Mirjana Lazic

Some results on symmetric double starlike trees

A tree is called starlike if it has exactly one vertex of degree greater than two. In [2] it was proved that two starlike trees are cospectral if and only if they are isomorphic. A tree is called double starlike if it has exactly two adjacent vertices of degree greater than two. We prove here that there exist no two cospectral non-isomorphic symmetric double starlike trees.

Interlacing theorem for the Laplacian spectrum of a graph

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.