  The presence of heavy baryons, such as $\Delta$-baryons and hyperons can
significantly impact various properties of Neutron Stars (NSs), like
oscillation frequencies, dimensionless tidal deformability, mass, and radii. We
explored these effects within the Density-Dependent Relativistic Mean Field
formalism. Our analysis considered $\Delta$-admixed NS matter in both
hypernuclear and hyperon-free scenarios, providing insights into particle
compositions and their effects on NS properties. Our study of non-radial
$f$-mode oscillations revealed a distinct increase in frequency due to the
additional baryons. The degree of increase was significantly influenced by the
meson-baryon coupling strengths. Notably, the coupling between
$\Delta$-resonances and $\sigma$-mesons played a highly influential role. In
some cases, it led to an approximately 20\% increase in the $f$-mode
oscillation frequency of canonical NSs. These couplings also affect other bulk
properties of NSs, including mass, radii, and dimensionless tidal deformability
($\Lambda$). Comparing our results with available observational data from
pulsars (NICER) and gravitational waves (LIGO-VIRGO collaboration), we found
strong agreement, particularly concerning $\Lambda$.
