  We study the electronic contribution to the main thermoelectric properties of
a molecular junction consisting of a single quantum dot coupled to graphene
external leads. The system electrical conductivity (G), Seebeck coefficient
($S$), and the thermal conductivity ($\kappa$), are numerically calculated
based on a Green's function formalism that includes contributions up to the
Hartree-Fock level. We consider the system leads to be made either of pure or
gapped-graphene. To describe the free electrons in the gapped-graphene
electrodes we used two possible scenarios, the massive gap scenario, and the
massless gap scenario, respectively. In all cases, the Fano effect is
responsible for a strong violation of the Wiedemann-Franz law and we found a
substantial increase of the system figure of merit $ZT$ due to a drastic
reduction of the system thermal coefficient. In the case of gapped-graphene
electrodes, the system figure of merit presents a maximum at an optimal value
of the energy gap of the order of $\Delta/D\sim$ 0.002 (massive gap scenario)
and $\Delta/D\sim$ 0.0026 (massless gap scenario). Additionally, for all cases,
the system figure of merit is temperature dependent.
