  Comparing with a wide range of covariant energy density functional models
based on the finite-range meson-exchange representation, the relativistic
mean-field models with the zero-range contact interaction, namely the
relativistic point-coupling models, are still infrequent to be utilized in
establishing nuclear equation of state (EoS) and investigating neutron star
properties, although comprehensive applications and achievements of them in
describing many nuclear properties both in ground and exited states are mature.
In this work, the EoS of neutron star matter is established constructively in
the framework of the relativistic point-coupling models to study neutron star
physics. Taking two selected functionals DD-PC1 and PC-PK1 as examples, nuclear
symmetry energies and several neutron star properties including proton
fractions, mass-radius relations, the core-crust transition density, the
fraction of crustal moment of inertia and dimensionless tidal deformabilities
are discussed. A suppression of pressure of neutron star matter found in the
functional PC-PK1 at high densities results in the difficulty of its prediction
when approaching to the maximum mass of neutron stars. In addition, the
divergences between two selected functionals in describing neutron star
quantities mentioned above are still large, ascribing to the less constrained
behavior of these functionals at high densities. Then it is expected that the
constraints on the dense matter EoS from precise and massive modern
astronomical observations, such as the tidal-deformabilities taken from
gravitational-wave events, would be essential to improve the parameterizing of
the relativistic point-coupling models.
