Problem of the Week
Hilton Memorial Lecture
There has long been an interest in bounds for the eigenvalues of the adjacency matrix of a graph. Recently this has spilled over to the Kirchhoff or Laplacian matrix, and even to signed graphs. I have extended some of these results to graphs with complex unit gains, and have also found new bounds for Laplacian eigenvalues of signed graphs. This talk will be a ramble around some interesting eigenvalue inequalities, old and new.