Kekulé Structures in Benzenoid Hydrocarbons

1. Front Matter

   Pages N2-XV

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2. Introduction

   • S. J. Cyvin, I. Gutman

   Pages 1-7

3. Benzenoid Systems: Basic Concepts

   • S. J. Cyvin, I. Gutman

   Pages 8-23

4. Kekulé Structures and their Numbers: General Results

   • S. J. Cyvin, I. Gutman

   Pages 24-32

5. Introduction to the Enumeration of Kekulé Structures

   • S. J. Cyvin, I. Gutman

   Pages 33-50

6. Non-Kekuléan and Essentially Disconnected Benzenoid Systems

   • S. J. Cyvin, I. Gutman

   Pages 51-58

7. Catacondensed Benzenoids

   • S. J. Cyvin, I. Gutman

   Pages 59-82

8. Annelated Benzenoids

   • S. J. Cyvin, I. Gutman

   Pages 83-103

9. Classes of Basic Benzenoids (I)

   • S. J. Cyvin, I. Gutman

   Pages 104-133

10. Classes of Basic Benzenoids (II): Multiple Zigzag Chain

    • S. J. Cyvin, I. Gutman

    Pages 134-154

11. Regular Three-, Four- and Five-Tier Strips

    • S. J. Cyvin, I. Gutman

    Pages 155-180

12. Classes of Basic Benzenoids (III)

    • S. J. Cyvin, I. Gutman

    Pages 181-199

13. Classes of Basic Benzenoids (IV): Rectangles

    • S. J. Cyvin, I. Gutman

    Pages 200-225

14. Regular Six-Tier Strips and Related Systems

    • S. J. Cyvin, I. Gutman

    Pages 226-244

15. Determinant Formulas

    • S. J. Cyvin, I. Gutman

    Pages 245-272

16. Algorithm: A Generalization

    • S. J. Cyvin, I. Gutman

    Pages 273-279

17. Pericondensed All-Benzenoids and Related Systems

    • S. J. Cyvin, I. Gutman

    Pages 280-290

18. Benzenoids with Repeated Units

    • S. J. Cyvin, I. Gutman

    Pages 291-313

19. Distribution of K, and Kekulé Structure Statistics

    • S. J. Cyvin, I. Gutman

    Pages 314-334

20. Back Matter

    Pages 335-349

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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).

• Combinatorics
• algorithms
• computational chemistry
• discrete mathematics
• graph
• graph theory
• complexity

• The Norwegian Institute of Technology, Division of Physical Chemistry, The University of Trondheim, Trondheim-NTH, Norway

  S. J. Cyvin

• Faculty of Science, University of Kragujevac, Kragujevac, Yugoslavia

  I. Gutman

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