This volume presents the fundamentals of graph theory and discusses specific chemical applications, providing a historical setting for the current interest in chemical graph theory and a background of the basic ideas and mathematical formalism of graph theory.
This volume presents the fundamentals of graph theory and discusses specific chemical applications, providing a historical setting for the current interest in chemical graph theory and a background of the basic ideas and mathematical formalism of graph theory.
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.
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.
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