  We present a systematic study of $f$-mode oscillations in neutron stars
containing hyperons, extending recent results obtained within the Cowling
approximation to linearized General Relativity. Employing a relativistic mean
field model, we find that the Cowling approximation can overestimate the
quadrupolar $f$-mode frequency of neutron stars by up to 30\% compared to the
frequency obtained in the linearized general relativistic formalism. Imposing
current astrophysical constraints, we derive updated empirical relations for
gravitational wave asteroseismology. The frequency and damping time of
quadrupole $f$-mode oscillations of hyperonic stars are found to be in the
range of 1.47 - 2.45kHz and 0.13 - 0.51 sec respectively. Our correlation
studies demonstrate that among the various parameters of the nucleonic and
hyperonic sectors of the model, the nucleon effective mass shows the strongest
correlation with mode characteristics and neutron star observables. Estimates
for the detectability of $f$-modes in a transient burst of gravitational waves
from isolated hyperonic stars is also provided.
