A nematic liquid-crystal director aligns along the armchair direction of graphene grown on a SiC substrate. The temperature-dependent textural change in the nematic phase is different from the usual texture on the alignment layer. The isotropic-nematic phase transition temperature decreases over time after cell fabrication. Tiny domains occur with the phase transition and appear to be merged from a critical temperature with decreasing temperature in the nematic phase. This is thought to be due to the transition occurring at the interface. On the other hand, the nematic liquid crystal in graphene grown on a Cu foil does not show textural changes, and the phase transition temperature does not decrease even after a long time has elapsed. X-ray fluorescence measurements indicate that silicon atoms exist in the liquid crystal possibly extracted from the SiC substrate. A model of first-order phase transition on the graphene surface has been proposed. This transition is accompanied by an inhomogeneous distribution of scalar order parameters and the transformation from a small multi-grained structure to a large domain distribution in the director field. This structural transformation takes place at a temperature different from that corresponding to the bulk transition. Such behavior may be explained by the adsorption process of silicon atoms in contact with the SiC-graphene interface.