  We study the thermoelectric properties of rectangular graphene rings
connected symmetrically or asymmetrically to the leads. A side-gate voltage
applied across the ring allows for the precise control of the electric current
flowing through the system. The transmission coefficient of the rings manifests
Breit-Wigner line-shapes and/or Fano line-shapes, depending on the connection
configuration, the width of nanoribbons forming the ring and the side-gate
voltage. We find that the thermopower and the figure of merit are greatly
enhanced when the chemical potential is tuned close to resonances. Such
enhancement is even more pronounced in the vicinity of Fano like
anti-resonances which can be induced by a side-gate voltage independently of
the geometry. This opens a possibility to use the proposed device as a tunable
thermoelectric generator.
