  We perform Monte Carlo simulations using the Wolff cluster algorithm of the
q=2 (Ising), 3, 4 and q=10 Potts models on dynamical phi-cubed graphs of
spherical topology with up to 5000 nodes. We find that the measured critical
exponents are in reasonable agreement with those from the exact solution of the
Ising model and with those calculated from KPZ scaling for q=3,4 where no exact
solution is available. Using Binder's cumulant we find that the q=10 Potts
model displays a first order phase transition on a dynamical graph, as it does
on a fixed lattice. We also examine the internal geometry of the graphs
generated in the simulation, finding a linear relationship between ring length
probabilities and the central charge of the Potts model
