  We investigate the constraints on the mass and radius of neutron stars by
considering the tidal deformability in the merge of neutron star binaries. In
order to extract the most reliable range of uncertainty from theory, we employ
models based upon the Skyrme force and density functional theory and select
models that are consistent with empirical data of finite nuclei, measured
properties of nuclear matter around the saturation density, and observation of
the maximum mass of neutron stars. From the selected models, we calculate the
Love number $k_2$, dimensionless tidal deformability $\Lambda$, and
mass-weighted deformability $\tilde{\Lambda}$ in the binary system. We find
that all the models considered in this work give $\tilde{\Lambda}$ less than
800 which is the upper limit obtained from the measurement of GW170817.
However, the model dependence of tidal deformability is manifest such that our
results on the tidal deformability exhibit critical sensitivity to the size of
neutron stars.
