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What are some of the best books on graph theory, particularly directed towards an upper division undergraduate student who has taken most the standard undergraduate courses? I'm learning graph theory as part of a combinatorics course, and would like to look deeper into it on my own. Thank you.

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14 Answers 14

up vote 17 down vote accepted

Try Bondy and Murty, Graph Theory. The previous version, Graph Theory with Applications, is available online.

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(Your second link is broken.) –  Zach Langley Apr 5 '11 at 23:11
@Zach, fixed, thanks. (I worked when I posted it.) –  lhf Apr 5 '11 at 23:15

Diestel's Graph Theory (which has a "free preview" online) is presented as a graduate textbook, but it does not really have any prerequisites.

It goes quite deep in some parts, and includes material (such as the chapter on the graph minor theorem) that you won't find in other textbooks. Some proofs have a sort of "how would someone ever think of that?" feel, but this may have been remedied in the fourth edition (I have the third).

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That's "Diestel". It may be noteworthy that this book has a German version, entitled without much originality "Graphentheorie". It's certainly the best introductory text for someone interested in the most theoretic aspects of graph theory. –  PseudoNeo Apr 5 '11 at 20:56
@PseudoNeo Ah, usually I don't make that typo, thanks. –  Harry Stern Apr 5 '11 at 22:32

The best introduction I could recommend for truly beginners is not a whole book on graph theory but A Walk Through Combinatorics, from Miklos Bona it has a large part of the book devoted to graph theory, from the very basics up to some intro to Ramsey theory

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Doug West, Introduction to Graph Theory. Rigorous but readable, proof based rather than simply descriptive, but the proofs are explanatory rather than simply justification of truth (by any arbitrary means). Even so may not be the best total beginner's book.

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I enjoyed Alan Tucker's Applied Combinatorics. It's split into two sections:

  • Graph Theory
  • Combinatorics

The first half covers things like coloring theorems, cycles, and all that stuff. The second half is all about generating functions, counting sets, etc.

I found the book to be pretty readable. There are a lot of problems to work, which was nice.

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You might find Graph Algorithms / Shimon Even interesting. Although it might probably hard to obtain.

Edit: You can get some of the chapters here.

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I have used Diestel's Graph Theory book mainly, but I found extremely helpful video lectures by professor L. Sunil Chandran from IISc Bangalore (here and here).

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graph theory by Narsingh Deo, PHI publication.

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This does not provide an answer to the question. To critique or request clarification from an author, leave a comment below their post - you can always comment on your own posts, and once you have sufficient reputation you will be able to comment on any post. –  learner Feb 25 '14 at 5:30

Here is Vadim Lozin's graph theory course. (Available for free from university of Warwick website )

It starts from scratch and most of theorems are prooved. I think it's pretty clear with many content.

It's not a book, but i hope it can help you.

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For advanced readers,

Graph Theory by Frank Harary

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I've enjoyed Introduction to Graph Theory by Wilson. Older version can be obtained for less than $5.

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Graph and Digraphs, 5th edition, by Chartrand, Lesniak, and Zhang. It is a graduate level text and gives a good introduction to many different topics in graph theory.

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Pearls in Graph Theory: A Comprehensive Introduction by Nora Hartsfield and Gerhard Ringel.

I used this book to teach a course this semester, the students liked it and it is a very good book indeed. The book includes number of quasiindependent topics; each introduce a brach of graph theory. It avoids tecchnicalities at all costs. I would include in the book basic results in algebraic graph theory, say Kirchhoff's theorem, I would expand the chapter on algorithms, but the book is VERY GOOD anyway.

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Graph Theory: Modeling, Applications, and Algorithms by Geir Agnarsson and Raymond Greenlaw is a really good book. see this discussion for reference.

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While this link may answer the question, it is better to include the essential parts of the answer here and provide the link for reference. Link-only answers can become invalid if the linked page changes. –  Shaun Oct 4 '14 at 12:17

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