  In this report we experimentally probe the non-equilibrium breakdown of the
quantum Hall state in monolayer graphene by injecting a high current density
($\sim$1A/m). The measured critical currents for dissipationless transport in
the vicinity of integer filling factors show a dependence on filling factor.
The breakdown can be understood in terms of inter Landau level (LL) scattering
resulting from mixing of wavefunctions of different LLs. To further study the
effect of transverse electric field, we measured the transverse resistance
between the $\nu=2$ to $\nu=6$ plateau transition for different bias currents
and observed an invariant point.
