Monomer-dimer problem on some networks

Zhang et al. (2012) obtained the exact formula for the number of all possible monomer-dimer arrangements and the asymptotic growth constant on a scale-free small-world network. In this note, we generalize this result and obtain the exact solution on the monomer-dimer model on many networks. Particularly, we prove that these networks have the same asymptotic growth constant of the number of monomer-dimer arrangements.