Specific types of spatial defects or potentials can turn monolayer graphene into a topological
material. These topological defects are classified by a spatial dimension D and they are systemati-
cally obtained from the Hamiltonian by means of its symbol H(k, r), an operator which generalises
the Bloch Hamiltonian and contains all topological information. This approach, when applied to
Dirac operators, allows to recover the tenfold classification of insulators and superconductors. The
existence of a stable Z-topology is predicted as a condition on the dimension D, similar to the clas-
sification of defects in thermodynamic phase transitions. Kekule distortions, vacancies and adatoms
in graphene are proposed as examples of such defects and their topological equivalence is discussed.