We employed x-ray absorption spectroscopy and x-ray magnetic circular dichroism to study the magnetic properties of single rare-earth (RE) atoms (Nd, Tb, Dy, Ho, and Er) adsorbed on the graphene/Ir(111) surface. The interaction of RE atoms with graphene results for Tb in a trivalent state with 4f^n-1 occupancy, and in a divalent state with 4fⁿ occupancy for all other studied RE atoms (n corresponds to the 4f occupancy of free atoms). Among the studied RE on graphene/Ir(111), Dy is the only one that shows magnetic hysteresis and remanence at 2.5 K. By comparing measured spectra and magnetization curves with multiplet calculations, we determine the energy diagram of the magnetic states and show for each element the magnetization reversal process that determines the timescale of its magnetic bistability.