Abstract
The Kekule structure count (K) of a planar graph (in the graph-theoretical sense) is obtainable as the Pfaffian of a skew-symmetric adjacency matrix. This principle was used to design a general computer program for theK numbers of coronoid systems. Thus it became possible for the first time to determineK, as a matter of routine, during the computer-aided generation and enumeration of all types of Kekulean coronoids, including those where perimeters of [4k] cycles are present. The methods are exemplified by a complete account (with figures andK numbers] of the 27 half essentially disconnected coronoids with the phenalene hole and 11 or 12 hexagons.
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