  We address a simple but fundamental issue arising in the study of graphene,
as well as of other systems that have a crystalline structure with more than
one atom per unit cell. For these systems, the choice of the tight-binding
basis is not unique. For monolayer graphene two bases are widely used in the
literature. While the expectation values of operators describing physical
quantities should be independent of basis, the form of the operators may depend
on the basis, especially in the presence of disorder or of an applied magnetic
field. Using the inappropriate form of certain operators may lead to erroneous
physical predictions. We discuss the two bases used to describe monolayer
graphene, as well as the form of the most commonly used operators in the two
bases. We repeat our analysis for the case of bilayer graphene.
