Ferromagnetic ground states of the Hubbard model on a complete graph

We use group theory to derive the exact analytical expression of the ferromagnetic ground states of the Hubbard model on a complete graph for arbitrary lattice sites f and for arbitrary fillings $N$. We find that for $t>0$ and for $N=f+1$ the ground state is maximally ferromagnetic with total spin $S=(f-1)/2$. For $N > f+1$ the ground state is still ferromagnetic but becomes degenerate with respect to $S$.