We apply eigenvalue interlacing techniques for obtaining lower and upper bounds for the sums of Laplacian eigenvalues of graphs, and characterize equality. This leads to generalizations of, and variations on theorems by Grone, and Grone & Merris. As a consequence we obtain inequalities involving bounds for some well-known parameters of a graph, such as edge-connectivity, and the isoperimetric number.
- Laplacian matrix
- graph spectra
- sum of eigenvalues
Abiad, A., Fiol, M. A., Haemers, W. H., & Perarnau, G. (2014). An interlacing approach for bounding the sum of Laplacian eigenvalues of graphs. Linear Algebra and its Applications, 448, 11-21. https://doi.org/10.1016/j.laa.2014.02.003