A set of low-strain commensurate interface structures for epitaxial graphene on SiC(0001) are obtained by combining rotated graphene supercells with m x m or m root 3 x m root 3R30 degrees SiC cells. For two among the interfaces with lowest strain, corresponding to 4 x 4 and 6 root 3 x 6 root 3R30 degrees SiC periodicities, we analyze the binding energy of the graphene/SiC(0001) interface in terms of bond energies resulting from the (partial) saturation of individual Si dangling bonds by C atoms of graphene. These bond energies are determined as a function of the relative lateral displacement between the surface Si atoms and the graphene honeycomb. We find that this model energy does not explain the variation of the binding energies obtained from direct density functional calculations for the full interfacial systems. Moreover, for a given interface, the lateral rearrangements of the Si and C atomic positions found upon relaxation do not lead to any significant increase of the model binding energy. These results indicate that the deformations of the graphene layer cannot be neglected in the modeling of the binding energy of the graphene/SiC(0001) system. (C) 2011 Elsevier B.V. All rights reserved.