Balancing the Pauling bond orders in Kekuléan benzenoid hydrocarbons

Abstract

We consider a cutting of the molecular graph B of a Kekuléan benzenoid molecule into two disconnected subgraphs, S and the other, by deleting from B certain edges. It is required that both subgraphs remain Kekuléan. 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 Kekuléan benzenoid system, the sum of the Pauling bond orders of the starred edges is equal to that for the unstarred edges.