Congratulations! You’ve reached the end of the book.
Well, almost. Apart from the bibliography, which is mostly of interest in case you want to look up one of the books or papers I’ve cited, there are two more chapters with actual mathematical content to them.
Appendix A is about writing proofs, especially writing proofs in graph theory. If you do not know how to write a proof at all, it might not be the best way to learn, because it is only one chapter, and there are entire books written on the subject. But if you know a bit about how to write a proof, this chapter will help you along.
Appendix B is similar, but with a more specific focus: proof by induction. Mathematical induction gets its own appendix for two reasons. First of all, it is a tricky proof technique to master. Second, graph theorists commonly encounter proofs by induction that do some unusual things you don’t see elsewhere. I want to try to prepare you for them a little.
I do not assume, in either Appendix A or Appendix B, that you’ve read past the first part of this book. I will, however, occasionally link you to some proofs later in the book that are good examples of what I’m talking about.