Phase transitions in the Hubbard model and ionic Hubbard model at half-filling on the honeycomb lattice are investigated in the strong coupling perturbation theory which corresponds to an expansion in powers of the hopping t around the atomic limit. Within this formulation we find analytic expressions for the single-particle spectrum, whereby the calculation of the insulating gap is reduced to a simple root finding problem. This enables high precision determination of the insulating gap that

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... s not require any extrapolation procedure. The critical value of Mott transition on the honeycomb lattice is obtained to be U_c≈ 2.38 t. Studying the ionic Hubbard model at the lowest order, we find two insulating states, one with Mott character at large U and another with single-particle gap character at large ionic potential, Δ. The present approach gives a critical gapless state at U=2Δ at lowest order. By systematically improving on the perturbation expansion, the density of states around this critical gapless phase reduces.