Density Matrix Of The Graph Can Be Divided Into,

The density matrix of a graph is the combinatorial laplacian of the graph normalized to have unit trace. Our propose is to research the separability of the density matrix of a graph on n = mpq vertices. We test the separability of the density matrix by researching the simple combinatorial condition (the "degree condition"), The condition is directly related to the PPT-criterion. It is proved that the degree condition is necessary for separability of tripartite states, then we conjecture that it is also sufficient. In fact, we point out that it is true for the density matrix of the nearest point graph. At last we will give examples to test and verify the conclusion.