The pinning of size-selected Au-N and Ni-N clusters on graphite, for N=7-100, is investigated by means of molecular dynamics simulations and the results are compared to experiment and previous work with Ag clusters. Ab initio calculations of the binding of the metal adatom and dimers on a graphite surface are used to parametrize the potentials used in the simulations. The clusters are projected normally towards a graphite surface and the value of the energy at which pinning first occurs, E-P, is determined. Pinning is shown to occur when a surface defect, made by the cluster interaction, is first produced. The simulations give a good agreement with the experimentally determined pinning energy thresholds and the heights of the clusters on the surface. The gold clusters are shown to be flatter and more spread out than the nickel clusters which are more compact.