Chemical Graph Theory: Introduction and Fundamentals

D Bonchev

CRC Press, Jan 1, 1991 - Science - 300 pages

"This volume presents the fundamentals of graph theory and then goes on to discuss specific chemical applications. Chapter 1 provides a historical setting for the current upsurge of interest in chemical graph theory. chapter 2 gives a full background of the basic ideas and mathematical formalism of graph theory and includes such chemically relevant notions as connectedness, graph matrix representations, metric properties, symmetry and operations on graphs. This is followed by a discussion on chemical nomenclature and the ... Show more This volume presents the fundamentals of graph theory and then goes on to discuss specific chemical applications. Chapter 1 provides a historical setting for the current upsurge of interest in chemical graph theory. chapter 2 gives a full background of the basic ideas and mathematical formalism of graph theory and includes such chemically relevant notions as connectedness, graph matrix representations, metric properties, symmetry and operations on graphs. This is followed by a discussion on chemical nomenclature and the trends in its rationalization by using graph theory, which has important implications for the storage and retrieval of chemical information. This volume also contains a detailed discussion of the relevance of graph-theoretical polynomials; it describes methodologies for the enumeration of isomers, incorporating the classical Polya method, as well as more recent approaches. The final chapter considers the interplay between graph theory and molecular orbital theory from the standpoint of graph spectral theory, highlighting the concept of topographical resonance in molecular species"--Back cover.

Contents

• THE ORIGINS OF CHEMICAL GRAPH THEORY Dennis H Rouvray: 1
• The First Use of Chemical Graphs: 3
• The Emergence of Structure Theory: 5
• The Concept of Valence: 10
• The Growth of Chemical Graph Theory: 16
• Isomer Enumeration Techniques: 18
• Early Additivity Studies: 22
• The Introduction of Topological Indices: 26
• Elementary Bonding Theory: 30
• Conclusion: 33
• References: 34
• ELEMENTS OF GRAPH THEORY FOR CHEMISTS Oskar E Polansky: 41
• What is a Graph and What Kinds of Graph Exist?: 42
• Some Graphtheoretical Terms: 45
• Connectedness of Graphs: 47
• Partitioning of a Graph: 54
• Planarity of Graphs: 57
• Line Graphs: 62
• Operations on Graphs: 63
• The Automorphism Group of a Graph: 67
• Matrix Representation and Eigenvalue Problems of Undirected Graphs: 78
• The Matrix Representation of Digraphs: 83
• Distances in Graphs and Digraphs: 85
• Metric and Topological Spaces for Simple Graphs: 89
• Graphs in Quantum Chemistry: 93
• Bibliography: 94
• Acknowledgment: 96
• NOMENCLATURE OF CHEMICAL COMPOUNDS Alan L Goodson: 97
• Development of Chemical Nomenclature: 101
• Development of Chemical Line Notations: 105
• Development of Graph Theory: 107
• Summary: 124
• References and Notes: 125
• POLYNOMIALS IN GRAPH THEORY Ivan Gutman: 133
• Polynomials: 136
• The Characteristic Polynomial: 137
• The Matching Polynomial: 150
• More Graphic Polynomials: 164
• References: 169
• ENUMERATION OF ISOMERS Alexandru T Balaban: 177
• Introduction: 178
• Definitions and Mathematical Background: 179
• Historical: 184
• Pólyas Theorem: 187
• Generalized Pólya Theorem: 197
• Ruchs Double Coset Formalism: 200
• De BruijnHararyPalmer Power Group Theory: 202
• Valence Isomers: 203
• Polyhexes: 210
• Diamond Hydrocarbons and Staggered Alkane Rotamers: 215
• Diastereomeric Annulenes: 216
• Isomers and Computer Programs for Their Generation: 219
• Isomerism and Reaction Graphs: 222
• Conclusion: 224
• References: 226
• GRAPH THEORY AND MOLECULAR ORBITALS Nenad Trinajstić: 235
• Introduction: 236
• Elements of Graph Spectral Theory: 237
• The Essence of Hückel Theory: 244
• Isomorphism of Hückel Theory and Graph Spectral Theory: 248
• The Spectrum of a Hückel Graph: 249
• The Number Nonbonding Molecular Orbitals: 251
• Total πElectron Energy: 255
• Topological Resonance Energy: 262
• Concluding Remarks: 272
• References: 273
• INDEX: 281

Bibliographic information

• Title: Chemical Graph Theory: Introduction and Fundamentals; Volume 1 of Chemical Graph Theory, Danail Bonchev; Chemical Graph Theory: Introduction and Fundamentals, Danail Bonchev; Mathematical chemistry, ISSN 1049-2801
• Author: D Bonchev
• Edition: illustrated
• Publisher: CRC Press, 1991
• ISBN: 0856264547, 9780856264542
• Length: 300 pages
• Subjects: Science / Chemistry / Industrial & Technical