  We model the electrons on a monolayer graphene in terms of the compact and
non-compact U(1) lattice gauge theories. The system is analyzed by the strong
coupling expansion and is shown to be an insulator due to dynamical gap
formation in/around the strong coupling limit. This is similar to the
spontaneous chiral symmetry breaking in strong coupling gauge theories. The
results from the compact and non-compact formulations are compared up to the
next-to-leading order of the strong coupling expansion. Excitonic modes and
their dispersion relations in the insulating phase are also investigated: it is
found that there arises a pseudo-Nambu--Goldstone mode obeying the
Gell-Mann--Oakes--Renner type formula.
