  Properties of graphene plasmons are greatly affected by their coupling to
phonons. While such coupling has been routinely observed in both near-field and
far-field graphene spectroscopy, the interplay between coupling strength and
mode losses, and its exceptional point physics has not been discussed. By
applying a non-Hermitian framework, we identify the transition point between
strong and weak coupling as the exceptional point. Enhanced sensitivity to
perturbations near the exceptional point is observed by varying the coupling
strength and through gate modulation of the graphene Fermi level. Finally, we
also show that the transition from strong to weak coupling is observable by
changing the incident angle of radiation.
