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I really like abstract algebra and I have come to appreciate graph theory more and more. I would like to check out algebraic graph theory to see what it's all about and get a feeling if it might be something for me.

I'm kind of looking for the book on this subject in the same sense that you might recommend Categories for the working mathematician to someone who wants to get into category theory. On the other hand I'm a not so bright undergrad so it must preferably not be on a too high level and be somewhat "accessible" and not require too much prerequisites.

Any suggestions?

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  • $\begingroup$ Related thread but more specific to linear algebra and graph theory, here. $\endgroup$
    – hhh
    Sep 4, 2016 at 12:54

3 Answers 3

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I have read "Algebraic Graph Theory" both by Norman Biggs and by Godsil & Royle. Biggs' book does not contain any exercises, Godsil's book does but without hints. Godsil references a web page with hints and errata which no longer exists (as of end 2014). I recommend both books because they complement each other nicely: there are theorms in Biggs' book which are proved only in Godsil's book and vice versa. Biggs starts with matrix theory and then switches to group theory, Godsil does it the other way around: he starts with group theory and switches to matrix theory. Before reading any one these books make yourself comfortable with graph theory in general (e.g., Diestel's GRAPH THEORY): otherwise you will not get the most of it because both Biggs and Godsil rely on the reader's knowledge of basic graph theory facts. Be ready to invest some time but you will be rewarded plenty: there are real gems to be found. If you have specific questions to one of the books just ask: I answer if I can.

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Four books on my shelf.

  1. Algebraic Graph Theory, Norman Biggs
  2. Algebraic Graph Theory, Godsil & Royle
  3. Graphs and Matrices, R. B. Bapat
  4. Graph Spectra, Brouwer and Haemers

The last two restrict themselves to matrix stuff. I learnt much from Biggs's book. No opinion on 2.

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    $\begingroup$ @JohnSmith: Better look into the second book of this list! (after looking at the name of the person who gave this (+1) answer...) $\endgroup$
    – azimut
    Feb 18, 2015 at 16:59
  • $\begingroup$ @azimut Oooops. Now I'm feeling really stupid. $\endgroup$
    – John Smith
    Aug 21, 2015 at 9:15
  • $\begingroup$ What should a beginner do when he first steps in spectral graph theory ;it is not possible to read 4 of the above books.Can you please specify @Godsil $\endgroup$
    – Learnmore
    May 12, 2016 at 4:17
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    $\begingroup$ @learnmore: Just pick the one that looks the most interesting to you and work through it carefully. The time you spend deciding is time wasted. $\endgroup$
    – Chris Godsil
    May 12, 2016 at 12:12
  • $\begingroup$ One more question ; which matrix out of Adjacency ,Incidence /Laplacian is more important in the study of this subject? $\endgroup$
    – Learnmore
    May 14, 2016 at 14:14
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Similar questions with a little bit different slant are seasonally reoccuring. I try to make some structure on the amount of information. Comment for more inclusions.

Threads from elementary level to more advanced level

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