I — Introduction.- 1 — Coronoid Hydrocarbons.- 1.1 Introduction.- 1.2 Cycloarenes.- 1.2.1 The Story of Kzkulen.- 1.2.2 Other Cycloarene.- 1.3 Corannulenes.- 1.4 Other Macrocyclic Conjugated Hydrocarbons.- 1.4.1 Introductio.- 1.4.2 Annulene.- 1.4.3 Annulenoannulene.- 1.4.4 Annelated Annulene.- 2 — Coronoids and Coronoid-Like Systems.- 2.1 Coronoid System.- 2.1.1 Basic Definitions.- 2.1.2 Terminology.- 2.2 Interlude.- 2.2.1 Coronoid Systems and Coronoid Hydrocarbons.- 2.2.2 Kekulé Structures.- 2.3 Non-Coronoid Systems.- 2.4 Degenerate Coronoid Systems.- 2.5 Quasi-Coronoid Systems.- 2.5.1 Coronene and Some of Its Derivatives.- 2.5.2 Helicenic Systems.- 2.6 Concluding Remarks.- II — Anatomy.- 3 — Anatomy: General Treatment.- 3.1 Introduction.- 3.2 Basic Concepts.- 3.2.1 Hexagon Modes and Some Structural Features.- 3.2.2 Vertices and Edges. Some Invariants.- 3.2.3 Extremal Values of Some Invariants.- 3.2.4 Coloring of Vertices. More Invariants.- 3.3 Classification.- 3.3.1 Introduction.- 3.3.2 Classification According to Internal Vertices.- 3.3.3 Kekuléan and non-Kekuléan Coronoids.- 3.3.4 The "neo” Classification.- 3.3.5 Introduction to Regular and Half Essentially Disconnected Coronoids.- 3.3.6 Regular Addition and Regular Tearing Down.- 3.3.7 The "rheo” and "rio” Classifications.- 3.3.8 Symmetry.- 3.4 Aromatic Sextets and All-Coronoids.- 3.4.1 Aromatic Sextet.- 3.4.2 Clar Structure.- 3.4.3 All-Coronoid.- 4 — Primitive Coronoids (I) and Annulenes: Anatomy.- 4.1 Introduction.- 4.2 Some Topological Properties of Primitive Coronoids.- 4.2.1 Definition.- 4.2.2 Corona Hole.- 4.2.3 Corners.- 4.2.4 Segments.- 4.2.5 Perimeters ".- 4.2.6 Symmetry.- 4.3 Notation.- 4.4 Associated Chain with a Primitive Coronoid.- 4.4.1 Definition.- 4.4.2 Single Unbranched Chains.- 4.5 Hollow Hexagon.- 4.6 Extremal Properties of the Corona Holes of Primitive Coronoids.- 4.7 Annulene.- III — Enumeration.- 5 — Enumeration: General Treatment and Coarse Classifications.- 5.1 Introduction.- 5.2 General Principles.- 5.3 Survey of Polyhexes.- 5.4 Some Coarse Classifications of Coronoids.- 5.4.1 Catacondensed and Pericondensed.- 5.4.2 The vio Classification.- 5.4.3 Classification According to Color Excess Benzenoids p. 67; Color Excess for Coronoids p. 68; Forms of Extremal Coronoids p. 70; Conjectures p. 72.- 5.4.4 Symmetry.- 5.5 Conclusion.- 6 — Primitive Coronoids (II) and Annulenes: Enumeration.- 6.1 Previous Work.- 6.2 Hollow Hexagons.- 6.2.1 Method of Generation (I).- 6.2.2 Symmetry Considerations.- 6.2.3 Enumeration Results.- 6.2.4 Method of Generation (II).- 6.2.5 Forms.- 6.3 Primitive Coronoids.- 6.3.1 Method of Generation (I).- 6.3.2 Method of Generation (II).- 6.3.3 Extended Computations.- 6.3.4 Forms.- 6.4 Primitive Coronoids with Constant Segment Lengths.- 6.4.1 Introductory Remarks.- 6.4.2 Primitive Coronoids with 2-Segments Only.- 6.4.3 Primitive Coronoids with Z-Segments Only, Especially for Z > 2.- 6.5 Annulenes.- 7 — Enumeration and Classification of Non-Primitive Coronoids.- 7.1 Non-Primitive Kekuléan Coronoids.- 7.1.1 Regular Systems.- 7.1.2 Irregular Systems.- 7.2 Classification According to the Color Excess.- 7.3 Concealed Non-Kekuléan Coronoids.- 8 — Enumeration and Classification of Coronoids with Definite Holes.- 8.1 Introduction.- 8.2 Supplementary Topological Properties.- 8.2.1 Outside and Inside Features.- 8.2.2 Basic Coronoid.- 8.3 Basic Coronoids.- 8.3.1 Generation and Enumeration.- 8.3.2 Forms.- 8.4 Definite Corona Holes.- 8.4.1 First Survey.- 8.4.2 Second Survey.- 8.4.3 Detailed Classification.- 9 — Enumeration: Numbers of Internal Vertices.- 9.1 Introduction.- 9.2 Coronoid Chemical Isomers.- 9.3 Computational Results.- 9.4 Corona Holes and their Invariants.- 9.4.1 Numbers of Corona Holes.- 9.4.2 Extremal Values Associated with Corona Holes.
The present studies of coronoid systems is a natural continua tion of the corresponding studies of benzenoid systems. Both topics are rooted in organic chemistry through certain polycyclic conjugated hydrocarbons, which are the chemical counterparts of the systems in question. HO'v'Tever, the scope of the present work and corresponding works on benzenoids goes far beyond a chemical motivation. These works are classified under mathematical chemistry, a relatively new designa tion. The book is supposed to have an interest for organic chemists within certain specialities, but still more for theoretical and mathe matical chemists. The last category has been characterized as enfants terribles in the foreword of the first issue of the Journal of Mathe matical Chemistry (1987). Finally, this book may have a considerable interest for mathematicians within combinatorics and gra~h theory. It is supposed that the book will be most useful for researchers, including graduate students, in the pertinent fields. The text contains no advanced mathematics whatsoever and should as such not represent any barrier even for undergraduate students. Here we wish to make some comments on the terminology, which is not standardized and is partly controversial in this field of topolo gical studies of polyhex (benzenoid and coronoid) systems.
I - Introduction.- 1 - Coronoid Hydrocarbons.- 2 - Coronoids and Coronoid-Like Systems.- II - Anatomy.- 3 - Anatomy: General Treatment.- 4 - Primitive Coronoids (I) and Annulenes: Anatomy.- III - Enumeration.- 5 - Enumeration: General Treatment and Coarse Classifications.- 6 - Primitive Coronoids (II) and Annulenes: Enumeration.- 7 - Enumeration and Classification of Non-Primitive Coronoids.- 8 - Enumeration and Classification of Coronoids with Definite Holes.- 9 - Enumeration: Numbers of Internal Vertices.
Inhaltsverzeichnis
I - Introduction.- 1 - Coronoid Hydrocarbons.- 2 - Coronoids and Coronoid-Like Systems.- II - Anatomy.- 3 - Anatomy: General Treatment.- 4 - Primitive Coronoids (I) and Annulenes: Anatomy.- III - Enumeration.- 5 - Enumeration: General Treatment and Coarse Classifications.- 6 - Primitive Coronoids (II) and Annulenes: Enumeration.- 7 - Enumeration and Classification of Non-Primitive Coronoids.- 8 - Enumeration and Classification of Coronoids with Definite Holes.- 9 - Enumeration: Numbers of Internal Vertices.
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