Counts of Resonance Structures and Related Items

3 Counts of Resonance Structures and Related Items. - Resonance-theoretic based enumerations seem to have been somewhat less studied dining the last two years, though a deeade or two ago there were tremendous niunbers of papers. For the case of Kekule-structure enumeration the methods we deem more powerfijl or elegant have been briefly indieated in Seetions 3.2 and 3.3. Perhaps the eurrent relative quietness of the field indieates that now developed methods are near optimum. StiU there has been some work. 

In a series of papers Dias has derived expressions for resonanee-strueture counts of several classes of mono- and diradical benzenoid hydrocarbons. The considered classes belong to polymer graphs which were extensively studied some 

Zhang and Zhang have strengthened Gutman s result on the extremal values of Hosoya and Merrifield-Simons indices for hexagonal chains. These two indices are defined as sums of the absolute values of coefficients of the matching 

The so-called algebraic structure count is closely related to Kekule structures but in many cases is more difficult to evaluate. It is defined as the absolute difference of the numbers of two parities positive and negative) of Kekule structures. This algebraic structure count coincides with K G) for benzenoids, but for more general alternants it has been advocated as a more reliable measure of aromaticity than K G). Closed expressions for several special classes have been derived by Gutman et Recently Graovac et al. have formulated 

Lin and Fan have described an algorithm for finding all so-called linearly independent and minimal linearly independent conjugated circuits in benzenoid hydrocarbons. A different resolution into different-shaped conjugated circuits has also been advocated elsewhere. In another paper Lin has used a simpler approach to count only the few smallest conjugated circuits. 

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