  The high-density behavior of the stellar matter composed of nucleons and
leptons under $\beta$~equilibrium and charge neutrality conditions is studied
with the Skyrme parametrizations shown to be consistent (CSkP) with the nuclear
matter, pure neutron matter, symmetry energy and its derivatives in a set of
$11$ constraints [Dutra {\it et al.}, Phys. Rev. C 85, 035201 (2012)]. The
predictions of these parametrizations on the tidal deformabilities related to
the GW170817 event are also examined. The CSkP that produce massive neutron
stars give a range of $11.86~\mbox{km} \leqslant R_{1.4} \leqslant
12.55~\mbox{km}$ for the canonical star radius, in agreement with other
theoretical predictions. It is shown that the CSkP are compatible with the
region of masses and radii obtained from the analysis of recent data from LIGO
and Virgo Collaboration (LVC). A correlation between dimensionless tidal
deformability and radius of the canonical star is found, namely, $\Lambda_{1.4}
\approx 3.16\times10^{-6}R_{1.4}^{7.35}$, with results for the CSkP compatible
with the recent range of $\Lambda_{1.4}=190_{-120}^{+390}$ from LVC. An
analysis of the $\Lambda_1\times\Lambda_2$ graph shows that all the CSkP are
compatible with the recent bounds obtained by LVC. Finally, the universal
correlation between the moment of inertia and the deformability of a neutron
star, named as the \mbox{$I$-Love} relation, is verified for the CSkP, that are
also shown to be consistent with the prediction for the moment of inertia of
the \mbox{PSR J0737-3039} primary component pulsar.
