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2022 | Buch

Graph and Network Theory

An Applied Approach using Mathematica®

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This textbook covers a diversity of topics in graph and network theory, both from a theoretical standpoint, and from an applied modelling point of view. Mathematica® is used to demonstrate much of the modelling aspects. Graph theory and model building tools are developed in tandem with effective techniques for solving practical problems via computer implementation. The book is designed with three primary readerships in mind. Individual syllabi or suggested sequences for study are provided for each of three student audiences: mathematics, applied mathematics/operations research, and computer science. In addition to the visual appeal of each page, the text contains an abundance of gems. Most chapters open with real-life problem descriptions which serve as motivation for the theoretical development of the subject matter. Each chapter concludes with three different sets of exercises. The first set of exercises are standard and geared toward the more mathematically inclined reader. Many of these are routine exercises, designed to test understanding of the material in the text, but some are more challenging. The second set of exercises is earmarked for the computer technologically savvy reader and offer computer exercises using Mathematica. The final set consists of larger projects aimed at equipping those readers with backgrounds in the applied sciences to apply the necessary skills learned in the chapter in the context of real-world problem solving. Additionally, each chapter offers biographical notes as well as pictures of graph theorists and mathematicians who have contributed significantly to the development of the results documented in the chapter. These notes are meant to bring the topics covered to life, allowing the reader to associate faces with some of the important discoveries and results presented. In total, approximately 100 biographical notes are presented throughout the book.

The material in this book has been organized into three distinct parts, each with a different focus. The first part is devoted to topics in network optimization, with a focus on basic notions in algorithmic complexity and the computation of optimal paths, shortest spanning trees, maximum flows and minimum-cost flows in networks, as well as the solution of network location problems. The second part is devoted to a variety of classical problems in graph theory, including problems related to matchings, edge and vertex traversal, connectivity, planarity, edge and vertex coloring, and orientations of graphs. Finally, the focus in the third part is on modern areas of study in graph theory, covering graph domination, Ramsey theory, extremal graph theory, graph enumeration, and application of the probabilistic method.

Inhaltsverzeichnis

Frontmatter

Topics in Network Optimisation

Frontmatter
Chapter 1. An introduction to graphs
Michael A. Henning, Jan H. van Vuuren
Chapter 2. Graph connectedness
Michael A. Henning, Jan H. van Vuuren
Chapter 3. Algorithmic complexity
Michael A. Henning, Jan H. van Vuuren
Chapter 4. Optimal paths
Michael A. Henning, Jan H. van Vuuren
Chapter 5. Trees
Michael A. Henning, Jan H. van Vuuren
Chapter 6. Location problems
Michael A. Henning, Jan H. van Vuuren
Chapter 7. Maximum flow networks
Michael A. Henning, Jan H. van Vuuren
Chapter 8. Minimum-cost network flows
Michael A. Henning, Jan H. van Vuuren

Topics in Classical Graph Theory

Frontmatter
Chapter 9. Matchings
Michael A. Henning, Jan H. van Vuuren
Chapter 10. Eulerian graphs
Michael A. Henning, Jan H. van Vuuren
Chapter 11. Hamiltonian graphs
Michael A. Henning, Jan H. van Vuuren
Chapter 12. Graph connectivity
Michael A. Henning, Jan H. van Vuuren
Chapter 13. Planarity
Michael A. Henning, Jan H. van Vuuren
Chapter 14. Graph colouring
Michael A. Henning, Jan H. van Vuuren
Chapter 15. Oriented graphs
Michael A. Henning, Jan H. van Vuuren

Topics in Modern Graph Theory

Frontmatter
Chapter 16. Domination in graphs
Michael A. Henning, Jan H. van Vuuren
Chapter 17. Ramsey theory
Michael A. Henning, Jan H. van Vuuren
Chapter 18. Extremal graph theory
Michael A. Henning, Jan H. van Vuuren
Chapter 19. Graph enumeration
Michael A. Henning, Jan H. van Vuuren
Chapter 20. The probabilistic method
Michael A. Henning, Jan H. van Vuuren
Backmatter
Metadaten
Titel
Graph and Network Theory
verfasst von
Michael A. Henning
Jan H. van Vuuren
Copyright-Jahr
2022
Electronic ISBN
978-3-031-03857-0
Print ISBN
978-3-031-03856-3
DOI
https://doi.org/10.1007/978-3-031-03857-0

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