First book on algebraic graph theory?

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?

Solution 1:

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.