Titlebook: Kekulé Structures in Benzenoid Hydrocarbons; S. J. Cyvin,I. Gutman Book 1988 Springer-Verlag Berlin Heidelberg 1988 Combinatorics.algorith

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,Kekulé Structures and their Numbers: General Results,n on generally valid statements, i.e. statements which hold for all benzenoids or for all Kekuléan benzenoids or (at least) for all catacondensed systems. We are, however, not going to list here the numerous known relations for ., which apply to more general classes of graphs (namely both benzenoid

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Classes of Basic Benzenoids (I),small parameters they degenerate to catacondensed systems. Some benzenoids related to those of the main classes are also treated. They are also basic in general, but may degenerate to composite or catacondensed systems, and even disconnected. Trivial cases of no hexagons with .=1 are also encountere

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Regular Three-, Four- and Five-Tier Strips,. The 3-tier strips are relatively simple and well known (Gordon and Davison 1952; Yen 1971; Cyvin 1986d). A systematic study of 4-tier strips has been performed more recently by Cyvin (1986d). Before that some studies of 5-tier strips had been published (Gordon and Davison 1952; Yen 1971; Ohkami an

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Benzenoids with Repeated Units,ins (see, e.g. Fig. 4.9 or CHART 6-II) may be considered as (trivial) benzenoids with repeated units. A less trivial example is the single chain with equal segments in a zigzag arrangement (CHART 6-II). Several typical examples are found among the all-benzenoid classes, both catacondensed (Section 6

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,Distribution of ,, and Kekulé Structure Statistics,he other hand it was known at that time that infinitely many benzenoids have .=9. Until quite recently the only known theorem about this question was: If .{B} = 2, then B = . (Gutman 1983). In other words, there exists one benzenoid with .=2. Furthermore, it was conjectured that there is one benzeno