  The tidal measurement of gravitational waves from the binary neutron star
merger event GW170817 allows us to probe nuclear physics that suffers less from
astrophysical systematics compared to neutron star radius measurements with
electromagnetic wave observations. A recent work found strong correlation among
neutron-star tidal deformabilities and certain combinations of nuclear
parameters associated with the equation of state. These relations were then
used to derive bounds on such parameters from GW170817 assuming that the
relations and neutron star masses are known exactly. Here, we expand on this
important work by taking into account a few new considerations: (1) a broader
class of equations of state; (2) correlations with the mass-weighted tidal
deformability that was directly measured with GW170817; (3) how the relations
depend on the binary mass ratio; (4) the uncertainty from equation of state
variation in the correlation relations; (5) adopting the updated tidal
deformability measurement from GW170817. Upon these new considerations, we find
GW170817 bounds on nuclear parameters (the incompressibility $K_0$, its slope
$M_0$ and the curvature of symmetry energy $K_{\mathrm{sym},0}$ at nuclear
saturation density) to be 81 MeV $\leq K_0 \leq$ 362 MeV, 1556 MeV $\leq M_0
\leq$ 4971 MeV, and -254 MeV $\leq K_\mathrm{sym,0} \leq$ 27 MeV, which are
more conservative than previously found with systematic errors more properly
taken into account.
