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It is shown that the unique sign structure of the ground state of the Hubbardmodel on honeycomb lattice, which is shown to be insensitive to the trapped$Z_{2}$ gauge flux when the system is defined on a torus, may cause the absenceof topological degeneracy on this bipartite system. Examples of variationalMott insulating state on the honeycomb lattice are given to illustrate theclose relation between the sign structure of the ground state and the (absenceof) topological degeneracy.

Absence of topological degeneracy in the Hubbard model on honeycomb lattice