  We have computed the properties of compact objects like neutron stars based
on equation of state (EOS) deduced from a core-envelope model of superdense
stars. Such superdense stars have been studied by solving the Einstein's
equation based on pseudo-spheroidal and spherically symmetric space-time
geometry. The computed star properties are compared with those obtained based
on nuclear matter equations of state. From the mass-radius ($M-R$) relationship
obtained here, we are able to classify compact stars in three categories: (i)
highly compact self -bound stars that represents exotic matter compositions
with radius lying below 9 km (ii) normal neutron stars with radius between 9 to
12 km and (iii) soft matter neutron stars having radius lying between 12 to 20
km. Other properties such as Keplerian frequency, surface gravity and surface
gravitational redshift are also computed for all the three types. The present
work would be useful for the study of highly compact neutron like stars having
exotic matter compositions.
