  This research paper complements our earlier qualitative study of the effect
of viscosity and thermal conductivity on the radial oscillation and relaxation
of non-rotating neutron stars. The fundamental and first two lowest-frequency
excited modes of radial oscillation have been computed in the high nuclear
density regime for a set of seven realistic equations of state (EoS) as
functions of central energy density. Various types of zero-temperature EoS of
cold nucleonic and hybrid nucleon-hyperon-quark matter models are used in the
inner core to determine the internal structure in and around the hydrostatic
equilibrium states and investigate the influence of each EoS on the dynamical
behaviour of non-rotating neutron stars. We confirm the principal results of
earlier, related studies that suggest an underlying correlation between the
frequency spectrum of the fundamental oscillation mode and the variation of the
adiabatic index over the high nuclear-density regime. We provide valuable
information to impose further constraints on the plausible set of realistic EoS
models, in addition to the practical applications for the rapidly evolving
field of asteroseismology of compact objects.
