Bounds for the Kekule Structure Count

Finding upper and lower bounds for the K-value of benzenoid systems is intimately related to the identification of benzenoids with extremal (minimum and maximum) number of Kekule structures. Clearly, such benzenoids are expected to possess unusual chemical properties (e.g. to be highly reactive or exceptionally stable). 

For catacondensed systems with h hexagons the following bounds have been obtained [81] 

Later Cyvin and Chen [82, 83] improved the above upper bound as  

Recently John [84] offered an even better upper bound, viz. 

The only available exact result of this kind, applicable to all benzenoid systems is a complicated, but by no means a sharp upper bound [85]  

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