  We investigate the non-radial oscillations of newly born neutron stars (NSs)
and strange quark stars (SQSs). This is done with the relativistic nuclear
field theory with hyperon degrees of freedom employed to describe the equation
of state for the stellar matter in NSs, and with both the MIT bag model and the
Nambu--Jona-Lasinio model adopted to construct the configurations of the SQSs.
We find that the gravitational-mode ($g$-mode) eigenfrequencies of newly born
SQSs are significantly lower than those of NSs, which is independent of models
implemented to describe the equation of state for the strange quark matter.
Meanwhile, the eigenfrequencies of the other modes of non-radial oscillations,
e.g., fundamental ($f$)- and pressure ($p$)-modes, are much larger than those
of the $g$-mode, and is related to the stiffness of the equation of states
(EoSs). In the light of the first direct observation of gravitational waves, it
is promising to employ the gravitational waves to identify the QCD phase
transition in high density strong interaction matter.
