  At high magnetic fields the conductance of graphene is governed by the
half-integer quantum Hall effect. By local electrostatic gating a \textit{p-n}
junction perpendicular to the graphene edges can be formed, along which quantum
Hall channels co-propagate. It has been predicted by Tworzid\l{}o and
co-workers that if only the lowest Landau level is filled on both sides of the
junction, the conductance is determined by the valley (isospin) polarization at
the edges and by the width of the flake. This effect remained hidden so far due
to scattering between the channels co-propagating along the \textit{p-n}
interface (equilibration). Here we investigate \textit{p-n} junctions in
encapsulated graphene with a movable \textit{p-n} interface with which we are
able to probe the edge-configuration of graphene flakes. We observe large
quantum conductance oscillations on the order of \si{e^2/h} which solely depend
on the \textit{p-n} junction position providing the first signature of
isospin-defined conductance. Our experiments are underlined by quantum
transport calculations.
