Variations on the Ising problem (Q1115451)

In a previous article we presented an exposition of the 2-dimensional Ising problem expressing it entirely in terms of enumerating even subgraphs of a labeled grid. On considering instead an unlabeled grid, the corresponding problem in graphical enumeration can be solved in the general n-dimensional case, thus providing a lower bound. A formulation of the analogous labeled and unlabeled problems for other regular graphs is proposed and it is discussed in particular for hypercubes.