We report the calculation of the solid-liquid interface tension of the graphene-water interaction by using molecular simulations. Local profiles of the interfacial tension are given through the mechanical and thermodynamic definitions. The dependence of the interfacial tension on the graphene area is investigated by applying both reaction field and Ewald summation techniques. The structure of the interfacial region close to the graphene sheet is analyzed through the profiles of the density and hydrogen bond number and the orientation of the water molecules. We complete this study by plotting the profiles of the components of the pressure tensor calculated by the Ewald summation and reaction field methods. We also investigate the case of a reaction field version consisting in applying a damped shifted force in the case of the calculation of the pressure components.