Polyhex enumeration

Corrections to numerical errors in literature data are found throughout this chapter. As a principle, a wrong number from polyhex enumerations is never quoted. 

It also happens that new researchers are being attracted to the field of polyhex enumerations. E. C. Kirby (Resource Use Institute, Pitlochry, Scotland, UK) may be reckoned as one of them, although his latest contributions [141,143] were preceded by some other enumeration-oriented works [85,153]. His latest work [141] makes a significant contribution to our understanding of all-benzenoids. Another name, which has recently entered the arena, is William C. Herndon (University of Texas at El Paso, Texas, USA). His enumerations [138], based on a computerized coding system for polyhexes [154], is particularly chemistry-oriented inasmuch as it takes stereoisomerism into account. 

The reader is referred to the Number of Benzenoids and Poly hex Hydrocarbons subsection for the definition and classification of benzenoids and polyhex hydrocarbons, as well as for additional references for this class of compounds, which is only partially reviewed because of space limitations. Let us recall that the direct counting approach has difficulties with molecules that cannot be represented by tree-like structures, such as pericondensed polyhexes. Furthermore, the counting approach caimot separate nonplanar polyhexes (helicenes) from planar benzenoids. Consequently, for benzenoids and polyhexes, enumeration is not only a valuable tool that provides a concise description of the structures being enumerated, but also enumeration computes isomer numbers that cannot be derived otherwise. 

HarF70 Harary, F., Read, R. C. Enumeration of tree-like polyhexes. Proc. Edin. Math. Soc. Ser. II 17 (1970) 1-13. 

Cyvin BN, Brunvoll J, Cyvin SJ (1992) Enumeration of Benzenoid Systems and Other Polyhexes. 162 65-180... 

BCH03] G. Brinkmann, G. Caporossi, and P. Hansen, A survey and new results on computer enumeration of polyhex and fusene hydrocarbons, Journal of Chemical Information and Computer Science 43-3 (2003) 842-851. 

BCC92] J. Brunvoll, B.N. Cyvin, and S. J. Cyvin, Enumeration of benzenoid systems and other polyhexes, Topics in Curr. Chem. 162 (1992) 65-180. 

Since computer enumeration methods are still hampered by the explosive growth in the number of polyhex isomers having more than eleven hexagonal rings, the most practical approach is the enumeration of select benzenoid groups of interest to chemists [8],... 

The results of enumerations and classifications of polyhexes are reviewed and supplemented with new data. The numbers are collected in comprehensive tables and supplied with a thorough documentation from an extensive literature search. Numerous forms of the polyhexes are displayed, either as dualists or black silhouettes on the background of a hexagonal lattice. In the latter case, the Kekule structure counts for Kekulean systems are indicated. Emphasis is laid on the benzenoid systems (planar simply connected polyhexes). 

In Sect. 3 some classical results of enumeration of polyhexes are reported. They include Klamer numbers , Harary-Read numbers and Lunnon numbers , which were so beautifully (but not infallibly) sorted out for the first time by the Dusseldorf-Zagreb group [ 1 Reference to the Dusseldorf-Zagreb numbers is also contained in Sect. 3. Furthermore, original supplements to the different tables are found therein. 

Section 6 deals with the enumeration of catacondensed simply connected polyhexes, i.e. catacondensed benzenoids and helicenes. 

In the following we give a survey of the different centres which at present are engaged in the enumeration of polyhexes by computers. 

There are five researchers or groups which have been involved in computer-aided enumerations of polyhexes after 1985 [18] ... 

Survey of Enumeration Results for All Polyhexes 3.1 Benzenoids and Coronoids... 

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