Abstract
In this work, connected graphs of order n and largest eigenvalue of the distance Laplacian matrix with multiplicity equal to \(n-4\) are investigated. A complete characterization is presented if n is one of its distance Laplacian eigenvalues with multiplicity one. We also present a conjecture about forbidden subgraphs of G when the multiplicity of its largest eigenvalue is \(n-4,\) and we analyze the case where G has diameter four.
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Acknowledgements
The research of the first author is supported by FCT-Fundação para a Ciência e a Tecnologia, under project UIDB/00297/2020. The research of the second, third and fourth author is partially supported by the National Council for Scientific and Technological Development (CNPq) with CNPq Grant 313335/2020-6; CNPq Grant 403963/2021-4; CNPq Grant 306262/2019-3 and CNPq Grant 403963/2021-4, respectively. The research of the third author is partially supported by FAPERJ with Grant E-20/2022-284573.
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Communicated by Carlos Hoppen.
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Fernandes, R., de Freitas, M.A.A., Silva, C.M.d. et al. On the multiplicities of distance Laplacian eigenvalues. Comp. Appl. Math. 42, 317 (2023). https://doi.org/10.1007/s40314-023-02460-1
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DOI: https://doi.org/10.1007/s40314-023-02460-1