The　separable　criterion　of　a　class　of　density　matrix　is　presented　by　studying　a　special　graph.　Using　graph　theory,　the　property　of　Laplacian　matrix,　the　positive　partial　transpose　criterion　and　the　relationship　of　degree　between　the　vertices　of　graph　and　the　corresponding　vertices　of　partial　transpose　of　the　graph,　the　separable　criterion　of　PE-matching　graph　in　Cp⊗Cq　and　C3⊗C4is　given　respectively.　In　Cp⊗Cqquantumsystems,　It　is　proven　that　if　the　partial　transpose　of　a　PE-matching　graph　on　n=pq　verticesis　not　a　PE-matching,　thedensity　matrix　of　this　graph　is　entanglement,　otherwise　it　is　PPT　(positive　partial　transpose).　It　is　also　presented　that　in　C3⊗C4　systems　if　the　density　matrix　of　PE-matching　graph　on　n=3×4　vertices　is　separable,　the　necessary　and　sufficient　condition　is　that　the　partial　transpose　of　this　graph　is　also　a　PE-matching　graph.　©,　2015,　Beijing　University　of　Technology.　All　right　reserved.