Introduction to Graph Theory (Dover Books on Mathematics)

This is an AMAZING book, the authors style is so clear, fun and entertaining, without much mathematical rigor. This is an excelent introduction to graph theory if I may say. Im an electrical engineer and been wanting to learn about the graph theory approach to electrical network analysis, surprisingly there is very little information out there, and very few books devoted to the subject. I started reading what is considered the reference in graph theory applied to electrical networks, namely "Linear Graphs and Electrical Networks" by Seshu and Reed, that book may be great when it comes to electrical networks, but it is just painful when explaining graph theory, just theorem after theorem followed by lengthy abstract proofs of such theorems. So I decided to look for something different to understand the basics of graph theory in a simpler way, and thus I found this book by Prof. Truedeau. This book is very well written, it has many examples and I never felt that the author skipped steps and assumed that the reader would fill in the blanks, everything is very detailed. The author seems to have a genuine interest on making things clear for the reader rather than displaying his vast knowledge on the subject. I must say however that I was disapointed that the book does not cover directed graphs, which are in fact needed for electrical network analysis and other physics related problems, yet most of the basics of graph theory are there. However I did fail to see basic concepts such as a "tree" (hidden under "open hamilton walk"), a "cut-set", the "rank" of a graph or the "nullity" of a graph and such, perhaps they are buried inside some of the end-of-chapter problems but I doubt it, some people may consider the use of such concepts belonging to a more advance graph theory book, although I think they are essential. Many chapters of the book are dedicated to the subject of planarity vs non planarity, and some basic concepts as the ones mentioned in the paragraph above were left out. This book by Prof. Trudeau has zero applied math examples, in fact the author begins the book by stating this is a purely mathematical book, however it serves as a great foundation for anyone wanting to understand graph theory. If you are like me, who is mostly interested in applied graph theroy, this book alone will not be enough, however this book is great to understand the basics of perhaps more difficult books on applied graph theory. So overall this is an amazing book, and the price is so low that makes this book a complete bargain, I highly recommend it.

The book arrived with a small water spot on the back cover, otherwise in good condition. This book is perfect for someone with little to no prior mathematical experience, other than maybe some high school algebra, it assumes pretty much no prior knowledge. As such it sacrifices some of the rigor you might be used to in a traditional math text, it's also wonderfully informal with just the right amount of humor to keep it from getting too dry, the author's writing style is reminiscent of Griffiths E&M. There are a lot of examples, which can feel like you're beating a dead horse, but it's better that it has more examples than necessary than not enough. I ordered this book after taking an undergraduate discrete math course, where graph theory was only touched on briefly; this was a nice second look at the subject. That being said, I think anyone with an interest in math could easily understand this book. I found that the explanation of isomorphisms and augmentations to be much more clear than my discrete book. The chapter on planar graphs seemed kind of long-winded, and if you are already familiar with what a graph is you could easily skip the first two chapters.

This is a superb first introduction to graph theory. It's highly accessible and easy to follow; personally, it helped me get interested in a topic I thought I hated but realized after study that I just hadn't had a good introduction to it. If you're looking for a place to start, or a good overview of the field, this is the book to start with; it's definitely prepared me for more advanced reading in the field. It's definitely elementary, so you might want to read more about the topic later (especially if you're interested in computer science applications like graph algorithms, which aren't covered), but if you haven't read much about the topic, are teaching yourself, or haven't taken topology yet, this is a great place to start. (Heck, maybe an overview of the field is all you actually want/need). The only odd thing structurally is that, when this book was initially going to press, the four-color theorem had just been proven. Rather than revise the appropriate section they chose to add an appendix describing the proof. It would've been a little better, in my opinion, to just revise the chapter in question.

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. You should also take a glance on "Introductory Graph Theory" by Gary Chartrand, which is perhaps a better written book.

This is easily one of the best maths textbooks I've read in a while. The approach to Graph Theory here is from the pure mathematics side and has the theory-lemma-proof style. However, it's a very easy read (yes, you can really read it on a bus). If you have no idea what graph theory is about and you want an easy start that assumes no prior knowledge of anything, this book is for you. A little caveat: This book was written before the four-color theorem was proved (ironically, in the same year: 1976), so it's a little outdated in this regard. He also mentioned that a bunch of other minor results hadn't been proven by the time he wrote the book, so take these with a grain of salt.

One of the best math books I have ever read. It states concepts as simply as they can be stated and explains them well through useful examples. This books is simply incredibly useful if you want an introduction to graph theory and I feel like it has prepared me to to tackle a a full course with something like Diestel's book. Honestly I wish this guy wrote all my math books, it would have saved me a ton of time and spared me the headaches.

I used this book (and Chatrand's introduction) for an independent study course at my college. Trudeau is extremely easy to read and he explains things very well. The problems in the book are interesting and are not generally difficult, although there are some challenging proof problems. It is a pure math book, as it notes in the great little preface, and has little in the way of applied problems. If you're looking for an intro book, for fun or study, this is a great pick. The only prerequisite knowledge is algebra and counting, along with mathematical thinking. The proofs assume familiarity with math, although this book functions independently of most math branches.

In my life I have read, perhaps, 20 books that have profoundly changed my world. I have been most fortunate lately to have stumbled upon two such books: 1. Parsing Techniques by Dick Grune and Ceriel Jacobs Not only is it packed with clearly explained information, but it is written in an eloquent, almost poetic way. As I read it I continually find myself saying, "Wow, wow, wow!." The authors clearly have a mastery of the English language. 2. Introduction to Graph Theory by Richard Trudeau The author claims that many students get bored with mathematics because the mathematics is tied to applications. He says that students should learn pure mathematics: let's take some very simple ideas and see where we can go with them. This totally blew me away. This is an unbelievably awesome book.