  Neutron stars represent unique laboratories, offering insights into the
physics of supranuclear-density matter and serving as potential hosts for dark
matter. This study explores the impact of dark matter cores on rapidly rotating
neutron stars through the two-fluid approximation, assuming minimal interaction
between baryonic matter and dark matter. The investigation employs
phenomenological models for fermionic and bosonic dark matter, revealing that
universal relations governing mass and radius changes due to rotation remain
largely unaffected in the presence of a dark matter core. Specifically, for a 5
% dark matter mass fraction, the percent deviations in total mass ($M_{tot}$),
the baryonic equatorial radius ($R_{Be}$), and polar-to-equatorial baryonic
radius ratio ($R_{ratioB}$) are within 3.9 %, 1.8 %, and 1.4 %, respectively.
These findings suggest that the universal relations governing neutron star
shape can be utilized to infer constraints on the properties of dark matter
cores even in cases where the dark matter significantly softens the neutron
star's equation of state.
