Rapid ways to recognize Kekuléan benzenoid systems

Abstract

This chapter presents rapid ways to determine whether or not a given benzenoid system possesses a Kekulé structure. Two simple were discovered by Sachs and the present author, respectively. Both algorithms operate by deleting vertices and edges from the benzenoid system examined. Emphasis is given to the algorithm proposed by the present author. The algorithm seems to be the simplest of the presently known ones. Its simplicity consists of the fact that is performed diagrammatically without the need for arithmetic operations. Also, simple procedures are described for examining two special classes of benzenoid systems; (1) the benzenoid systems with consecutively located peaks on the perimeters, (2) R:S with a normal benzenoid system S. Meanwhile, some concepts, such as monotonic paths, generalized benzenoid systems, convex pairs and quasi-benzenoid systems, are reviewed. Some structural properties of benzenoid systems are described with detailed exposition.