Aimed at “the mathematically traumatized,” this text offers nontechnical coverage of graph theory with exercises.
A stimulating excursion into pure mathematics aimed at “the mathematically traumatized,” but great fun for mathematical hobbyists and serious mathematicians as well. This book leads the reader from simple graphs through planar graphs, Euler’s formula, Platonic graphs, coloring, the genus of a graph, Euler walks, Hamilton walks, and a discussion of The Seven Bridges of Konigsberg. Includes exercises—1976 edition.
- Engaging Introduction to Graph Theory: Designed to captivate both math enthusiasts and those who may be apprehensive about mathematics, this book offers a stimulating excursion into the world of pure mathematics.
- Accessible to All Levels: With only high school algebra as a prerequisite, this book is suitable for anyone interested in exploring the fascinating realm of graph theory.
- Comprehensive Coverage: From simple graphs to advanced topics like planar graphs, Euler’s formula, Platonic graphs, coloring, and more, this book provides a thorough exploration of key concepts in graph theory.
- Interactive Learning: Each chapter includes exercises to reinforce understanding and provide opportunities for practical application of the concepts covered.
- Clear and Concise Writing: The book is written with clarity and elegance, making complex mathematical concepts accessible and easy to follow.
Michael A. Chary –
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.
J. R. G. Mendonca –
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.
D. Amos –
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.
JOAT –
The author uses a very rich and engaging writing style that truly lends itself to explaining the material. At its very core, the discipline can seem a little confusing after the first perusal; but given a couple of hours the reader will be able to grasp the concepts discussed in this book. I give it a 5/5.
Brian –
Dover Books on Mathematics can be hit and miss. This one is a definite hit. One does not need a lot of math knowledge to understand the fundamental concepts or enjoy the material.
L.Bruno –
As Far As I’ve Gotten, Trudeau’s book seems to be a little clearer and easier to follow than Chartrand’s (Introductory Graph Theory, also by from Dover).
That being said, Chartrand’s book provides a balance with Trudeau’s, providing alternatives and balance between the two.
Forest Guy –
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.
Roger Costello –
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.
Manuel Bermudez –
I originally bought this book to supplement my undergraduate Graph Theory Course. Although it was not the required text it did help me throughout the course. The required book was “Pearls in Graph Theory” by Nora Hartsfield and Gerhard Ringel. Both books combined helped me get an “A.” For $3.99 you cannot beat the price!!!
Kent –
This is a good book for those just generally interested in math. Lays out the foundations for set theory well. This is not the math most people would have learned in school.
M. Kovarik –
At only $4, this is probably the best, beginner-friendly introduction to graph theory you can get. I’ve assisted in a mathematics summer program for gifted high school students. I’ve recommend this book to them. They loved it.
The subject is approachable and clearly discusses the concepts behind the mathematics. This book can act as a very good introduction to combinatorial/algebraic topology. Interestingly, Hamiltonian and Eulerian walks is treated at the end of the text instead of the beginning. Everything is very readable.
Cesar J. Machado R –
I am a begginer with these wonderful branch of mathematics, through its pages I have started to comprenhend from the basis the main concepts of Graph Theory.
Eugênio Silva Rezende –
If you’re interested in algorithms and graph theory applied to computer science, that’s not the book for you. It’s essentially a book for mathematicians.
Frank –
The topic was new to me, the material developed in a fairly logical manner, not boring but the mathematics does get demanding at points. The author notes this and encourages continued reading. I agree. Actually the material covered is wider than graph theory. The text ought to be accessible to math enthusiasts in high school.
Ryan McNamara –
Apparently the difference between “pure” mathematics is that pure mathematics attempts to explain to you *why* mathematical concepts are true and why they need to be defined the way they are. The math I was taught in school was a “just shut up and memorize *how* (not why) to solve the problems.” The actual subject matter is fascinating and very different from any math I’ve been exposed to. My issue, though, is that the proofs were sometimes way too difficult to follow as a beginner; he could have done a better job helping you connect the dots of reasoning for people unfamiliar to pure mathematics (the stated audience of this book). But so many light bulbs went off in my head reading this and I so many times thought “that’s amazing” that I have to rate this 5 stars.
