Periodic static ab initio studies are conducted of hexagonal bilayer ice (HBL) and basal layers of ice-1h adsorbed on graphene using the model BLYP-D in CRYSTAL09. Eight high-symmetry periodic forms of HBL are optimized, of which four have lower energy; their electronic binding energy to graphene is similar to 1.6 kcal/mol per abutting H2O. Optimized geometries have the property of maximizing the occurrence of a certain O-H-C alignment motif. One lattice is selected for more detailed study. Its 2-D shear translation potential energy surface is found to have barrier heights in two zigzag directions of similar to 140 cal/mol per abutting H2O. A second hexagonal bilayer can be added and the electronic binding energy drops from similar to 1.7 to similar to 1.0 kcal/mol per abutting H2O. For ice-1h monolayer adsorbed on graphene, a proton-ordered form in which half of the O's nearest the graphene carry a proton pointing toward graphene is preferred over proton-ordered forms in which either all or none of those O's have H's pointing toward graphene. Cohesive energy for two-layer ice-1h on graphene is 0.66 kcal/mol of H2O higher than for HBL, supporting experimental evidence that the graphene+HBL isomer is more stable. However, the HBL and two-HBL structures are unstable or at best metastable with respect to four layers of ice-1h.