Graph Theory Applications

1. Front Matter

   Pages i-xvii

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2. The Theory of Graphs

   1. Front Matter

      Pages 1-1

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   2. Basic Ideas

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      Pages 3-16

   3. Connectivity

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      Pages 17-25

   4. Trees

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      Pages 27-41

   5. Traversability

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      Pages 43-52

   6. Planarity

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      Pages 53-73

   7. Matrices

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      Pages 75-92

   8. Digraphs

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      Pages 93-122

   9. Coverings and Colourings

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      Pages 123-143

   10. Algorithms

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       Pages 145-181

   11. Matroids

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       Pages 183-191

3. Applications

   1. Front Matter

      Pages 193-193

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   2. Miscellaneous Applications

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      Pages 195-223

   3. Operations Research

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      Pages 225-267

   4. Electrical Engineering

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      Pages 269-290

   5. Industrial Engineering

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      Pages 291-321

   6. Science

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      Pages 323-341

   7. Civil Engineering

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      Pages 343-359

4. Back Matter

   Pages 361-386

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Over the last 30 years graph theory has evolved into an important math­ ematical tool in the solution of a wide variety of problems in many areas of society. The purpose of this book is to present selected topics from this theory that have been found useful and to point out various applications. Some important theoretical topics have been omitted as they are not es­ sential for the applications in Part II. Hence Part I should not be seen as a well-rounded treatise on the theory of graphs. Some effort has been made to present new applications that do not use merely the notation and ter­ minology of graphs but do actually implement some mathematical results from graph theory. It has been written for final undergraduate year or first year graduate students in engineering, mathematics, computer science, and operations research, as well as researchers and practitioners with an inter­ est in graph theoretic modelling. Suggested plans for the reading of the book by people with these interests are given later. The book comprises two parts. The first is a brief introduction to the mathematical theory of graphs. The second is a discussion on the applications of this material to some areas in the subjects previously mentioned. It is, of course, possi­ ble to read only the first part to attempt to gain an appreciation of the mathematical aspects of graph theory. However even the purest of mathe­ maticians is strongly recommended to delve seriously into the second part.

• Graph theory
• Matching
• algorithms
• graphs
• mathematics
• network
• combinatorics

L.R. Foulds

Graph Theory Applications

"This book put[s] together the theory and applications of graphs in a single, self-contained, and easily readable volume . . . the fundamentals of graph theory are presented in a very accessible way . . . Each part is divided into chapters, each concluding with a summary and a nice collection of exercises . . . The book can serve as an excellent textbook for a course in graph theory either at the undergraduate or graduate level. It can also be used by researchers in application areas who use graph theory in their research or by pure graph theorists who want to know about the applications of their research."—ZENTRALBLATT MATH

• Department of Management Systems, University of Waikato, Hamilton, New Zealand

  L. R. Foulds

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