Light-emitting diodes in the UV-C spectral range (UV-C LEDs) can potentially replace bulky and toxic mercury lamps in a wide range of applications including sterilization and water purification. Several obstacles still limit the efficiencies of UV-C LEDs. Devices in flip-chip geometry suffer from a huge difference in the work functions between the p-AlGaN and high-reflective Al mirrors, whereas the absence of UV-C transparent current spreading layers limits the development of UV-C LEDs in standard geometry. Here it is demonstrated that transfer-free graphene implemented directly onto the p-AlGaN top layer by a plasma enhanced chemical vapor deposition approach enables highly efficient 275nm UV-C LEDs in both, flip-chip and standard geometry. In flip-chip geometry, the graphene acts as a contact interlayer between the Al-mirror and the p-AlGaN enabling an external quantum efficiency (EQE) of 9.5% and a wall-plug efficiency (WPE) of 5.5% at 8V. Graphene combined with a ≈1nm NiOx support layer allows a turn-on voltage <5V. In standard geometry graphene acts as a current spreading layer on a length scale up to 1mm. These top-emitting devices exhibit a EQE of 2.1% at 8.7V and a WPE of 1.1%.