Reddit reviews Introductory Combinatorics (5th Edition)

I recommend Brualdi's Introduction to Combinatorics. I've used the book to teach a course that was an introduction to combinatorics and graph theory and found it readable, informative, and a good source of problems and applications.

Specifically Graph Theory? Pearls In Graph Theory was the one that I used in my undergraduate course. It covers some algorithms and the theory behind completeness, infinite lattices, etc. Fun stuff!

If you want a more combinatorial view of things (ie: not so specialized with regards to Graph Theory), I highly recommend Brualdi's Introductory Conbinatorics as bucket1004 said. I also used that one for my combinatorics course and I loved it.

Disclaimer: There's some errata in the edition that I used. I'm not so sure how much better the new editions are.

I liked Richard Brualdi's Introductory Combinatorics (Amazon Link) due to the broad nature of topics presented. There are also good solutions guides too, which I find appealing when first getting in to a topic and doing the exercises.

If you pursue graph theory from there, there are plenty of books that are great, including free online editions like Diestel's book. http://diestel-graph-theory.com/.

Neither of these are the end all, be all for these topics, and they give you a taste of a lot of nice topics. Combinatorics is quite diverse, and I have yet to see one book that can come close to encompassing every high point. From there, you can usually look for "TOPIC NAME" + lectures notes and find something worthwhile.

OK..

http://www.amazon.com/Contemporary-Abstract-Algebra-Joseph-Gallian/dp/0547165099/

http://www.amazon.com/Algorithm-Design-Jon-Kleinberg/dp/0321295358/

http://www.amazon.com/Introduction-Algorithms-Thomas-H-Cormen/dp/0262033844/

http://www.amazon.com/Introductory-Combinatorics-5th-Richard-Brualdi/dp/0136020402/

http://www.amazon.com/Artificial-Intelligence-Modern-Approach-3rd/dp/0136042597/

And I guarantee you those nice amazon prices aren't that steeply discounted around the start of the semester, and certainly not in any brick-and-mortar bookstore.

The combinatorics class I'm in right now is using Richard Brualdi's Introductory Combinatorics. I'm a fan of it.