  We study the attractive SU($N$) Hubbard model with particle-hole symmetry.
The model is defined on a bipartite lattice with the number of sites $N_A$
$(N_B)$ in the $A$ $(B)$ sublattice. We prove three theorems that allow us to
identify the basic ground-state properties: the degeneracy, the fermion number,
and the SU($N$) quantum number. We also show that the ground state exhibits
charge density wave order when $|N_A-N_B|$ is macroscopically large. The
theorems hold for a bipartite lattice in any dimension, even without
translation invariance.
