Quantum　entanglement　is　one　of　the　most　fascinating　features　of　quantum　theory　and　has　numerous　applications　in　quantum　information　processing　and　communication.　Many　unsolved　problems　in　classical　information　theory　can　be　solved　by　bipartite　entanglement　and　multipartite　entanglement.　In　this　paper,　the　separable　criterion　of　classes　of　density　matrices　was　studied.　The　separable　criterion　of　two　classes　of　graphs　was　presented　by　studying　two　classes　of　special　graphs　in　multipartite　systems.　Firstly,　the　concept　of　union　graph　was　generalized.　The　separability　of　union　graphs　of　simple　graph　in　multipartite　quantum　systems　was　proven　by　the　method　of　graph＇s　layer　and　the　property　of　Laplacian　matrices.　Secondly,　a　class　of　graph　was　constructed　by　the　concept　of　partially　symmetric　and　graph＇s　layer.　Combining　the　properties　of　graph　and　graph＇s　layer,　this　class　of　graph　and　the　properties　of　the　relevant　Laplacian　matrices　were　analyzed.　The　research　shows　that　the　classes　of　graph　represent　a　separable　state　in　multipartite　quantum　systems.　©　2018,　Editorial　Department　of　Journal　of　Beijing　University　of　Technology.　All　right　reserved.