Interface Theory of Benzenoids

Abstract

We propose here a novel tool for chemical graph theory, referred to in the following as the interface theory of benzenoids, designed for constructing, enumerating, and characterizing Clar covers of arbitrary benzenoids. The presented interface theory uses the new concepts of fragments and interfaces to express an arbitrary Clar cover of a benzenoid B as a collection of covering characters for the interface bonds in B. A set of fundamental theorems demonstrates that the interface theory is internally consistent. In particular, we are able to establish the necessary and sufficient conditions required for the existence and uniqueness of a Clar cover in terms of interface bond coverings. The proposed theoretical framework can be conveniently and efficiently used for determining whether a given benzenoid is Kekulean, for finding its Clar covers and Kekule structures, for computing its ZZ polynomials, as well as deriving closed forms of ZZ polynomials for whole families of structurally related benzenoids, and for many other interesting applications. We believe that the presented here interface theory of benzenoids opens up new vistas in chemical graph theory and may revolutionize the field in the future.