  We study the relationship between the partial synchronous (PaS) state and the
coupling structure in general dynamical systems. By the exact proof, we find
the sufficient and necessary condition of the existence of PaS state for the
coupling structure. Our result shows that the symmetry of the coupling
structure is not the equivalent condition which is supposed before but only the
sufficient condition. Furthermore, for the existence of the PaS state, the
general structure is the equal-degree random.
