  We study the properties of non-rotating and rotating neutron stars for a new
set of equations of state (EOSs) with different high density behaviour obtained
using the extended field theoretical model. The high density behaviour for
these EOSs are varied by varying the $\omega-$meson self-coupling and
hyperon-meson couplings in such a way that the quality of fit to the bulk
nuclear observables, nuclear matter incompressibility coefficient and
hyperon-nucleon potential depths remain practically unaffected. We find that
the largest value for maximum mass for the non-rotating neutron star is
$2.1M_\odot$. The radius for the neutron star with canonical mass is $12.8 -
14.1$ km provided only those EOSs are considered for which maximum mass is
larger than $1.6M_\odot$ as it is the lower bound on the maximum mass measured
so far. Our results for the very recently discovered fastest rotating neutron
star indicate that this star is supra massive with mass $1.7 - 2.7M_\odot$ and
circumferential equatorial radius $12 - 19$ km.
