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We analyze various possible superconducting pairing states and their relative stabilities in lightly doped graphene. It is shown that, when inter-sublattice electron-electron attractive interaction dominates and the Fermi level is close to the Dirac points, the system will favor intra-valley spin-triplet p + ip pairing state. Based on the novel pairing state, we further propose a scheme for doing topological quantum computation in graphene by engineering local strain fields and external magnetic fields. [ABSTRACT FROM AUTHOR]