Chemical Graph Theory

Bonchev/, D

1. THE ORIGINS OF CHEMICAL GRAPH THEORY/Dennis H. Rouvray -- 1. Introduction -- 2. The first Use of Chemical Graphs -- 3. The Emergence of Structure Theory -- 4. The Concept of Valence -- 5. The Growth of Chemical Graph Theory -- 6. Isomer Enumeration Techniques -- 7. Early Additivity Studies -- 8. The Introduction of Topological Indices -- 9. Elementary Bonding Theory -- 10. Conclusion -- 11. References -- 2. ELEMENTS OF GRAPH THEORY FOR CHEMISTS/Oskar E. Polansky -- 1. What is a Graph and What Kinds of Graph Exist? -- 2. Some Graph-theoretical Terms -- 3. Connectedness of Graphs -- 4. Partitioning of a Graph -- 5. Planarity of Graphs -- 6. Line Graphs -- 7. Operations on Graphs -- 8. The Autolllorphism Group of a Graph -- 9. Matrix Representation and Eigenvalue Problems of Undirected Graphs -- 10. The Matrix Representation of Digraphs -- 11. Distances in Graphs and Digraphs -- 12. Metric and Topological Spaces for Simple Graphs -- 13. Graphs in Quantum Chemistry -- 14. Weighted Graphs -- 15. Bibliography -- Acknowledgment -- 3. NOMENCLATURE OF CHEMICAL COMPOUNDS/Alan L. Goodson -- 1. Introduction -- 2. Development of Chemical Nomenclature -- 3. Development of Olemical Line Notations -- 4. Development of Graph Theory -- 5. Application of Graph Theory Olemical Nomenclature -- 6. Summary -- 7. References and Notes -- 4. POLYNOMIALS IN GRAPH THEORY/Ivan Gutman -- 1. Why Polynomials in Graph Theory? -- 2. On Olemical Applications of Graphic Polynomials -- 3. Polynomials -- 4. The Characteristic Polynomial -- 5. The Matching Polynomial -- 6. More Graphic Polynomials -- 7. References -- 5. ENUMERATION OF ISOMERS/Alexandru T. Balaban -- 1. Introduction -- 2. Definitions and Mathematical Background -- 3. Historical -- 4. Polya 's Theorem -- s. Generalized Polya Theorem -- 6. Ruch's Double Coset Formalism -- 7. De Bruijn-Harary-Palmer Power Group Theory -- 8. Valence Isomers -- 9. Polyhexes -- 10. Diamond Hydrocarbons and Staggered Alkane Rotamers -- 11. Diastereomeric Annulenes -- 12. Isomers and Compucer Programs for Their Generation -- 13. Isomerism and Reaction Graphs -- 14. Conclusion -- References -- 6 GRAPH THEORY AND MOLECULAR ORBITALS/Nenad TrlnajstiC -- 1. Introduction -- 2. Elements of Graph Spe:cttal Theory -- 3. The Essence of Hilckel Theory -- 4. Isomorphism of Hilckel Theory and Graph Spe:cttal Theory -- s. The Spectrum of a Hilckel Graph -- 6. The Number Non-bonding Molecular Orbitals -- 7. Totalx-Electton Energy -- 8. Topological Resonance Energy -- 9. Concluding Remarks -- 10. References -- INDEX.