Using the Anderson model Hamiltonian and the non-equilibrium Green's function method, the decoupled states and antiresonance presenting in the electronic transport through N-quantum-dot ring embodied in A-B interferometer are studied theoretically. We find that the symmetry of the coupled-dot system and the magnetic flux through the Aharonov-Bohm (A-B) interferometer are two physical mechanisms responsible for the decoupled states. Even-odd parity oscillations occur in linear conductance spectra of such a highly symmetric quantum dot ring, due to even or odd molecular state decoupling from the leads by tuning the structure parameters, i.e., the magnetic flux. The results provide a new model for the designing of the nano-device.