Monomer-dimer model on a scale-free small-world network

► We first address the monomer-dimer problem on scale-free small-world networks. ► We obtain an exact formula for the number of all monomer-dimer arrangements. ► We find the dimer-monomer constant of the network. ► The constant is much less than that for some graphs without scale-free behavior. ► Scale-free networks have a distinct structure as opposed to regular lattices and fractals.