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.