Locating Eigenvalues of a Symmetric Matrix whose Graph is Unicyclic

R. O. Braga, V. M. Rodrigues, R. O. Silva


We present a linear-time algorithm that computes in a given real interval the number of eigenvalues of any symmetric matrix whose underlying graph is unicyclic. The algorithm can be applied to vertex- and/or edge-weighted or unweighted unicyclic graphs. We apply the algorithm to obtain some general results on the spectrum of a generalized sun graph for certain matrix representations which include the Laplacian, normalized Laplacian and signless Laplacian matrices.


Symmetric matrix, eigenvalue location, unicyclic graph.

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DOI: https://doi.org/10.5540/tcam.2021.022.04.00659

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Trends in Computational and Applied Mathematics

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