  Similar to the compactness parameter ($\beta=M/R$), the gravitational binding
energy (GBE) is also a characteristic parameter which can reflect the internal
structure of a neutron star and thus can be used to expressing the universal
relations. Scaling by the stellar mass, this investigation demonstrates a
perfect universal relation between the GBE and the moment of inertia, where
both of the normal neutron stars and the quark stars satisfy the same universal
relation.
  Moreover, a fine empirical relation between the GBE and the tidal
deformability is proposed, where the difference of the relations can be used to
distinguish wether a pulsar is a normal neutron star or a quark star if the
stellar mass and the tidal deformability can be observed or estimated rather
accurately.
  These universal relations provide a potential way to estimate the GBE if the
stellar mass and the moment of inertia/the tidal deformability are precisely
measured.
