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Motivated by the recent numerical simulations for doped $t$-$J$ model on thehoneycomb lattice, we study superconductivity of singlet and triplet pairing onthe honeycomb lattice Hubbard model. We show that a superconducting state withcoexisting spin-singlet and spin-triplet pairings is induced by theantiferromagnetic order near half filling. The superconducting state we obtainhas a topological phase transition that separates a topologically trivial stateand a nontrivial state with Chern number two. Possible experimental realizationof such a topological superconductivity is also discussed.

Coexistence of antiferromagnetism and topological superconductivity on the honeycomb lattice Hubbard model