  We investigate the one-dimensional strongly correlated electron models which
have the resonating-valence-bond state as the exact ground state. The
correlation functions are evaluated exactly using the transfer matrix method
for the geometric representations of the valence-bond states. In this method,
we only treat matrices with small dimensions. This enables us to give
analytical results. It is shown that the correlation functions decay
exponentially with distance. The result suggests that there is a finite
excitation gap, and that the ground state is insulating. Since the
corresponding non-interacting systems may be insulating or metallic, we can say
that the gap originates from strong correlation. The persistent currents of the
present models are also investigated and found to be exactly vanishing.
