  We show that for graphene with any finite difference in the on-site energy
between the two sub-lattices ($\Delta$), The optical absorption edge is
determined by the $\Delta$. The universal conductance will be broken and the
conductance near the band edge varies with frequency as $1/\omega^2$. Moreover,
we have identified another universal conductance for such systems without
inversion symmetry, i.e., the onset conductance at the band edge is $%
\sigma_c=2\sigma_0=\pi e^2/2h$, independent of the size of the band gap. The
total integrated optical response is nearly conserved despite of the opening of
the band gap.
