A graphene layer is formed on a crystallographic surface having a non-hexagonal symmetry. The crystallographic surface can be a surface of a single crystalline semiconductor carbide layer. The non-hexagonal symmetry surface of the single crystalline semiconductor carbide layer is annealed at an elevated temperature in ultra-high vacuum environment to form the graphene layer. During the anneal, the semiconductor atoms on the non-hexagonal surface of the single crystalline semiconductor carbide layer are evaporated selective to the carbon atoms. As the semiconductor atoms are selectively removed, the carbon concentration on the surface of the semiconductor-carbon alloy layer increases. Despite the non-hexagonal symmetry of the surface of the semiconductor-carbon alloy layer, the remaining carbon atoms can coalesce to form a graphene layer having hexagonal symmetry.