We study molecular transistors where graphene nanoribbons act as three metallic electrodes connected to a ring-shaped 18-annulene molecule. Using the nonequilibrium Green function formalism combined with density functional theory, recently extended to multiterminal devices, we show that these nanostructures exhibit exponentially small transmission when the source and drain electrodes are attached in a configuration with destructive interference of electron paths around the ring. The third electrode, functioning either as an attached infinite-impedance voltage probe or as an "air-bridge" top gate covering half of molecular ring, introduces dephasing that brings the transistor into the "on" state with its transmission in the latter case approaching the maximum limit for a single conducting channel device. The current through the latter device can also be controlled in the far-from-equilibrium regime by applying a gate voltage.