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New Polynomial-Based Molecular Descriptors with Low Degeneracy

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  • Matthias Dehmer
  • Laurin A J Mueller
  • Armin Graber

Abstract

In this paper, we introduce a novel graph polynomial called the ‘information polynomial’ of a graph. This graph polynomial can be derived by using a probability distribution of the vertex set. By using the zeros of the obtained polynomial, we additionally define some novel spectral descriptors. Compared with those based on computing the ordinary characteristic polynomial of a graph, we perform a numerical study using real chemical databases. We obtain that the novel descriptors do have a high discrimination power.

Suggested Citation

  • 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.
    • Handle: RePEc:plo:pone00:0011393
    DOI: 10.1371/journal.pone.0011393
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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. 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.
    3. 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.
    4. 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.

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