  A Kubo formalism is used to calculate the electronic and optical conductivity
of a graphene superlattice with Y-shaped kekul\'e bond texture, similar to that
visualized in recent experiments. We show that new conduction channels between
the valleys in graphene are opened by the kekul\'e distortion. This intervalley
contribution to the electronic transport is not present in pristine graphene
and here appears due to the folding of the Dirac cones $K$, $K'$ on top of each
other. The contribution of intervalley transport to the conductivity of
graphene, as well as the modification of the intravalley transport, are
analyzed in detail for different frequency, temperature, chemical potential and
scattering rate limits. We obtain analytical expressions for the conductivity
that reproduce previous expressions used to fit experimental measurements in
graphene and compare with direct numerical evaluations of the Kubo formula,
finding great agreement. The optical absorption arising from intervalley
transitions displays a maximum at a special frequency that can be tuned by
doping. Our results show how the single parameter describing the valley
coupling in this system could be obtained by measuring graphene's optical
absorbance in the region where interband transitions are blocked by the
impurities. Finally, we use Fermi's golden rule to independently verify some of
the previous results.
