  Within the relativistic mean-field model, we investigate the properties of
dark matter (DM) admixed neutron stars, considering non-rotating objects made
of isotropic matter. We adopt the IOPB-I hadronic equation of state (EOS) by
assuming that the fermionic DM within super-symmetric models has already been
accreted inside the neutron star (NS). The impact of DM on the mass-radius
relationships and the radial oscillations of pulsating DM admixed neutron stars
(with and without the crust) are explored. It is observed that the presence of
DM softens the EOS, which in turn lowers the maximum mass and its corresponding
radius. Moreover, adding DM results in higher frequencies of pulsating objects
and hence we show the linearity of fundamental mode frequency of canonical NS
with DM Fermi momentum. We also investigate the profile of eigenfunctions
solving the Sturm-Liouville boundary value problem, and verify its validity.
Further, we study the stability of NSs considering the fundamental mode
frequency variation with the mass of the star, and verify the stability
criterion $\partial M/\partial\rho_c > 0$. Finally, the effect of the crust on
the large frequency separation for different DM Fermi momenta is shown as well.
