  By employing four typical equation of states (EOSs) of the inner crust
matters, the constraint on properties of low-mass neutron stars are
theoretically investigated. Based on the well known fact that there is a big
gap between the neutron stars and white dwarfs in the mass-radius sequence of
compact stars, here we explicitly point out the forbidden region for the
central density and stellar radius to form a compact stars, that is, there is
no compact star in the nature having central density in the region from about
$10^{12}~kg/m^3$ to $10^{17}~kg/m^3$, and there is also no compact star having
a radius in the region from about 400 km to 2000 km. It is found that for a
low-mass neutron star with central densities at subnuclear densities, the
stellar mass is mainly determined by the softness of the EOS at the higher
density region ($ > 10^{16}~\textrm{kg.m}^{-3}$) while the stellar radius is
dependent on the softness of the EOS at lower density region ($ <
10^{16}~\textrm{kg.m}^{-3}$). For a stable neutron star with stellar mass near
the minimum mass, the Keplerian period is several hundred millisecond, the
moment of inertia is in an order of $10^{37} kg\cdot m^{2}$, and the surface
gravitational redshift is in an order of $10^{-4}$.
