The magnetic-field dependence of the energy spectrum, wave function, binding energy and oscillator strength of exciton states confined in a circular graphene quantum dot (CGQD) are obtained within the configuration interaction (CI) method. We predict that: (1) excitonic effects are very significant in the CGQD as a consequence of a combination of geometric confinement, magnetic confinement and reduced screening; (2) two types of excitons (intravalley and intervalley excitons) are present in the CGQD because of the valley degree of freedom in graphene; (3) the intravalley and intervalley exciton states display different magnetic-field dependencies due to the different electron-hole symmetries of the single-particle energy spectra; (4) with increasing magnetic field, the exciton ground state in the CGQD undergoes an intravalley to intervalley transition accompanied by a change of angular momentum; (5) the exciton binding energy does not increase monotonically with the magnetic field due to the competition between geometric and magnetic confinements; and (6) the optical transitions of the intervalley and intravalley excitons can be tuned by the magnetic field and valley-dependent excitonic transitions can be realized in CGQD.
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