  In the last few decades, lots of universal relations between different global
physical quantities of neutron stars have been proposed to constrain the
unobservable or hard to be observed properties of neutron stars. But few of
them are related to the gravitational redshift or the gravitational binding
energy, especially for the fast rotating neutron stars. Here we will focus on
the universal relations related to these two quantities. Based on 11 equations
of state (EOSs) from the predictions of microscopic nuclear many-body theories
for normal or hybrid neutron stars, we proposed a set of new quasi-universal
relations under three rotating cases: static, general rotating and Keplerian
rotating. These new quasi-universal relations provide a potential way to
constrain or estimate the unobservable or hard to be observed properties of
neutron stars.
