We have carried out an extensive grand canonical Monte Carlo simulation to investigate the adsorption of neon and xenon on graphite. The adsorbate collision diameters of neon and xenon are smaller and greater respectively, than the commensurate graphite lattice spacing lambda = (root 3 x root 3)R30 degrees of 0.426 nm. Simulated isotherms and isosteric heats were obtained using a graphite model that has been shown to describe successfully the adsorbate transitions for krypton, methane and nitrogen by Prasetyo et al. (2017), which have collision diameters close to lambda. Neon does not exhibit commensurate (C) packing because the gain in the intermolecular potential interactions in the incommensurate (IC) packing when molecules move away from carbon hexagon centres, does not compensate for the increase in the solid-fluid potential energy. Xenon, on the other hand, exhibits IC packing because its molecular size is greater than lambda. Nevertheless, at a sufficiently high chemical potential, the first layer of xenon changes from the IC to C packing (in contrast to what is observed for krypton, nitrogen and methane). This transition occurs because the decrease in the xenon intermolecular interactions is sufficiently compensated by the increase in the solid-fluid interaction, and the increase in the fluid-fluid interactions between molecules in the first layer and those in the second layer. This finding is supported by the X-ray diffraction study by Mowforth et al. (1986) and Morishige et al. (1990). (C) 2018 Elsevier Inc. All rights reserved.