  We theoretically study absorption by an undoped graphene layer decorated with
arrays of small particles. We discuss periodic and random arrays within a
common formalism, which predicts a maximum absorption of $50\%$ for suspended
graphene in both cases. The limits of weak and strong scatterers are
investigated and an unusual dependence on particle-graphene separation is found
and explained in terms of the effective number of contributing evanescent
diffraction orders of the array. Our results can be important to boost
absorption by single layer graphene due to its simple setup with potential
applications to light harvesting and photodetection based on energy (F\"orster)
rather than charge transfer.
