  The effect of an Aharonov-Bohm (AB) pseudo magnetic field on a two
dimensional electron gas in graphene is investigated. We consider it modeled as
in the usual AB effect but since such pseudo field is supposed to be induced by
elastic deformations, the quantization of the field flux is abandoned. For
certain constraints on the orbital angular momentum eigenvalues allowed for the
system, we can observe the zero Landau level failing to develop, due to the
degeneracy related to the Dirac valleys $K$ and $K^\prime$ which is broken. For
integer values of the pseudo AB flux, the actual quantum Hall effect is
preserved. Obtaining the Hall conductivity by summing over all orbital angular
momentum eigenvalues, the zero Landau levels is recovered. Since our problem is
closed related to the case where topological defects on a graphene sheet are
present, the questions posed here are helpful if one is interested to probe the
effects of a singular curvature in these systems.

Mesoscale and Nanoscale Physics;Quantum Physics