  {\it Background.} We investigate possible correlations between neutron star
observables and properties of atomic nuclei. Particularly, we explore how the
tidal deformability of a 1.4 solar mass neutron star, $M_{1.4}$, and the
neutron skin thickness of ${^{48}}$Ca and ${^{208}}$Pb are related to the
stellar radius and the stiffness of the symmetry energy. {\it Methods.} We
examine a large set of nuclear equations of state based on phenomenological
models (Skyrme, NLWM, DDM) and {\it ab-initio} theoretical methods (BBG,
Dirac-Brueckner, Variational, Quantum Monte Carlo). {\it Results.} We find
strong correlations between tidal deformability and NS radius, whereas a weaker
correlation does exist with the stiffness of the symmetry energy. Regarding the
neutron skin thickness, weak correlations appear both with the stiffness of the
symmetry energy, and the radius of a $M_{1.4}$. {\it Conclusion.} The tidal
deformability of a $M_{1.4}$ and the neutron-skin thickness of atomic nuclei
show some degree of correlation with nuclear and astrophysical observables,
which however depends on the ensemble of adopted EoS.
