ABSTRACT

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.

chapter 1|2 pages

Introduction

chapter 2|2 pages

The First Use of Chemical Graphs

chapter 3|5 pages

The Emergence of Structure Theory

chapter 4|6 pages

The Concqit of Valence

chapter 5|2 pages

The Growth of Chemical Gn^h Theory

chapter 6|4 pages

Isomer Enumeration Techniques

chapter 7|4 pages

Early Additivity Studies

chapter 8|4 pages

The Introduction of Topological Indices

chapter 9|3 pages

Elementary Bonding Theory

chapter 10|1 pages

Conclusion

chapter 11|7 pages

References

part 2|1 pages

ELEMENTS OF GRAPH THEORY FOR CHEMISTS

chapter 1|3 pages

What is a Graph and What Kinds of Graph Exist?

ByOskar E. Polansky

chapter 2|2 pages

Some Graph-theoretical Terms

chapter 3|7 pages

Connectedness of Graphs

chapter 4|3 pages

Partitioning of a Grtqrh

chapter 5|5 pages

Planarity of Graphs

chapter 6|1 pages

Line Graphs

chapter 7|4 pages

Operations on Graphs

chapter 8|11 pages

The Automorphism Group of a Graph

chapter 10|2 pages

The Matrix Representation of Digraphs

chapter 11|4 pages

Distances in Gr^hs and Digraphs

chapter 14|1 pages

Weighted Graphs

chapter 15|2 pages

Bibliography

chapter |1 pages

Acknowledgment

chapter 1|4 pages

Introduction

ByAlan L. Goodson

chapter 2|4 pages

Development of Chemical Nomenclature

chapter 3|2 pages

Development of Chemical Line Notations

chapter 4|1 pages

Development of Graph Theory

chapter 6|1 pages

Summary

chapter 7|8 pages

References and Notes

chapter 1|2 pages

Why Polynomials in Graph Theory?

ByIvan Gutman

chapter 3|1 pages

Polynomials

chapter 4|13 pages

The Characteristic Polynomial

chapter 5|14 pages

The Matching Polynomial

chapter 6|5 pages

More Graphic Polynomials

chapter 7|8 pages

References

part 5|1 pages

ENUMERATION OF ISOMERS

chapter 1|1 pages

Introduction

chapter 2|5 pages

Definitions and Mathematical Background

chapter 3|3 pages

Historical

chapter 4|10 pages

Pólya’s Theorem

chapter 5|3 pages

Generalized Pólya Theorem

chapter 6|2 pages

Ruch’s Double Coset Formalism

chapter 8|7 pages

Valence Isomers

chapter 9|5 pages

Polyhexes

chapter 11|3 pages

Diastereomeric Annulenes

chapter 13|2 pages

Isomerism and Reaction Graphs

chapter 14|2 pages

Conclusion

chapter 11|9 pages

References

part 6|1 pages

GRAPH THEORY AND MOLECULAR ORBITALS

chapter 1|1 pages

Introduction

chapter 2|7 pages

Elements of Graph Spectral Theory

chapter 3|4 pages

The Essence of HUckel Theory

chapter 5|2 pages

The Spectrum of a Hiickel Graph

chapter 6|4 pages

The Number Non-bonding Molecular Orbitals

chapter 7|7 pages

Total Pi-Electron Energy

chapter 8|10 pages

Topological Resonance Energy

chapter 9|1 pages

Concluding Remarks