Books recommendation on Graph Theory (Beginner level)

Question

What are some of the best books on graph theory, particularly for the beginners. Thank you.

Answer 1

You can use the book by R.B.J.T. Allenby, Alan Slomson, How to Count An Introduction to Combinatorics. It is rather a (Probably the best) book for rudimentary combinatorics, but here in the chapter $9$, Detailed introduction to Graphs are given. After studying these, you can study higher standard books on this topic. but this is hard to find. So, Edgar G. Goodaire and Michael M. Parmenter. Discrete Mathematics with Graph Theory is a good alternative.

Answer 2

I quess Graph Theory by F.Harary is the best one. There are a lot of properties of different graphs. And at the end of all paragraphs, you could check yourself and try to solve some problem.

Answer 3

I thought A First Course in Graph Theory by Gary Chartrand and Ping Zhang was an excellent, soft introduction to graph theory when I first learned it in undergrad. Not to mention the actual textbook is very cheap!

Answer 4

I'm partial to Doug West. It's very thorough, friendly, and well written. You'll get the basics- trees, connectivity, independent sets, matchings, flows, and colorings. West also covers advanced topics like Ramsey Theory, spectral graph theory, random graphs and matroids. He also has an appendix on NP-Completeness proofs, which are relevant to computer scientists. I would consider West to be a more classical graph theory text.

I haven't used Bondy-Murty, but I've heard good things about it.

Diestel is a solid book, but it is not a beginner level book. Diestel does cover a lot of material that West doesn't, but it's covered at a more mathematically mature manner. Diestel is a text that covers topics you should see if you are attending graph theory conferences. It covers more modern graph theory.

If you are looking for a brief introduction, Nick Loehr's Bijective Combinatorics text has a solid chapter on graph counting. One could teach the graph theory unit in an undergraduate Applied Combinatorics course from this one chapter in Loehr.

I would discourage you from using Alan Tucker's Applied Combinatorics text. It's good for problems but has terrible exposition.