The mono- and bilayer graphene show different startling properties that give rise to prominent investigations led by the scientific community. More particularly, the relativistic character of the electrons in graphene at low energies has a significant effect on their behavior in the presence of a magnetic field, hence the peculiar structure of Landau levels and the anomalous quantization of the integer quantum Hall effect. Indeed, the most curious and unusual points are the existence of a lowest Landau level independent of the field intensity and the absence of the nu=0 quantum Hall plateau. Nevertheless, in recent experiments new plateaus have been observed at sufficiently strong fields that cannot be explained within the simplest non-interacting model for graphene. A possible interpretation for the appearance of these plateaus resides in broken symmetries that lead to degeneracy lifting. The most obvious is the one acting on the spin due to the Zeeman effect, but in more recent studies, this is coupled with a mechanism of electron-hole pairing known as magnetic catalysis, which accounts for the interactions between quasiparticles and brings about various Dirac mass terms in addition to spin gaps. The effect of these additional terms in the Dirac Hamiltonian on the quantum Hall plateau structure can be determined by analyzing the spectrum of graphene edge states. This has been well carried out for the case of monolayer graphene whereas for the bilayer it has not been studied in the most general case of broken symmetries. In this work I will discuss the spectrum of mono- and bilayer graphene edge states in a generic scenario of broken symmetries, and analyze the spatial dependence of their wave functions in the case of zig-zag and armchair edges.