  We investigate the effect of $\Delta$ baryons on the radial oscillations of
neutron and hyperon stars, employing a density-dependent relativistic
mean-field model. The spin-$3/2$ baryons are described by the Rarita-Schwinger
Lagrangian density. The baryon-meson coupling constants for the spin-3/2
decuplet and the spin-1/2 baryonic octet are calculated using a unified
approach relying on the fact that the Yukawa couplings present in the
Lagrangian density of the mean-field models must be invariant under the SU(3)
and SU(6) group transformations. We calculate the 20 lowest eigenfrequencies
and corresponding oscillation functions of $\Delta$-inclusive nuclear
(N+$\Delta$) and hyperonic matter (N+H+$\Delta$) by solving the Sturm-Liouville
boundary value problem and also verifying its validity. We see that the lowest
mode frequencies for N+$\Delta$ and N+H EoSs are higher as compared to the pure
nucleonic matter because of the deltas and hyperons present. Furthermore, the
separation between consecutive modes increases with the addition of hyperons
and $\Delta$s.
