The desorption kinetics for benzene and cyclohexane from a graphene covered Pt(111) surface were investigated using temperature-programmed desorption (TPD). The benzene desorption spectra show well-resolved monolayer and multilayer desorption peaks. The benzene monolayer and submonolayer TPD spectra for coverages greater than similar to 0.1 ML have nearly the same desorption peak temperature and have line hi shapes which are consistent with first-order desorption kinetics. For benzene coverages greater than 1 ML, the TPD spectra align on a common leading edge which is consistent with zero-order desorption. An "inversion" procedure in which the prefactor is varied to find the value that best reproduces the entire set of experimental desorption spectra was used to analyze the benzene data. The inversion analysis of the benzene TPD spectra yielded a desorption activation energy of 54 +/- 3 kJ/mol with a prefactor of 10(17 +/- 1) s(-1). The TPD spectra for cyclohexane also have well-resolved monolayer and multilayer desorption features. The desorption leading edges for the monolayer and the multilayer TPD spectra are aligned indicating zero-order desorption kinetics in both cases. An Arrhenius analysis of the monolayer cyclohexane TPD spectra yielded a desorption activation energy of 53.5 +/- 2 kJ/mol with a prefactor of 10(16 +/- 1) ML s(-1).