Graphene substrates have recently been found to generate Raman enhancement. Systematic studies using different Raman probes have been implemented, but one of the most commonly used Raman probes, rhodamine 6G (R6G), has yielded controversial results for the enhancement effect on graphene. Indeed, the Raman enhancement factor of R6G induced by graphene has never been measured directly under resonant excitation because of the presence of intense fluorescence backgrounds. In this study, a polarization-difference technique is used to suppress the fluorescence background by subtracting two spectra collected using different excitation laser polarizations. As a result, enhancement factors are obtained ranging between 1.7 and 5.6 for the four Raman modes of R6G at 611, 1,183, 1,361, and 1,647 cm -1 under resonant excitation by a 514.5 nm laser. By comparing these results with the results obtained under non-resonant excitation (632.8 nm) and pre-resonant excitation (593 nm), the enhancement can be attributed to static chemical enhancement (CHEM) and tuning of the molecular resonance. Density functional theory simulations reveal that the orbital energies and densities for R6G are modified by graphene dots.