The Laplacian Eigenvalues and Invariants of Graphs
  In this paper, we investigate some relations between the invariants (including vertex and edge connectivity and forwarding indices) of a graph and its Laplacian eigenvalues. In addition, we present a sufficient condition for the existence of Hamiltonicity in a graph involving its Laplacian eigenvalues. 
Rong-Ying Pan, Jing Yan, Xiao-Dong Zhang
math.CO