We study the relativistic quadrupole oscillations (l = 2) of strange-quark
stars by calculating their quasi-normal modes, and we thus explore the poss
ibility of using these oscillation frequencies and damping times to differe
ntiate among relativistic polytropic stars, neutron stars, pure light-quark
stars, and hybrid neutron stars with quark cores. We found that, whereas t
he general features of the w-mode spectra of quark stars and hybrid neutron
stars are very similar to those of relativistic polytropes, they differ in
the higher mode frequencies for both axial and polar oscillations. The pro
files off-modes for quark stars are different from those of realistic neutr
on stars, and from that we conclude that quark and strange-quark stars are
more efficient gravitational-waves radiators than pure neutron stars. Also,
the damping times of various modes are rather sensitive to the details of
the quark model, such as the Bag constant, quark-gluon interactions, and qu
ark mass corrections.