  On the basis of generations of 1-dimensional and 2-dimensional graph states,
we generate a 3-dimensional N3-qubit graph state based on the Josephson charge
qubits. Since any two charge qubits can be selectively and effectively coupled
by a common inductance, the controlled phase transform between any two-qubit
can be performed. Accordingly, we can generate arbitrary multi-qubit graph
states corresponding to arbitrary shape graph, which meet the expectations of
various quantum information processing schemes. All the devices in the scheme
are well within the current technology. It is a simple, scalable and feasible
scheme for the generation of various graph states based on the Josephson charge
qubits.
