Balancing the Pauling bond orders in Kekulean benzenoid hydrocarbons

We consider a cutting of the molecular graph B of a Kekulean benzenoid molecule into two disconnected subgraphs, S and the other, by deleting from B certain edges. It is required that both subgraphs remain Kekulean. The edges involved in this cutting are classified as starred and unstarred. A starred edge is incident to a starred carbon site of the subgraph S, whereas an unstarred edge to an unstarred carbon site of S. The following regularity is established: for any above-described cutting of any Kekulean benzenoid system, the sum of the Pauling bond orders of the starred edges is equal to that for the unstarred edges. (C) 2004 Elsevier B.V. All fights reserved.