Matthias
  • Shi, Yongtang
  • Mowshowitz, Abbe

Abstract

In this paper we define novel graph measures based on the complex zeros of the partial Hosoya polynomial. The kth coefficient of this polynomial, defined for an arbitrary vertex v of a graph, is the number of vertices at distance k from v. Based on the moduli of the complex zeros, we calculate novel graph descriptors on exhaustively generated graphs as well as on trees. We then evaluate the uniqueness of these measures, i.e., their ability to distinguish between non-isomorphic graphs. Detecting isomorphism for arbitrary graphs remains a challenging problem for which highly discriminating graph invariants are useful heuristics.

Suggested Citation

  • Dehmer, Matthias & Shi, Yongtang & Mowshowitz, Abbe, 2015. "Discrimination power of graph measures based on complex zeros of the partial Hosoya polynomial," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 352-355.
    • Handle: RePEc:eee:apmaco:v:250:y:2015:i:c:p:352-355
    DOI: 10.1016/j.amc.2014.10.048
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    References listed on IDEAS

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    1. 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.
    2. Matthias Dehmer & Martin Grabner & Boris Furtula, 2012. "Structural Discrimination of Networks by Using Distance, Degree and Eigenvalue-Based Measures," PLOS ONE, Public Library of Science, vol. 7(7), pages 1-15, July.
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    Cited by:

    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.
    2. Lang, Rongling & Li, Tao & Mo, Desen & Shi, Yongtang, 2016. "A novel method for analyzing inverse problem of topological indices of graphs using competitive agglomeration," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 115-121.
    3. Matthias Dehmer & Frank Emmert-Streib & Yongtang Shi & Monica Stefu & Shailesh Tripathi, 2015. "Discrimination Power of Polynomial-Based Descriptors for Graphs by Using Functional Matrices," PLOS ONE, Public Library of Science, vol. 10(10), pages 1-10, October.
    4. Yang, Yu & Liu, Hongbo & Wang, Hua & Fu, Hongsun, 2015. "Subtrees of spiro and polyphenyl hexagonal chains," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 547-560.
    5. 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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