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{\bf Zhen Wang and Zhixi Wang}
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{\bf The Tripartite Separability of Density Matrices of Graphs}
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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 prove 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.



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