= Solution
On a connected <bipartite graph>, every exchange bond can attain its lower classical energy $-JS^2$. Set $\mathbf S_i=S\mathbf n$ on one sublattice and $\mathbf S_j=-S\mathbf n$ on the other, for any unit vector $\mathbf n$. This <Néel state> minimizes all bonds simultaneously and has
$$
\boxed{E_{\rm cl}=-JS^2\times\text{number of bonds}.}
$$
The direction $\mathbf n\in S^2$ parametrizes the continuous orientation degeneracy; disconnected components can choose their orientations independently.
A triangular lattice illustrates <geometric frustration>. For three fixed-length spins on a triangle,
$$
\mathbf S_1\cdot\mathbf S_2+\mathbf S_2\cdot\mathbf S_3+\mathbf S_3\cdot\mathbf S_1
=\tfrac12|\mathbf S_1+\mathbf S_2+\mathbf S_3|^2-\tfrac32S^2.
$$
The minimum requires their sum to vanish, giving coplanar $120$-degree spins rather than antiparallel alignment on every bond. A three-sublattice pattern realizes this condition on the nearest-neighbour triangular lattice. Its energy per bond is $-JS^2/2$, and global rotations produce equivalent classical states.
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