We have performed path-integral Monte Carlo calculations to study ${}^{4}$He adsorption on a single graphene sheet. The ${}^{4}$He-substrate interaction was assumed to be a pairwise sum of the helium-carbon potentials constructed by Carlos and Cole to fit helium scattering data from a graphite surface. We employed both an anisotropic 6-12 Lennard-Jones potential and a spherical 6-12 potential. For both potentials, the first ${}^{4}$He layer has the C${}_{1/3}$ commensurate structure at a surface density of 0.0636 \AA{}${}^{\ensuremath{-}2}$. Vacancy states created in the C${}_{1/3}$ commensurate solid, however, behave differently depending on the ${}^{4}$He-substrate interaction: a cluster of localized vacancies are formed with the fully anisotropic 6-12 pair potentials while mobile vacancies are found to induce finite superfluid fractions with the substrate potential based on only the isotropic parts of the inter-atomic pair potentials. For the second helium layer we find that exchange among ${}^{4}$He adatoms results in quantum melting of a C${}_{7/12}$ commensurate structure, which is registered to a first-layer triangular solid. The possible stabilization of this commensurate structure with the addition of ${}^{3}$He impurities is discussed.