Multiparticle entanglement in graph-diagonal states: Necessary and   sufficient conditions for four qubits
  The characterization of genuine multiparticle entanglement is important for entanglement theory as well as experimental studies related to quantum information theory. Here, we completely characterize genuine multiparticle entanglement for four-qubit states diagonal in the cluster-state basis. In addition, we give a complete characterization of multiparticle entanglement for all five-qubit graph states mixed with white noise, for states diagonal in the basis corresponding to the five-qubit Y-shaped graph, and for a family of graph states with an arbitrary number of qubits. 
Otfried G\"uhne, Bastian Jungnitsch, Tobias Moroder, Yaakov S.   Weinstein
quant-ph