  We investigate the effects of dark matter (DM) on the nuclear equation of
state (EoS) and neutron star structure, in the relativistic mean field theory,
both in the absence and presence of a crust. The $\sigma-\omega$ model is
modified by adding a WIMP-DM component, which interacts with nucleonic matter
through the Higgs portal. This model agrees well with previous studies which
utilized either a more complicated nuclear model or higher-order terms of the
Higgs potential, in that DM softens the EoS, resulting in stars with lower
maximum masses. However, instabilities corresponding to negative pressure
values in the low-energy density regime of the DM-admixed EoS are present, and
this effect becomes more prominent as we increase the DM Fermi momentum. We
resolve this by confining DM in the star's core. The regions of instability
were replaced by three types of crust: first by the
Friedman-Pandharipande-Skyrme (FPS), Skyrme-Lyon (SLy) and BSk19 EoS from the
Brussels-Montreal Group, which can be represented by analytical approximations.
For a fixed value of the DM Fermi momentum $p_F^{DM}$, the DM-admixed neutron
star does not have significant changes in its mass with the addition of the
crusts. However, the entire mass-radius relation of the neutron star is
significantly affected, with an observed increase in the radius of the star
corresponding to the mass. The effect of DM is to reduce the mass of the star,
while the crust does not affect the radius significantly, as the value of the
$p_F^{DM}$ increases.
