We have performed low temperature scanning tunnelling spectroscopy measurements on graphene epitaxially grown on Ru(0001). An inelastic feature, related to the excitation of a vibrational breathing mode of the graphene lattice, was found at 360 meV. The change in the differential electrical conductance produced by this inelastic feature, which is associated with the electron-phonon interaction strength, varies spatially from one position to other of the graphene supercell. This inhomogeneity in the electronic properties of graphene on Ru(0001) results from local variations of the carbon-ruthenium interaction due to the lattice mismatch between the graphene and the Ru(0001) lattices. The experimental realization of graphene 1 has boosted the research on this material, finding unique electronic properties.2,3 The prospective use of graphene in optics, electronic devices, 4 and chemical sensors 5 has also motivated a large number of studies devoted to develop different fabrication methods and characterization techniques. Among a variety of growth methods, epitaxial growth of graphene on transition metal substrates has been intensively studied because of its high efficiency and sample quality. [6][7][8] Nevertheless, the role of the substrate in the electronic properties of graphene devices can be very important 9 and it has to be studied in detail. For example, the extraction of photogenerated carriers in graphene photodetectors relies on spatial variations of the potential at the graphene/metal contacts. Often epitaxially grown graphene presents a variety of moir e patterns due to the lattice mismatch with the different transition metal substrates and a spatial modulation of the electronic structure, e.g., the local density of states of the graphene layer has been observed. 10 The electron-phonon coupling (EPC) in graphene, which is responsible of a variety of properties from ballistic transport to excited-state dynamics, depends on the electronic density or doping level through the deformation potential.11 A possible spatial modulation of the electron-phonon interaction, however, has not been studied in these systems.In this letter, we present low-temperature scanning tunnelling microscopy (STM) and inelastic electron tunnelling spectroscopy (IETS) measurements in monolayer graphene epitaxially grown on a Ru(0001) surface, which show a strong inelastic feature that can be attributed to the interaction between the tunnelling electrons and a breathing vibrational mode of the graphene layer. The intensity of this inelastic feature, which is proportional to the electronphonon coupling strength and phonon density of states, varies spatially following the periodic Moir e pattern originated by the graphene/Ru(0001) lattice mismatch.The samples were prepared in an ultra-high vacuum (UHV) chamber with a base pressure in the range of 10 À11 Torr. The substrate is a single crystal of Ru exposing the (0001) surface, which was cleaned in UHV by ion sputtering and annealing to 1400 K. The graphene samples are grown under UHV c...