Resonance in elemental benzenoids (Q1917335)

This is concerned with enumerating bond structures on benzenoid graphs consisting of strips of a plane hexagonal lattice. The various ways of placing the double bonds are in \(1 - 1\) correspondence with placing non-overlapping dimers on the lattice, effectively a solved problem. This can also be related to the enumeration of directed self-avoiding walks on the lattice. These enumeration problems are extended to cylindrical graphs closed at the end by near-benzenoid caps. All these enumeration problems can be expressed in transfer matrix form, the eigenvalues of which are listed for a number of cases.