ELA, Volume 16, pp. 90-98, March 2007, abstract.
Interlacing for Weighted Graphs Using the Normalized
Laplacian
Steve Butler
The problem of relating the eigenvalues of the normalized
Laplacian for a weighted graph G and G-H, for H a subgraph
of G is considered. It is shown that these eigenvalues
interlace and that the tightness of the interlacing is
dependent on the number of nonisolated vertices of H.
Weak coverings of a weighted graph are also defined and
interlacing results for the normalized Laplacian for such a
covering are given. In addition there is a discussion about
interlacing for the Laplacian of directed graphs.