  Dijkgraaf and Vafa have conjectured that the effective superpotentials for
N=1 four-dimensional supersymmetric gauge theories can be given by the planar
diagrams of matrix models. We examine some special models with cubic and
quartic tree level superpotentials for adjoint chiral superfield \Phi. We
consider the effective superpotentials for the classical vacuum \Phi=0 for U(N)
and SO(N)/Sp(N) gauge theories. We evaluate the effective superpotentials
exactly in terms of the matrix model and in terms of closed string theory on
Calabi-Yau geometry with fluxes. As a result we find their perfect agreements.
