In the last hundred years benzenoid hydrocarbons have constantly attracted the attention of both experimental and theoretical chemists. In spite of the fact that some of the basic concepts of the theory of benzenoid hydrocarbons have their origins in the 19th and early 20th century, research in this area is still in vigorous expansion. The present book provides an outline of the most important current theoretical approaches to benzenoids. Emphasis is laid on the recent developments of these theories, which can certainly be characterized as a significant advance. Em phasis is also laid on practical applications rather than on "pure" theory. The book assumes only some elementary knowledge of organic and physical chemistry and requires no special mathematical training. Therefore we hope that undergraduate students of chemistry will be able to follow the text without any difficulty. Since organic and physical chemists are nowadays not properly acquaint ed lVith the modern theory of benzenoid molecules, we hope that they will find this book both useful and informative. Our book is also aimed at theoretical chemists, especially those concerned with the "topological" features of organic molecules. The authors are indebted to Dr. WERNER SCHMIDT (Ahrensburg, FRG) for valuable discussions. One of the authors (1. G.) thanks the Royal Norwegian Council for Scientific and Industrial Research for financial support during 1988, which enabled him to stay at the University of Trondheim and write the present book. Trondheim, July 1989 Ivan Gutman Sven J. Cyvin Contents Chapter 1 Benzenoid Hydrocarbons .

This text is an attempt to outline the basic facts concerning Kekule 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).

In this collection from the working group meeting of November 2001, contributors formulate problems, share ideas and approaches, and plan an agenda for future interactions. Their fields included theoretical and applied computer science, statistics, discrete and non-discrete mathematics, chemistry and information science, and the topics centered on

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