Introduction to Graph Theory by Professor Jacques Verstraete.
This book is still a draft, and you may find some typos or gaps—if you do, please let us know! I will try to maintain an "errata" page here. I also recommend having another book available as a reference (this is always a good idea in math courses). Here are some possible references on the course webpage, many of which are free to download through the UCSD library. (Requires you to be on campus or use the UCSD VPN.)
Combinatorics and Graph Theory by Harris, Hirst, and Mossinghoff.
(A standard introductory graph theory text. It includes many/most of the topics in our course, but omits some of the algortimic graph theory we'll be covering.)
Graphs and Applications by Aldous and Wilson.
(Similar coverage to the previous book; it is a bit longer, and also perhaps a bit more conversational in style.)
A Tour through Graph Theory by Saoub.
(Very approachable writing, and covers most of the topics we'll be learning (including alrogirithms) but is not rigorous. This could be a great book to read before or after lectures to help understand definitions and build intuition.)
Graphs, Networks, and Algorithms by Jungnickel.
(More advanced/technical, and includes most or all of the topics we'll be covering, plus many more).
Introduction to Graph Theory, by West.
(Rigorous and comprehensive—a standard reference).
Graph Theory And Its Applications, by Gross and Yellen
(Another comprehensive reference. Has more focus on algorithms and computer science appications.).