  Equilibrium sequences were developed for rotating NS in the relativistic
mean-field interaction framework using four density-dependent equations of
state for the NS matter. These sequences were constructed for the observed
rotation frequencies of 25, 317, 346, 716, and 1122 Hz. The bounds of sequences
were calculated in each model to determine the stability region. The
gravitational mass, quadrupole moment, polar, forward and backward redshifts,
and Kerr parameter were calculated. DDF and DD-ME$\delta$ were unable to
properly describe the low-frequency neutron stars, PSR J0348+432, PSR
J1614-2230 , and PSR J0740+6620 rotate at a frequency of 25, 317, and 346 Hz,
respectively. All the selected EOSs properly described the rotation of PSR
J1748-244ad, and PSR J1739-285 at a frequency of 716 and 1122 Hz, respectively.
The mass of these stars was in the range of [0.68, 2.14]M$_{\odot}$ and [1.67,
2.24]M$_{\odot}$, respectively. The polar, forward and backward redshifts, and
the quadrupole moment were calculated in all selected rotating frequencies and
the Keplerian sequence. The results were consistent with observations.
Confirming the mass of $1.5^{+0.4}_{-1.0}M_{\odot}$ for EXO 0748-676, our
result will be close to the observed value, and the EOSs used in this study
properly describe this star. The extremum of Kerr parameter, polar, forward and
backward redshifts in all models reached constant values of, a/M$\approx$ 0.7,
Z$_{p}\approx$ 0.8, Z$_{eq}^{f}\approx$ -0.3 and Z$_{eq}^{b}\approx$ 2.2. These
behaviors of redshifts and Kerr parameter are approximately independent of EOS.
The observed behaviors must evaluate by other EOSs to find universal relations
for these quantities. Also, a limit value was found for each of these
parameters. In this case where these parameters are greater than the limit
value, the star can rotate at a frequency equal to or greater than $\nu$= 1122
Hz.
