This repository contains a collection of theorems and sample problems for the graph theory originally targetting the comprehensive exam at Arizona State University. Most of the theorems are found in Diestel's Graph Theory and when a theorem number is mentioned, that number refers to the 3rd edition. Most of the proofs that are provided are generally similar to proofs in Diestel's Graph Theory or West's Introduction to Graph Theory. This document is somewhat incomplete, some proofs are missing, some proofs are better described as proof summaries, and the occasional proof may be incorrect. Corrections/additions/improvements to this document are welcome and can be submitted to this documents GitHub page located at https://github.com/rjoursler/graph_notes.