Introduction to Graph Theory Paperback – 5 Mar 1996
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From the Back Cover
Graph Theory has recently emerged as a subject in its own right, as well as being an important mathematical tool in such diverse subjects as operational research, chemistry, sociology and genetics. Robin Wilson's book has been widely used as a text for undergraduate courses in mathematics, computer science and economics, and as a readable introduction to the subject for non-mathematicians.
The opening chapters provide a basic foundation course, containing such topics as trees, algorithms, Eulerian and Hamiltonian graphs, planar graphs and colouring, with special reference to the four-colour theorem. Following these, there are two chapters on directed graphs and transversal theory, relating these areas to such subjects as Markov chains and network flows. Finally, there is a chapter on matroid theory, which is used to consolidate some of the material from earlier chapters.
For this new edition, the text has been completely revised, and there is a full range of exercises of varying difficulty. There is new material on algorithms, tree-searches, and graph-theoretical puzzles. Full solutions are provided for many of the exercises.
Robin Wilson is Dean and Director of Studies in the Faculty of Mathematics and Computing at the Open University.
About the Author
Robin Wilson is Emeritus Professor of Pure Mathematics at the Open University, and Emeritus Professor of Geometry at Gresham College, London. He is also a former Fellow in Mathematics at Keble College, Oxford University, and now teaches at Pembroke College. He has written and edited almost 40 books on graph theory, combinatorics, the history of mathematics, and music, and is very involved with the communication and popularisation of mathematics.--This text refers to an out of print or unavailable edition of this title.
Top customer reviews
The book covers all the basic terms and theories, and then tackles the classic problems: traveling salesmen, map colouring, who you should marry (!) etc. It provides detailed proofs for those who like that kind of thing, while still being a accessible book for those who want to skip the reasoning to move straight onto the algorithms for solving problems.
It does, however, have some down-points. The later chapters rely quite heavily on ideas introduced during the more complex exercises. Although this is pointed out by the author, it wouldn't help those wanting to dip into sections. In addition, the book flits somewhat rapidly through flow calculations and could also do with updating to include some mention of small-world theory in order to really cover all that's likely to be interesting to a beginner. Otherwise a sound introduction for a broad audience.
This book is printed upon good quality paper in a strong binding. The text is of a good size so those who need spectacles to read can manage better and its easier to read when holding the book.
*Briefly, what is graph Theory?
G. T. is a way of displaying relationships within information elements using finite sets of nodes and lines (edges). You may have heard of some of these such as the famous 'konigsberg' bridges problem, and the London underground.
* Items explored
At this level of studies, the following are discussed more widely, isomorphic graphs ( p. 9) that vary between relationships, chemical molecules, optimising of travel networks ' the Minimum Connector Problem' (p. 52-53) and 'Kirchoff' laws '/ Euler methods within small electrical networks (p. 54) operated with tree diagrams / planar graphs and network flows. These are really useful and well explained.
* Items discussed in In more depth
In more rewarding manner it concentrates upon 'Chinese Postman Problem' (p. 38 - 40) and 'Travelling Salesman Problem' (p. 41- 42 ) , deep or broad data searches, 'Weighted Activity Networks (Digraph) ' (p. 100 - 105). These are quite interesting to follow through and see how they operate. Basically, its the shortest way around a map of a place without repeating a road already used.
* important items in depth
A later part is to explore how to stop maps of countries having the same bordering colours, Chapter 6, (p. 81 -99). These methods have been applied in undergraduate programming studies to compose code and simulate the actions of road mapping software. If you read these book at these points makes its very clear and revealing explanation of the concepts. The coding for this is not in this book, however.
Its a nice book on a new - to - me topic. Its classed as an easier mathematical topic as so its needs less prerequisite studies than some other topics. Its still a satisfying easier topic at this undergraduate level. There are many examples questions and worked versions in the back pages of the book.
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