Locating Eigenvalues of a Symmetric Matrix whose Graph is Unicyclic - Braga, R. O.; Rodrigues, V. M.; Silva, R. O. (Trends in Computational and Applied Mathematics, 2021)
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.