  We address the question of how the Aharonov-Bohm flux $\Phi_{AB}$ can affect
the energy levels of graphene magnetic quantum dots (GMQDs) of radius $R$. To
answer this question, we consider GMQDs induced by a magnetic field $B$ and
subjected to two different gaps - an internal gap $\Delta_1$ and an external
gap $\Delta_2$. After determining the eigenspinors and ensuring continuity at
the boundary of the GMQDs, we formulate an analytical equation describing the
corresponding energy levels. Our results show that the energy levels can
exhibit either a symmetric or an asymmetric behavior depending on the valleys
$K$ and $K'$ together with the quantum angular momentum $m$. In addition, we
find that $\Phi_{AB}$ causes an increase in the band gap width when $\Delta_1$
is present inside the GMQDs. This effect is less significant when a gap is
present outside, resulting in a longer lifetime of the confined electronic
states. Further increases in \(\Phi_{AB}\) reduce the number of levels between
the conduction and valence bands, thereby increasing the band gap. These
results demonstrate that the electronic properties of graphene can be tuned by
the presence of the AB flux, offering the potential to control the behavior of
graphene-based quantum devices.
