ELA, Volume 8, pp. 128-139, August 2001, abstract.

The third smallest eigenvalue of the Laplacian matrix

Sukanta Pati

Let G be a connected simple graph. The relationship 
between the third smallest eigenvalue of the Laplacian 
matrix and the graph structure is explored. For a tree 
the complete description of the eigenvector corresponding 
to this eigenvalue is given and some results about the 
multiplicity of this eigenvalue are given.