  We consider the monomer-dimer model on weighted graphs embedded in surfaces
with boundary, with the restriction that only monomers located on the boundary
are allowed. We give a Pfaffian formula for the corresponding partition
function, which generalises the one obtained by Giuliani, Jauslin and Lieb for
graphs embedded in the disk. Our proof is based on an extension of a bijective
method mentioned in their paper, together with the Pfaffian formula for the
dimer partition function of Cimasoni-Reshetikhin.
