Subgraph generating functions in chemistry— An example for perfect matchings on honeycomb fragments

Abstract

The analogous role of subgraph generating functions in statistical mechanics and in quantum-chemical theory is noted. To illustrate the analogy, the example of perfect matchings on hexagonal animals is considered. Isomorphisms to two types of multiple-walk problems are noted to reveal a “hidden order”, with physical relevance. This is further used to accomplished an enumeration of the perfect matchings on a class of hexagonal-animal strips of with and length.