We report studies of the thermal and non-thermal interaction of benzene and toluene vapors with the Ru(0001) surface, a model cap layer for multilayer mirrors (MLM), using temperature programmed desorption (TPD), X-ray photoelectron spectroscopy (XPS), low energy ion scattering (LEIS), electron stimulated desorption (ESD), low electron energy diffraction (LEED), and scanning tunneling microscopy (STM). A low energy electron source (100 eV) is used to simulate radiation damage on the surface produced by EUV photons. Heating of adsorbed hydrocarbons leads to a stepwise dehydrogenation and buildup a self-limited carbon monolayer. Graphene monolayer and bilayer formation on Ru by hydrocarbon pyrolysis or by carbon segregation from the sample bulk is examined as a possible way to reduce the surface contamination rate. The binding energy of the hydrocarbon molecule is found to be smaller on a graphene layer than on disordered carbon. Electron bombardment of both bare and graphene covered Ru surface in the presence of benzene and toluene leads to C-buildup. However, the presence of a graphene monolayer on Ru surface reduces the electron-induced carbon growth rate at low electron flux conditions.