Kekulé Structures in Benzenoid Hydrocarbons (Lecture Notes in Chemistry, 46)

This text is an attempt to outline the basic facts concerning Kekul€ structures in benzenoid hydrocarbons: their history, applica­ tions and especially enumeration. We further pOint out the numerous and often quite remarkable connections between this topic and various parts of combinatorics and discrete mathematics. Our book is primarily aimed toward organic and theoretical chemists interested in the enume­ ration of Kekule structures of conjugated hydrocarbons as well as to scientists working in the field of mathematical and computational chemistry. The book may be of some relevance also to mathematicians wishing to learn about contemporary applications of combinatorics, graph theory and other branches of discrete mathematics. In 1985, when we decided to prepare these notes for publication, we expected to be able to give a complete account of all known combi­ natorial formulas for the number of Kekule structures of benzenoid hydrocarbons. This turned out to be a much more difficult task than we initially realized: only in 1986 some 60 new publications appeared dealing with the enumeration of Kekule structures in benzenoids and closely related topics. In any event, we believe that we have collec­ ted and systematized the essential part of the presently existing results. In addition to this we were delighted to see that the topics to·which we have been devoted in the last few years nowadays form a rapidly expanding branch of mathematical chemistry which attracts the attention of a large number of researchers (both chemists and mathematicians). Front Matter....Pages N2-XV Introduction....Pages 1-7 Benzenoid Systems: Basic Concepts....Pages 8-23 Kekulé Structures and their Numbers: General Results....Pages 24-32 Introduction to the Enumeration of Kekulé Structures....Pages 33-50 Non-Kekuléan and Essentially Disconnected Benzenoid Systems....Pages 51-58 Catacondensed Benzenoids....Pages 59-82 Annelated Benzenoids....Pages 83-103 Classes of Basic Benzenoids (I)....Pages 104-133 Classes of Basic Benzenoids (II): Multiple Zigzag Chain....Pages 134-154 Regular Three-, Four- and Five-Tier Strips....Pages 155-180 Classes of Basic Benzenoids (III)....Pages 181-199 Classes of Basic Benzenoids (IV): Rectangles....Pages 200-225 Regular Six-Tier Strips and Related Systems....Pages 226-244 Determinant Formulas....Pages 245-272 Algorithm: A Generalization....Pages 273-279 Pericondensed All-Benzenoids and Related Systems....Pages 280-290 Benzenoids with Repeated Units....Pages 291-313 Distribution of K , and Kekulé Structure Statistics....Pages 314-334 Back Matter....Pages 335-349 This text outlines the basic facts concerning Kekulé structures in benzenoid hydrocarbons: their history, applications and especially enumeration. The book is primarily aimed at organic and theoretical chemists interested in the enumeration of Kekulé structures of conjugated hydrocarbons as well as to scientists working in the field of mathematical and computational chemistry. The level of mathematics required from the reader matches the skills of normally educated undergraduate chemistry students. Furthermore, all important combinatorial formulas are exemplified and illustrated by pertinent special cases. The book may be of some relevance also to mathematicians wishing to learn about contemporary applications of combinatorics, graph theory and other branches of discrete mathematics Contents: Introduction Benzenoid Systems: Basic Concepts Kekulé Structures and Their Numbers: General Results Introduction to the Enumeration of Kekulé Structures Non-Kekuléan and Essentially Disconnected Benzenoid Systems Catacondensed Benzenoids Annelated Benzenoids Classes of Basic Benzenoids (I) Classes of Basic Benzenoids (II): Multiple Zigzag Chain Regular Three-, Four- and Five-Tier Strips Classes of Basic Benzenoids (III) Classes of Basic Benzenoids (IV): Rectangles Regular Six-Tier Strips and Related Systems Determinant Formulas Algorithm: A Generalization Pericondensed All-Benzenoids and Related Classes Benzenoids with Repeated Units Distribution of K, and Kekulé Structure Statistics Bibliography Subject Index.