  The density matrix of a graph is the combinatorial laplacian matrix of a
graph normalized to have unit trace. In this paper we generalize the
entanglement properties of mixed density matrices from combinatorial laplacian
matrices of graphs discussed in Braunstein {\it et al.} Annals of
Combinatorics, {\bf 10}(2006)291 to tripartite states. Then we proved that the
degree condition defined in Braunstein {\it et al.} Phys. Rev. A {\bf 73},
(2006)012320 is sufficient and necessary for the tripartite separability of the
density matrix of a nearest point graph.
