The aims of this paper is to propose a feasible scheme for preparation of graph states up to six vertices, which are not equivalent under LU (Local unitary) transformations and graph isomorphisms, and special kind of N-atoms graph state (GHZ state, cluster state, ring state and complete state). First we show a two-qubit system (two-atoms with two-levels) how to acquire the maximal entanglement after interaction time tc. Then, we generalize this method to mentioned above cases.
