Customer Reviews

Introduction to Graph Theory (Dover Books on Mathematics)

5 star:		(5)
4 star:		(3)
3 star:		(1)
2 star:		(0)
1 star:		(0)

 

 

One of the better Dover books I've picked up... but keep in mind it is a (very basic) introduction.

The book gives an introduction to graph theory (take the "introduction to" part of the title very seriously). To give an idea of the depth of this book, I read this book in about 6 hours prior to taking a course in graph theory (an undergraduate and graduate student mixed course), and the material in the book was covered in class in about 4 lectures (there were about 30 lectures in the course). This isn't to say the book isn't good (because it is), but I just have to emphasize it is a basic introduction.

What gives this book 5 stars is that it was written very well and made the material very interesting. I would recommend this book to someone looking to understand the very basics of graph theory, but I would not to someone looking for a thorough introduction to graph theory.

For reference, titles of chapters: 1) Pure Mathematics; 2) Graphs; 3) Planar Graphs; 4) Euler's Formula; 5) Platonic Graphs; 6) Coloring; 7) The Genus of a Graph; 8) Euler Walks and Hamilton Walks.

Mr. Trudeau has done a fabulous job of introducing graph theory in a way which is understandable and intellectually provocative. He mentions that some of the problems are easy, and that some have been unsolved. In both cases, they both are fully illustrative of the subject matter. If you want to begin exploring graph theory, this book is for you!

This book introduces graph theory terminology and elementary results to the absolute beginner. It does a nice job of presenting the material in the format "motivation-example-definitions-theorem-proof-remarks", which I find pedagogical.

Interspersed throughout the text are some historical remarks and a lot of author's personal opinions on what mathematics is or should be. This last piece of the text I liked least, since I do not agree with the author many times. He defends the position that "pure mathematics" is "real mathematics", and that "applied mathematics" follows from the "real thing" (he actually states this literally in the introduction of the book). This view has been debunked so many times along the history of the subject that it is quite irritating to see it expressed so categorically.

But the book is not about math philosophy, so I recommend it as a warm up to those interested in more heavy-duty graph theory.

I like this book as an intro to graph theory. I already had a little background in graph theory and a graduate degree in mathematics before I got this book, but I think that less experienced readers with an interest in pure math will enjoy this book. It's readable and conversational, and special attention is given to introducing pure mathematics and proof.

Wonderful book to read! If you want to get started in graph theory, this is your first stop. Go through all the proofs and problems, and you're on your way!

For anyone interested in graph theory who has not taken many upper level math classes, or has yet to take a course in discrete mathematics, this is a great introduction. For anyone, at any level, this is a fun and entertaining read. The book reads as if the author were standing in front of you at the chalkboard, masterfully teaching you the basics of the material, almost in layman's terms (but not quite), all with a witty sense of humor and a tendency towards anecdotes.

The material is in no way thorough, nor treated very rigorously. All the basics are there and taught in an intuitive manner. There are numerous exercises, none of which is difficult, but all of which are interesting to someone who is new to graph theory. Some of the key results that are simple to prove are done so in the exercises, encouraging readers to discover things for themselves.

Downsides: If you are looking for a rigorous book on graph theory, look elsewhere. But that is really the only downside!

Overall: I liked graph theory before reading this book. I loved graph theory after reading the first chapter.

This book provides a good but not rigorous great introduction to graph theory. The best audience is someone with mathematical ability but little education beyond high school or introductory math. That is, knowledge of analysis or higher is not required. Having finished this book, one could go on to the book entitled graph theory by the same publisher. It's hard to beat Dover's prices and selection for math books. The style of the book is conversational except for one more proof-oriented chapter. At the end of each chapter are graded problems with answers, a great plus for self-study.

Chapter on planar graphs is superbly done, with very easy to understand proofs and plenty of illustrations. Overall, a great introductory text

This book make you want to know more about graph theory. The concepts are first intuitively explained and then formally stated. The numerous examples are completely treated and then easy to follow. R. Trudeau devoted a large part of the book to the puzzling problems of planar graphs and coloring and explains them in a very pleasant manner. As a result, these problems almost appear as trivial (which of course is not the case).

The main criticism I would make is the following. This book is a corrected and enlarged version of another book. Unfortunately, the updating is not very convincing when the "four color problem" is a conjecture in the body of the book and a theorem in footnotes and afterwords.