  In the context of the determination of stellar properties using
asteroseismology, we study the influence of rotation and convective-core
overshooting on the properties of red-giant stars. We used models in order to
investigate the effects of these mechanisms on the asymptotic period spacing of
gravity modes ($\Delta \Pi_1$) of red-giant stars that ignite He burning in
degenerate conditions (M$\lesssim$2.0 M$_{\odot}$). We also compare the
predictions of these models with Kepler observations. For a given $\Delta\nu$,
$\Delta \Pi_1$ depends not only on the stellar mass, but also on mixing
processes that can affect the structure of the core. We find that in the case
of more evolved red-giant-branch (RGB) stars and regardless of the transport
processes occurring in their interiors, the observed $\Delta \Pi_1$ can provide
information as to their stellar luminosity, within ~10-20%. In general, the
trends of $\Delta \Pi_1$ with respect to mass and metallicity that are observed
in Kepler red-giant stars are well reproduced by the models.
