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Encoding structural information uniquely with polynomial-based descriptors by employing the Randić matrix

Author

Listed:
  • Dehmer, M.
  • Moosbrugger, M.
  • Shi, Y.

Abstract

In this paper we define novel graph measures based on the zeros of the characteristic polynomial by using the Randić matrix. We compute the novel graph descriptors on exhaustively generated graphs and trees and demonstrate that the measures encode their structural information uniquely. These results are compared with the same graph measures but based on the eigenvalues of the classical characteristic polynomial of a graph. Finally we interpret our findings that are evidenced by numerical results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:268:y:2015:i:c:p:164-168
    DOI: 10.1016/j.amc.2015.04.115
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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. 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.
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    Cited by:

    1. 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.
    2. 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).
    3. Dehmer, Matthias & Chen, Zengqiang & Shi, Yongtang & Zhang, Yusen & Tripathi, Shailesh & Ghorbani, Modjtaba & Mowshowitz, Abbe & Emmert-Streib, Frank, 2019. "On efficient network similarity measures," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
    4. Alikhani, Saeid & Ghanbari, Nima, 2015. "Randić energy of specific graphs," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 722-730.
    5. 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).

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