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 equation of states by assuming that the dark matter particles are inside the star. 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 equation of states 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 (ρ ¯), and dimensionless tidal deformability (Λ ) of the neutron star. Significant changes have been seen in the f -mode frequencies with and without hyperons/dark matter or hyperons +dark matter. Substantial correlations are observed between canonical frequencies and Λ (f_1.4-Λ_1.4) and maximum frequencies and canonical Λ (f_max-Λ_1.4).