  The Casimir force between two infinitely thin parallel sheets in a setting of
$N$ such sheets is found. The finite two-dimensional conductivities, which
describe the dispersive and absorptive properties of each sheet, are taken into
account, whereupon the theory is applied to interacting graphenes. By exploring
similarities with in-plane optical spectra for graphite, the conductivity of
graphene is modeled as a combination of Lorentz type oscillators. We find that
the graphene transparency and the existence of a universal constant
conductivity $e^2/(4\hbar)$ result in graphene/graphene Casimir interaction at
large separations to have the same distance dependence as the one for perfect
conductors but with much smaller magnitude.
