The explicit determination of the number of monomer–dimer arrangements on a network is a theoretical challenge, and exact solutions to monomer–dimer problem are available only for few limiting graphs with a single monomer on the boundary, e.g., rectangular lattice and quartic lattice; however,...

The problem of spanning trees is closely related to various interesting problems in the area of statistical physics, but determining the number of spanning trees in general networks is computationally intractable. In this paper, we perform a study on the enumeration of spanning trees in a...