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An extended eigenvalue-free interval for the eccentricity matrix of threshold graphs

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Abstract

We show that the eigenvalue-free interval for the eccentricity matrix of every threshold graph can be extended from \((-2,-1)\), as shown in [Z. Qiu, Z. Tang, On the eccentricity spectra of threshold graphs. Discrete Appl. Math. 310, 75–85 (2022)], to \((-1-\sqrt{2},-2)\cup (-2,-1)\), and to a larger interval if we exclude certain pathological cases. Our results are based on the fact that the characteristic matrix of the quotient matrix of the eccentricity matrix of a threshold graph is row equivalent to a particular tridiagonal matrix.

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Acknowledgements

We would like to thank anonymous referees for their careful reading.

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Authors and Affiliations

  1. Department of Mathematics, Kuwait University, Safat, 13060, Kuwait

    Milica Anđelić

  2. Kuwait College of Science and Technology, P.O. Box 27235, Block 4, Safat, 13133, Doha District, Kuwait

    Carlos M. da Fonseca

  3. Chair of Computational Mathematics, University of Deusto, Bilbao, Spain

    Carlos M. da Fonseca

  4. School of Electrical Engineering, University of Belgrade, Bulevar kralja Aleksandra 73, 11 000, Beograd, Belgrade, Serbia

    Tamara Koledin

  5. Faculty of Mathematics, University of Belgrade, Studentski trg 16, 11 000, Beograd, Belgrade, Serbia

    Zoran Stanić

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  1. Milica Anđelić
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  2. Carlos M. da Fonseca
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  3. Tamara Koledin
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  4. Zoran Stanić
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Correspondence to Milica Anđelić.

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Anđelić, M., Fonseca, C.M.d., Koledin, T. et al. An extended eigenvalue-free interval for the eccentricity matrix of threshold graphs. J. Appl. Math. Comput. 69, 491–503 (2023). https://doi.org/10.1007/s12190-022-01758-3

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  • DOI: https://doi.org/10.1007/s12190-022-01758-3

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