Interlacing Theorem for the Laplacian Spectrum of a Graph

Mirjana Lazić

It is well known that the Interlacing theorem for the Laplacian spectrum of a finite graph and its induced subgraphs is not true in a general case. In this paper we completely describe all simple finite graphs for which this theorem is true. Besides, we prove a variant of the Interlacing theorem for Laplacian spectrum and induced subgraphs of a graph which is true in general case.