  We write down matrix models for Ising spins with zero external field on the
vertices of dynamical triangulated random surfaces (DTRS) and dynamically
quadrangulated random surfaces (DQRS) and compare these with the standard
matrix model approach which places the spins on the dual $\phi^3$ and $\phi^4$
graphs. We show that the critical temperatures calculated in the DTRS and DQRS
models agree with those deduced from duality arguments in the standard
approach. Using the DQRS model we observe that the Ising antiferromagnet still
undergoes a phase transition to a Neel (checkerboard) ordered ground state
which is absent because of frustration in the other cases.
