  We investigate the effects of the odd-state part of bare $\Lambda \Lambda$
interactions on the structure of neutron stars (NSs) by constructing equations
of state (EOSs) for uniform nuclear matter containing $\Lambda$ and $\Sigma^-$
hyperons with use of the cluster variational method. The isoscalar part of the
Argonne v18 two-nucleon potential and the Urbana IX three-nucleon potential are
employed as the interactions between nucleons, whereas, as the bare $\Lambda N$
and even-state $\Lambda \Lambda$ interactions, two-body central potentials that
are determined so as to reproduce the experimental data on single- and
double-$\Lambda$ hypernuclei are adopted. In addition, the $\Sigma^- N$
interaction is constructed so as to reproduce the empirical single-particle
potential of $\Sigma^-$ in symmetric nuclear matter. Since the odd-state part
of the $\Lambda \Lambda$ interaction is not known owing to lack of experimental
data, we construct four EOSs of hyperonic nuclear matter, each with a different
odd-state part of the $\Lambda \Lambda$ interaction. The EOS obtained for NS
matter becomes stiffer as the odd-state $\Lambda \Lambda$ interaction becomes
more repulsive, and correspondingly the maximum mass of NSs increases. It is
interesting that the onset density of $\Sigma^-$ depends strongly on the
repulsion of the odd-state $\Lambda \Lambda$ interaction. Furthermore, we take
into account the three-baryon repulsive force to obtain results that are
consistent with observational data on heavy NSs.
