  We calculate the baryon-meson coupling constants for the spin-1/2 baryonic
octet and spin-3/2 decuplet in a unified approach relying on symmetry arguments
such as the fact that the Yukawa couplings, present in the Lagrangian density
of the Walecka-type models, must be an invariant under SU(3) and SU(6) group
transformations. The coupling constants of the baryon with the scalar $\sigma$
meson are fixed to reproduce the known potential depths for the hyperons and
$\Delta$ resonances, in an approach that can be extended to all particles. We
then apply the calculated coupling constants to study neutron star matter with
hyperons and deltas admixed to its composition. We conclude that the $\Delta^-$
is by far the most important exotic particle that can be present in the neutron
star interior. It is always present, independent of the chosen
parameterization, and might appear in almost every known neutron star, once its
onset happens at very low density. Yet, its presence affects the astrophysical
properties of the canonical 1.4 M$_\odot$ star, and, in some cases, it can even
contribute to an increase in the maximum mass reached.
