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  • Introduction to Graph Theory (Dover Books on Mathematics)

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Introduction to Graph Theory (Dover Books on Mathematics) 2nd Edition


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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.

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From the Publisher

Big Ideas, Simple Concepts—An Accessible Intro to Graphs

Introduction to Graph Theory

Suitable for anyone interested in exploring the fascinating realm of graph theory

  • Clear, Nontechnical Approach – Explains key topics like planar graphs, Euler’s formula, graph coloring, and Hamiltonian paths in a relaxed, accessible style.
  • Discover Classic Puzzles and Problems – Explore famous concepts like the Seven Bridges of Königsberg and Platonic graphs.
  • Perfect for Self-Study or Supplementary Reading – A great resource for students, teachers, or hobbyists looking to enjoy the beauty of pure math.
  • Exercises Included – Thought-provoking problems reinforce understanding and invite hands-on exploration.

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About the author

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Richard J. Trudeau
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Customer reviews

4.6 out of 5 stars
608 global ratings

Customers say

Customers find this book to be a wonderful introduction to graph theory, providing fundamentals right away and serving as a great math book. Moreover, the content is engaging, with one customer noting it's loaded with enjoyable problems. Additionally, the book is easy to read and understand the basics, with excellent prose that makes the subject accessible.
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44 customers mention informative, 39 positive, 5 negative
Customers find the book informative, describing it as a wonderful introduction to graph theory that provides the fundamentals right away and serves as a great introduction to mathematical thinking.
...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....Read more
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 personalityRead more
really a good introduction. clear and to the point. with enough to get started. touches all the elements you need....Read more
...They are concise, on point, and informative. This book is no exception. The writing is light. Explanations are clear....Read more
34 customers mention content, 32 positive, 2 negative
Customers find the book entertaining and engaging, with one mentioning it is loaded with enjoyable problems.
Great book! Gives you the fundamentals right away and get you functional in Graph Theory fairly quicklyRead more
This is an AMAZING book, the authors style is so clear, fun and entertaining, without much mathematical rigor....Read more
This is a good book for those just generally interested in math. Lays out the foundations for set theory well....Read more
Entertaining and informative, the author plays with difficult material with clarity and precision....Read more
25 customers mention mathematics, 18 positive, 7 negative
Customers appreciate the mathematical content of the book, describing it as a pure math text with a focus on graph theory, and one customer notes that it helps develop logical reasoning skills.
...It's essentially a book for mathematicians.Read more
...Good Dover Mathematics.Read more
...in a fairly logical manner, not boring but the mathematics does get demanding at points. The author notes this and encourages continued reading....Read more
...the authors style is so clear, fun and entertaining, without much mathematical rigor....Read more
15 customers mention readability, 11 positive, 4 negative
Customers find the book easy to read and understand the basics, with one customer noting that the author handles difficult material with clarity.
An excellent read for a non-mathematician! Clear, simple, engaging. Needed for Computer Science class in high school.Read more
Well written! Very clearRead more
...in the paperback version of this book is so small that it is difficult to read. The leading (i.e., the space between lines) is also small....Read more
...However, it's a very easy read (yes, you can really read it on a bus)....Read more
13 customers mention writing style, 12 positive, 1 negative
Customers appreciate the writing style of the book, describing it as eloquent and excellent, with one customer noting its poetic approach to explaining graphs.
Well written! Very clearRead more
Very nice introduction. Prose is excellent. This book can be used to teach high school students graph theory and college students scientific writing.Read more
The author uses a very rich and engaging writing style that truly lends itself to explaining the material....Read more
Some basic math understanding required but still well-written.Read more
the book arrived broken
2 out of 5 stars
the book arrived broken
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Top reviews from the United States

  • Reviewed in the United States on January 25, 2015
    Format: PaperbackVerified Purchase
    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.
    42 people found this helpful
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  • Reviewed in the United States on June 19, 2020
    Format: PaperbackVerified Purchase
    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.
    4 people found this helpful
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  • Reviewed in the United States on April 24, 2015
    Format: PaperbackVerified Purchase
    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.
    13 people found this helpful
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  • Reviewed in the United States on November 10, 2009
    Format: PaperbackVerified Purchase
    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.
    21 people found this helpful
    Report

Top reviews from other countries

  • Oliver Kolle
    5.0 out of 5 stars Reine Mathematik der Graphen
    Reviewed in Germany on August 27, 2016
    Format: PaperbackVerified Purchase
    Ich habe das Buch komplett durchgearbeitet. Eine exzellente Einführung in die Materie. Die wichtigsten Themen werden behandelt: Isomorphie, Planarität, Euler-Formel, Eulersche und Hamiltonsche Pfade. Auch Graphen auf topologischen Oberflächen (Kugel, Torus, Doppeltorus usw.)
    Das Buch ist kein Standardwerk zur Graphentheorie, weil Bäume und gerichtete Graphen nicht behandelt werden. Auch Algorithmen und Anwendungen werden nicht angesprochen. Dies alles soll aber keineswegs den Wert des Werkes schmälern.
    Es handelt sich schon um ein richtiges Mathebuch, d.h. Lemma, Satz, Beweis, Korollar - Die Beweise werden sehr verständlich und ausführlich ausgeführt - zudem gibt es immer zahlreiche Beispiele.
    Die Übungsaufgaben sollte man unbedingt (zumindest) ansehen - weil hier einige neue Definitionen und Eigenschaften von Graphen eingeführt werden!
    Ich habe zu Hause viele angefangene Mathebücher - bei "Indroduction to Graph Theory" bin ich wegen des tollen, motivierenden Stils bis zum Schluss bei der Stange geblieben.
  • JOSE GASPAR LOREN EGEA
    4.0 out of 5 stars Muy útil
    Reviewed in Spain on February 16, 2014
    Format: PaperbackVerified Purchase
    Contiene un gran cantidad de información sobre este interesante tema. Es accesible para cualquier científico interesado en la teoría de grafos.
  • Edoardo Angeloni
    4.0 out of 5 stars Un elenco di teoremi veramente utile.
    Reviewed in Italy on February 28, 2020
    Format: PaperbackVerified Purchase
    Dopo una rassegna di elementi basilari della teoria dal punto di vista assiomatico, diventa importante l'introduzione del teorema di Eulero. Lakatos ha spiegato il significato di questo teorema considerandolo quasi un teorema empirico più che un risultato deduttivo. Dal punto di vista storico non va tralasciato il teorema dei quattro colori, perché ha spiegato che in certi casi gli algoritmi informatici possono simulare efficacemente la dimostrazione logica del matematico. Poi entrano in gioco nella geometria algebrica moderna concetti decisivi come quello di genus e di Hamiltoniana.
  • p_mpki_
    5.0 out of 5 stars Great book for beginners like me
    Reviewed in Japan on January 7, 2024
    Format: eTextbookVerified Purchase
    I could understand this book after struggling, without any background of Graph theory. I felt that the author was enthusiastic to make readers funs of Graph.
  • Ana Isabel Bezerra Cavalcanti
    5.0 out of 5 stars Excelente introdução à teoria de grafos e excelente estímulo ao estudo da matemática pura
    Reviewed in Brazil on January 22, 2022
    Format: PaperbackVerified Purchase
    Uso esse produto para minhas pesquisas acadêmicas.