Open AccessLocating Eigenvalues of a Symmetric Matrix whose Graph is Unicyclic
Author(s) -
Rodrigo Orsini Braga,
Vanderlei Moraes Rodrigues,
Rafaela Oliveira da Silva
Publication year - 2021
Publication title -
trends in computational and applied mathematics
Language(s) - English
Resource type - Journals
ISSN - 2676-0029
DOI - 10.5540/tcam.2021.022.04.00659
Subject(s) - laplacian matrix , combinatorics , eigenvalues and eigenvectors , mathematics , vertex (graph theory) , graph , spectral graph theory , laplace operator , algebraic connectivity , discrete mathematics , line graph , graph power , physics , mathematical analysis , quantum mechanics
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.