Kekulé Structures in Benzenoid Hydrocarbons

1 - Introduction.- 1.1 Benzenoid Hydrocarbons.- 1.2 Historical Remarks.- 1.3 Importance of Kekulé Structures in the Theory of Benzenoid Hydrocarbons.- 2 - Benzenoid Systems: Basic Concepts.- 2.1 Introduction.- 2.2 Definitions and Relations.- 2.3 Classifications of Benzenoids.- 3 - Kekulé Structures and Their Numbers: General Results.- 3.1 Introduction.- 3.2 Theorems About K Numbers.- 3.3 Vertices and Edges in Kekulé Structures.- 3.4 Lower and Upper Bounds of K.- 3.5 Benzenoids with Extremal K.- 3.6 Generation of Normal Benzenoids.- 3.7 Isoarithmicity.- 4 - Introduction to the Enumeration of Kekulé Structures.- 4.1 Schematic Survey.- 4.2 Empirical Methods.- 4.3 Combinatorial Formulas, Especially for the Single Linear Chain.- 4.4 Recurrence Relations for Single Linear and Zigzag Chains.- 4.5 Summation Formulas for Single Linear and Zigzag Chains.- 4.6 Algorithms for Single Linear and Zigzag Chains.- 4.7 Combinatorial Formula for the Single Zigzag Chain.- 4.8 Treatment of a Pericondensed Benzenoid: The Parallelogram.- 4.9 General Remarks.- 4.10 Other Methods.- 5 - Non-Kekuléan and Essentially Disconnected Benzenoid Systems.- 5.1 Introduction.- 5.2 Introductory Examples.- 5.3 The Müller-Muller-Rodloff Rule.- 5.4 Characterization of Concealed Non-Kekuléan Benzenoid Systems.- 5.5 Segmentation.- 6 - Catacondensed Benzenoids.- 6.1 Previous Work.- 6.2 Single Unbranched Chain.- 6.3 Branched Chain.- 6.4 Catacondensed Ladder.- 6.5 Catacondensed All-Benzenoids and Related Systems.- 6.6 Limit Values Involving K Numbers.- 7 - Annelated Benzenoids.- 7.1 Definitions.- 7.2 Previous Work.- 7.3 Annelation to a Linear Chain.- 7.4 Annelation to a Zigzag Chain.- 7.5 Further Developments.- 7.6 Discussion of the Formulas.- 7.7 Algorithm.- 7.8 Dictionary of K Numbers withRelevance to Annelation.- 7 9 Annelation of Two Single Chains.- 7.10 Annelations of Special Benzenoids.- 8 - Classes of Basic Benzenoids (I).- 8.1 Introduction.- 8.2 Hexagon.- 8.3 Chevron.- 8.4 Ribbon.- 8.5 Parallelogram.- 9 - Classes of Basic Benzenoids (II): Multiple Zigzag Chain.- 9.1 Definition.- 9.2 Previous Work.- 9.3 Auxiliary Benzenoid Class.- 9.4 Recurrence Relations for A (n,m) with Fixed Values of n.- 9.5 Combinatorial K Formulas for A (n,m,l) With Fixed Values of m.- 9.6 Combinatorial K Formulas for Z (m,n) With Fixed Values of m.- 9.7 The Polynomial Pm(n) = K{Z(m,n)}.- 9.8 Algorithm.- 9.9 Some General Formulations.- 10 - Regular Three-, Four- and Five-Tier Strips.- 10.1 Previous Work.- 10.2 Definitions.- 10.3 Classification of Regular t-Tier Strips.- 10.4 Examples of Non-Regular t-Tier Strips.- 10.5 Dictionary of K Formulas For Regular 3-, 4- and 5-Tier Strips.- 10.6 Methods of Derivation of K Formulas for t-Tier Strips.- 10.7 The 4-Tier Zigzag Chain.- 11 - Classes of Basic Benzenoids (III).- 11.1 Introduction.- 11.2 Pentagons.- 11.3 Triangles.- 11.4 Streamers and Goblets.- 12 - Classes of Basic Benzenoids (IV): Rectangles.- 12.1 Definitions.- 12.2 Prolate Rectangle.- 12.3 Oblate Rectangle.- 12.4 Auxiliary Benzenoid Classes.- 12.5 Modified Oblate Rectangles.- 12.6 Some General Formulations Concerning Oblate Rectangles.- 13 - Regular Six-Tier Strips and Related Systems.- 13.1 Introduction.- 13.2 Six-Tier Strips.- 13.3 Supplement to the Methods of Derivation of K Formulas For t-Tier Strips.- 13.4 Auxiliary Benzenoid Classes.- 13.5 Two-Parameter K Formulas for Some Multiple Chains.- 13.6 Generalized Auxiliary Class.- 13.7 Étagère.- 13.8 Some Seven-Tier Strips: A Summing UP.- 14 - Determinant Formulas.- 14.1 Introduction.- 14.2 Hexagon.- 14.3Chevron.- 14.4 Ribbon.- 14.5 Parallelogram.- 14.6 Zigzag Chains.- 14.7 Pentagons.- 14.8 Oblate Rectangle.- 15 - Algorithm: A Generalization.- 15.1 Introduction.- 15.2 General Principles.- 15.3 Multiple Chains.- 15.4 Multiple Chains with Truncated Rows.- 15.5 Parallelogram with Truncated and Augmented Rows.- 15.6 Constructable Benzenoids.- 16 - Pericondensed All-Benzenoids and Related Classes.- 16.1 Introductory Remarks.- 16.2 All-Benzenoid Classes Including Modifications.- 16.3 Reticular All-Benzenoids.- 17 - Benzenoids with Repeated Units.- 17.1 Introduction.- 17.2 Fused Repeated Units.- 17.3 Condensed Repeated Units.- 17.4 Benzenoids with Hexagonal and Trigonal Symmetries.- 18 - Distribution of K, and Kekulé Structure Statistics.- 18.1 Introduction and Previous Work.- 18.2 Distribution of K.- 18.3 Average Values of K, and Related Quantities.- 18.4 Number of Normal Benzenoids with a Given K.