We investigate the non-self-averaging properties of the dynamics of Ising, 4-state Potts and 10-state Potts models in single-cluster Monte Carlo simulations on quenched ensembles of planar, trivalent ( ³ ) random graphs, which we use as an example of relevant quenched connectivity disorder. We employ a novel application of scaling techniques to the cumulative probability distribution of the autocorrelation times for both the energy and magnetization in order to discern non-self-averaging. Although the specific results discussed here are for quenched random graphs, the method has quite general applicability.