Graph Theory You Need Before Undergrad Research: in 8 undergrad lectures

The purpose of this book is to serve as an introduction to graph theory for students who are interested in undergraduate research experiences or independent study courses and projects. It is a short resource to get the nuts and bolts of introductory graph theory concepts. With this background, students can be more equipped to dive into a more specific field within graph theory that is more pertinent to their undergraduate research or independent study interests.For students, think of this book as an awesome first step to understanding the basics of graph theory, especially if you haven't taken a course that covers graph theory or a related subject. For instructors, professors, and/or undergraduate research mentors, think of this as a fantastic resource to give your students a leap into your research program or an independent study course or project.Why this book though? What makes this book stand out? There are plenty of graph theory resources out there; why this one?A significant difference between the style of writing in this book as compared to other math texts is that it is written with the intent of bridging intuition and proof writing. Oftentimes, math books don't present the intuition behind a proof before presenting the proof. This book takes the perspective that intuition and colloquial language are key to bridging students from their understanding of concepts to formal proof writing.Another marked difference in this book is that each section has exercises, one of them being an "Extension Problem''. The extension problems are not necessarily open problems (that is, problems that mathematicians still do not know the answer to), but are problems that have the flavor of what one might encounter during an undergraduate research experience in graph theory. These problems might be open ended, don't follow directly from the content provided in the corresponding section, and are intended to be exploratory for students.The contents of the book are inspired by the graph theory section of a Discrete Mathematics course that I have taught at several institutions. The book focuses on undirected graphs with no loops or parallel edges (if that means nothing to you right now, that's no worry!) Topics include an introduction to graphs, walks and paths, connectivity, coloring, trees and planarity. Read more