The combinatorial structure of graphene

We think of graphene patches as regions of the hexagonal tessellation of the plane. In Section 3.1, we introduce basic parameters of graphene patches and describe the relationships between them. In Section 3.2, we discuss results about Kekule structures (double bond structures) for graphene patches. In Section 3.3, we generalize the results about Kekule structures for general patches, including disordered graphene patches (graphene with some non-hexagonal faces) as well as more general structures. Section 3.4 describes the topological structure of disordered graphene patches.