Impacts of dark matter on the $f$-mode oscillation of hyperon star

We investigate the $f$-mode oscillation of the dark matter admixed hyperon star within the relativistic Cowling approximation. The macroscopic properties are calculated with the relativistic mean-field (RMF) equation of states by assuming that the dark matter particles are inside it. The coupling constants between hyperons and scalar mesons are fixed by fitting with hyperon potential depth, while for hyperons and vector mesons, we use SU(6) symmetry group method. The $f$-mode oscillation frequencies (only for $l=2$) are calculated with four different neutron star equation of states. We also check the effects of hyperons/dark matter and hyperons with dark matter EOSs on the $f$-mode oscillations varying with different astrophysical quantities such as mass ($M$), radius ($R$), compactness ($M/R$), surface red-shift ($Z_s$), average density ($\bar{\rho}$), dimensionless tidal deformability ($\Lambda$) of the neutron star. Some significant changes have been seen on the $f$-mode frequencies with and without hyperons/dark matter or hyperons+dark matter. Substantial correlations are observed between canonical frequency and $\Lambda$ ($f_{1.4}-\Lambda_{1.4}$) and maximum frequency and canonical $\Lambda$ ( $f_{max}-\Lambda_{1.4}$)