This document discusses the Hofstadter butterfly model for the honeycomb lattice structure of graphene. It shows that the Hall conductivity σH in an energy gap must satisfy a Diophantine equation relating σH, the magnetic flux per unit cell p/q, and an integer s. For the honeycomb lattice, the conjecture is that σH lies in the window (-q,q) rather than the typical (-q/2,q/2). The bulk-edge correspondence relates σH to the number of edge state crossings in the Brillouin zone. Numerical results for σH calculated from the edge state spectrum agree with the Diophantine equation in 99.8% of cases.