Spectral conditions for a graph to be Hamilton-connected
  In this paper we establish some spectral conditions for a graph to be Hamilton-connected in terms of the spectral radius of the adjacency matrix or the signless Laplacian of the graph or its complement. For the existence of Hamiltonian paths or cycles in a graph, we also give a sufficient condition by the signless Laplacian spectral radius. 
Gui-Dong Yu, Yi-Zheng Fan
math.CO