Title: Eigenvalue interlacing in digraphs
| Speaker: | Krystal Guo |
| Affiliation: | University of Waterloo |
| Room: | MC 5501 |
Abstract: The interplay between eigenvalues of graphs and graph properties has been well-studied. Many spectral bounds, such as those for diameter and for chromatic number, are known. The spectra of digraphs, however, is a relatively unexplored area.
There are many obstacles to extracting information from the eigenvalues of the adjacency matrix of a digraph; there may be complex eigenvalues and the matrix need not be diagonalizable. In addition, the powerful method of eigenvalue interlacing does not apply in this setting.
In order to use interlacing to find spectral bounds for digraph properties, it is advantageous to study different matrices which capture the adjacency of the digraph. In this talk, we bound interesting digraph properties using the Laplacian matrix and the Hermitian adjacency matrix. This is partly based on joint work with Bojan Mohar.