Impacts of dark matter on the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>f</mml:mi></mml:math> -mode oscillation of hyperon star

We investigate the $f$-mode oscillation of dark matter admixed hyperon star within relativistic Cowling approximation. The macroscopic properties are calculated with mean-field equation states by assuming that particles inside star. frequencies (only for $l=2$) four different neutron states. also check effects hyperons/dark and hyperons on oscillations varying astrophysical quantities such as mass ($M$), radius ($R$), compactness ($M/R$), surface red-shift (${Z}_{s}$), average density ($\overline{\ensuremath{\rho}}$), dimensionless tidal deformability ($\mathrm{\ensuremath{\Lambda}}$) Significant changes have been seen in without or $\mathrm{hyperons}+\mathrm{dark}$ matter. Substantial correlations observed between canonical $\mathrm{\ensuremath{\Lambda}}$ (${f}_{1.4}\ensuremath{-}{\mathrm{\ensuremath{\Lambda}}}_{1.4}$) maximum (${f}_{\mathrm{max}}\ensuremath{-}{\mathrm{\ensuremath{\Lambda}}}_{1.4}$).