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.)
A Tour through Graph Theory by Saoub.
(Very approachable writing, and covers most of the topics we'll be learning (including algorithms) but is not rigorous. This could be a great book to read before or after lectures to help understand definitions and build intuition.)
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, Networks, and Algorithms by Jungnickel.
(More advanced/technical, and includes most or all of the topics we'll be covering, plus many more).
Graphs and Applications by Aldous and Wilson.
(Very approachable writing, but maybe less comprehensive/rigourous than some of the other books; could be good to read before/after class to build intuition.)
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.)
Learning How to Learn by Oakley, Sejnowski, and McConville.
This is an awesome (and very approachably-written) book about how to learn new technical material and solve hard problems. I first read this book a few years ago because my parents happened to have a copy; it really changed the way I think about learning math, and it's been helpful to me in my own math research. Particularly if Math 154 is one of your first proof-based math classes, you may find yourself needing to use new strategies. For example, what should you do if you're stuck on a proof, or if you don't know where to start? How do you read a difficult passage in a math textbook? This book gives a really nice framework for addressing some of these questions.
The Code Book by Simon Singh.
Not related to this class, just a super fun book related to math! I read this as an undergraduate after one of my professors recommended it, and I enjoyed it so much that I ended up taking two cryptography classes.
Crucial Conversations by Patterson, Grenny, McMillan, and Switzler (available online through UCSD).
Also not related to this class, just a wonderful book about how to approach hard conversations. I firmly believe that college is not just about learning academic content, but also about learning skills for life; some of those skills are more "academic," like problem-solving or close reading of dense or technical writing, but some are personal or relational. And many of the most important and difficult skills are subtle things that we may not even realize can be taught or learned! The ability to approach difficult conversations with grace is a huge skill that pays dividends in every area of life; it is a lifelong project (I am definitely still working on it!), but this book gives a great framework to build and develop this skill.