Chemical Graph Theory: Introduction and Fundamentals

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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.
 

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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
Polynomials
136
The Characteristic Polynomial
137
The Matching Polynomial
152
More Graphic Polynomials
164
References
169
ENUMERATION OF ISOMERS Alexandru T Balaban
177
Introduction
178
Definitions and Mathematical Background
179

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
Historical
184
Pólyas Theorem
187
Generalized Pólya Theorem
197
Ruchs Double Coset Form ism
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 7Electron Energy
256
Topological Resonance Energy 262
262
Concluding Remarks
272
References
273
INDEX
281
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Bonchev\, D

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