Based on the size-dependent cohesive energy formula for two-dimensional materials, we investigate the gap openings in graphene layers regarding distinct interfacial interaction from substrates. Depending on the interfacial physicochemical nature, the gap is opened weakly induced by the van der Waals interaction but readily by the chemical bonding. Relative to the former, in essence, the distinct opening behavior for the latter comes from the substantial change in atomic cohesive energy of graphene associated with the coordination imperfection. Our predictions agree with the available experimental or computer simulation results for graphene layers on layered BN or bulk truncated SiC. The present work is of benefit for the application of graphene in electronics.