Cyvin, S: Theory of Coronoid Hydrocarbons II

Benzenoid.- 3.3.3 Naphthalenic Coronoid.- 3.3.4 Extremal Coronoid.- 3.4 First Enumeration Results for Benzenoids and Coronoids.- 3.5 Smallest Multiple Coronoids.- 3.5.1 Introduction.- 3.5.2 Basic Assumptions.- 3.5.3 Algorithm for Construction of Smallest Multiple Coronoids.- 3.5.4 Discussion and Depiction of Forms.- 3.5.5 Pericondensed Smallest Multiple Coronoids.- 3.6 Perfect and Imperfect Extremal Coronoids.- 3.6.1 Introduction.- 3.6.2 Numbers of Hexagons and of Internal Vertices.- 3.6.3 Catacondensed Extremal Coronoids.- 3.6.4 Extension to Pericondensed Extremal Coronoids.- 3.7 Chemical Formulas.- 3.7.1 Introduction and Notation.- 3.7.2 Inequalities for the Formula Coefficients.- 3.7.3 Table of Formulas.- 3.8 Numbers of Isomers.- 3.8.1 Definition and Notation.- 3.8.2 Numerical Values.- 4 - Invariants of Single Coronoids.- 4.1 Introduction.- 4.2 Summary of Invariants and Relations Between Them.- 4.2.1 Summary of Relations.- 4.2.2 Connectivity and the Dias Parameter.- 4.3 Maximum Number of Internal Vertices, and Minimum Number of Hexagons.- 4.3.1 Maximum Number of Internal Vertices, and Extremal Single Coronoids.- 4.3.2 Minimum Number of Hexagons.- 4.3.3 Spiral Walk.- 4.3.4 Perforated Polycircumcoronenes.- 4.4 Possible Values of Invariants.- 4.5 Upper and Lower Bounds for Some Invariants.- 4.5.1 General.- 4.5.2 Functions of the Number of Hexagons and of the Number of Internal Vertices.- 4.5.3 Functions of Invariants Other Than the Number of Hexagons and the Number of Internal Vertices.- 4.6 Minimum Number of Vertices of Degree Two, and Maximum Number of Hexagons.- 4.6.1 Minimum Number of Vertices of Degree Two.- 4.6.2 Maximum Number of Hexagons, and Circular Single Coronoids.- 4.6.3 Spiral Walk.- 4.6.4 Detailed Analysis.- 5 - Chemical Formulas of Single Coronoids.- 5.1 Introduction.- 5.2 Terminology.- 5.3 Inequalities in Terms of the Formula Coefficients.- 5.3 1 When is a Given Formula Compatible With a Single Coronoid?.- 5.3.2 Supplementary Inequalities.- 5.4 Circumscribing and Excising.- 5.4.1 Introduction.- 5.4.2 Definitions of Circumscribing and Excising for Coronoids.- 5.4.3 Possibilities of Circumscribing and Excising.- 5.4.4 Generalization for k-Fold Circumscribing and k--Fold Excising.- 5.4.5 Core Coronoids.- 5.4.6 Algebraic Treatment.- 5.4.7 Catacondensed Single Coronoids.- 5.4.8 Naphthalenic Single Coronoids.- 5.5 Extremal Single Coronoids and Some of Their Subclasses.- 5.5.1 Extremal Single Coronoids.- 5.5.2 Circumextremal Single Coronoids.- 5.5.3 Circular Single Coronoids.- 5.6 Extreme Single Coronoids.- 5.6.1 Definition.- 5.6.2 Formula.- 5.6.3 Nonextremal Extreme Single Coronoids.- 5.7 Table of Formulas.- 5.8 Single Coronoid Isomers and Number of Edges.- 6 - Further Studies of The Chemical Formulas of Single Coronoids.- 6.1 Introduction.- 6.2 Ground Forms and Higher Members.- 6.2.1 Introduction.- 6.2.2 Definitions and Preliminary Treatment.- 6.2.3 Perfect and Imperfect Ground Forms.- 6.2.4 Formulas for Perfect Ground Forms and for Higher Members.- 6.2.5 Formulas for Imperfect Ground Forms.- 6.2.6 Depictions.- 6.2.7 Mapping of Formulas.- 6.3 Formula Index.- 6.4 A Property of Circumscribing.- 6.5 Building-Up.- 6.5.1 Introduction and Basic Concepts.- 6.5.2 Fundamental Building-Up Principle.- 6.5.3 Addition Units.- 6.5.4 Application of the Fundamental Building-Up Principle to Isomers.- 6.5.5 Simplified Building-Up Principles.- 6.5.6 Formations Available for Addition.- 6.5.7 Further Deductions.- Supplement.- Introductory Remarks.- Summary of Formulas and Definitions.- Conclusion.- 7 - Generation and Enumeration of Single Coronoid Isomers.- 7.1 Tabulation of Complete Data.- 7.1.1 Introduction and Survey.- 7.1.2 Classification According to neo and the Color Excess.- 7.1.3 Classification According to the Corona Holes.- 7.2 Forms.- 7.3 Methods of Generation.- 7.3.1 Introduction.- 7.3.2 Application of the Fundamental Building-Up Principle.- 7.3.3 Perforating Benzenoids.- 7.3.4 Examples and Discussion.- 7.4 Circular Single Coronoids.- 7.4.1 Introduction.- 7.4.2 Methods.- 7.4.3 Sample Analysis.- 7.4.4 Extension to All Circular Single Coronoids.- 7.5 Circular Benzenoids Perforated by Phenalene Hole.- 7.5.1 Introduction.- 7.5.2 The Systems.- 7.5.3 Results of Enumeration.- 7.6 Circular Benzenoids Perforated by Coronene Hole.- 7.6.1 Introduction.- 7.6.2 The Systems.- 7.6.3 Results of Enumeration.- 7.7 Supplementary Enumeration Data.- 8 - Theorems for Single Coronoids.- 8.1 Introduction.- 8.2 Some Basic Concepts.- 8.2.1 Additions.- 8.2.2 Alternating Cycles.- 8.2.3 Edge Cuts.- 8.3 A Property of Kekulé Structures.- 8.4 Essentially Disconnected Single Coronoids.- 8.4.1 Properties and Lemmas.- 8.4.2 Main Theorem.- 8.4.3 "Essentially Disconnected Coronoids" are Essentially Disconnected.- 8.5 Normal Single Coronoids.- 8.6 Regular Single Coronoids.- 8.6.1 Definition.- 8.6.2 A Criterion for a Single Coronoid to be Regular.- 8.7 Half Essentially Disconnected Single Coronoids.- 8.7.1 Introductory Remark.- 8.7.2 Main Theorem.- 8.7.3 New Definition.- 8.7.4 Example.- 8.8 Kekuléan and Non-Kekuléan Single Coronoids.- 8.8.1 Introduction.- 8.8.2 Old Theorem.- 8.8.3 Additional Basic Concepts and Properties.- 8.8.4 Main Theorem.