  Neutron stars are commonly considered as astronomical objects having
highdensity interiors and an inner core region in which various hadronic matter
phases are expected. Several studies show that the inner structures affect
macroscopic phenomena of the star. However, we know that the inner structures
of the star strongly depend on the equation of state (EOS). The EOS of
high-density matter is still not clear and several recent observations indicate
restrictions to EOSs. Theoretical studies should elucidate EOSs at high density
and/or high temperature. For instance, many theoretical studies have attempted
to account for the rotation effect of rapidly rotating neutron stars (i.e.,
pulsars). Accordingly, we also apply our EOSs to rapidly rotating stars.
Furthermore, neutron stars generate a strong magnetic field. Several recent
studies indicate that this magnetic field exerts restrictions on the EOS. In
this paper, we focus on the investigation of the inner structures and the
application of our EOSs to rotating stars. We find that one of our EOSs is
consistent with observations, and another is inconsistent. We also find an
important relation between the radius and rotation.