Vladimir Zuzukin –
Classic text. Excellent and gentle introduction to network theory. It is as challenging and rigorous as you want to make it. Read it for enjoyment and understanding. Tackle the exercises for the challenge. I highly recommend it as foundational for any new student of graphs and networks, especially prior to tackling a modern MOOC on this subject.
Maxwell Bach –
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.
EJS –
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.
byron munoz –
Well written book on the subject. Very basic, but it will give you enough for what the title states. Good Dover Mathematics.
Austen Jones –
So approachable! Not many math textbooks lend themselves well to being used as light reading material (full disclosure: I am a mathematics major so my definition of light reading material may differ from yours). Does not require formal exposure to pure mathematics, just an interest in the topic and a general understanding of logical reasoning.
Constantine Nagorny –
Great introduction for those who study as a mathematicians…
And besides, the Dover outlines math books are really helping!!!
Boris Glebov –
Dover has put a great number of short introductory books on scientific topics, and I have generally found them to be excellent. They are concise, on point, and informative. This book is no exception. The writing is light. Explanations are clear. It serves up a wonderful introduction to the subject by explaining the basic terms and theorems. Though it is well short of being a rigorously formal book, it gives a good sense of the subject area, and I was actually able to make almost immediate practical use of its material (figuring out whether a circuit I was designing could fit onto a single-sided board).
Ovid –
This book really is what it claims to be, an Introduction to Graph Theory. Now, take in mind that the material is very condensed (like many dover books), there’s a large amount of examples and exercises, which made it very good for someone who wishes to self-taught. It’s cheap price also make it a very good deal.
Alex R Delp –
If you wanna go HAM on some graphs this problem set is amazing. Ideas build on each other and the small incremental discoveries you make interlock and lead to more exciting discoveries that honesty have me turnt on some graphs.
lucho –
Clear, yet not because of that lacks in rigor.
A gem that has endured the pace of time in this rapidly evolving field.
Ilia S Geltser –
An excellent read for a non-mathematician! Clear, simple, engaging. Needed for Computer Science class in high school.
Real Al –
A very good introduction to the field. Easy to fall into with an excellent progression to the more complex. I gained quite a bit of insight, and found this book enabled me to conceive of applications in disciplines such as Gene sequencing, and the Stock MARKET. A necessary read for Quants.
Sensor2 –
Dover is a fantastic nest of graph theory: This book is a good coverage of the topic!
Teddy –
detailed introduction that quickly gets you up and running conceptually.
Alfred M. Powell –
Book as advertised and arrived within estimated time
BOZ –
Awesome Dover Reprint of Classic on Graph Theory. Presumes only high school Algebra as prerequisite.
Necessary intro for Math Majors, sweet little book for advanced or curious high school student.
Kay R –
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.
DBeck –
I got this book after having learned some graph theory and proofs for discreet math classes. I think Trudeau has a very accessible writing style when it comes to breaking down these very technical definitions. The only problem I have is that I believe there could have been more detail, since, at least for me, I would have needed more to really understand the proofs better. I could walk through the proofs of the theorems he did, but I don’t think he gave me enough to be able to make a lot of progress in the practice exercises, or some of the lemmas left to the reader, which was kind of a confidence killer. But probably that amount of detail would ruin the purpose of the book in the first place.
Jeremiah Ruesch –
Entertaining and informative, the author plays with difficult material with clarity and precision. The microwave reader, like me, will have an easy time understanding the basics and find intuition to miss challenging topics.
Guybrush Deepwood –
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.
Mostafa –
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.
A Gre –
This is a great intro book and it helped to contrast the typical math book to show that you can write a math book with personality