The Connection Between the Adjacency Matrix and the Boundary Code of Benzenoid Hydrocarbons

In this work we wish to report a method for computing the adjacency matrix of benzenoid hydrocarbons from their boundary codes. The carbon skeletons of benzenoids will be depicted by graphs, called benzenoid graphs• , which can be constructed in the plane by assembhng h regular hexagons in such a way that two hexagons have exactly one joint edge or are disjoint, and the covered area in the plane is simply connected3•4• This restriction excludes benzenoid hydrocarbons with a »hole« in the interior, e. g. corannulenes. Since benzenoid graphs represent networks of hexagons5•6, it is also customary to call them, for brevity, polyhexes7• Another name used for these structures is arenes8• In the present report we will use the term polyhex for a benzenoid hydrocarbon.