Molecular dynamics (MD) simulations are performed to obtain mode I and II fracture energies and cohesive laws for bulk epoxy and interfaces formed between epoxy and single-layer graphene (SLG), multilayer graphene (MLG), and multilayer graphene oxide (MLGO). The elastic moduli and ultimate tensile and shear strengths of epoxy--graphene interfaces are calculated from uniaxial tension and simple shear loadings. The results show that Young's modulus and the ultimate tensile strength increase relative to bulk epoxy, whereas the shear modulus and ultimate shear strength are reduced. Failure of epoxy--graphene interfaces in tension occurs due to the formation of voids in the epoxy. Failure in shear is due to tangential slipping at the interface. Under mixed mode conditions, the shear modulus and shear strength decrease with increasing tensile load. The critical energy release rate G_c for the studied epoxy--SLG/MLG/MLGO systems are obtained using a continuum fracture mechanics approach and are found to be significantly lower than for bulk epoxy. All of the results are combined to define mode I and II cohesive laws for bulk epoxy and epoxy--SLG/MLG/MLGO interfaces that can be used in theoretical models and numerical methods, such as finite elements, that employ cohesive zones.