  We consider a lattice of spin-1 particles with a general pairwise interaction
$ [ {\rm cos} \gamma ({\bf S}_{l} \cdot {\bf S}_{l+1}) \
  + {\rm sin} \gamma ({\bf S}_{l} \cdot {\bf S}_{l+1})^2 \
  ]$. We show that, for a large class of lattices with even number of sites,
the ground state for the region $ - {3 \pi \over 4} < \gamma < - {\pi \over 2}$
belongs to total spin $S_{\rm tot} = 0$, whereas the state of minimum excited
energy but with finite $S_{\rm tot}$ belongs to $S_{\rm tot} = 2$. These
results are constrasted with the generalized Marshall theorems, applicable to a
bipartite lattice and $ - {\pi \over 2} < \gamma \le 0$.

Superconductivity;Strongly Correlated Electrons