Adventures in Graph Theory

This textbook explores and illustrates connections between graph theory and diverse fields of mathematics such as calculus on manifolds, group theory, algebraic curves, Fourier analysis, cryptography, and other areas of combinatorics. These pathways from graph theory serve as a guide to higher mathematics for the reader. The authorsaccomplish this by presenting deep applications of graph theory in a user-friendlymanner. The first chapter is introductory in nature illustrating basic definitions of graph theory and polynomial invariants for graphs. Recent results in mathematics are included throughout the book, as well as profuse examples of graphs, how they arise, and their uses in order to encourage the reader's own analysis. And, for reference, Sage code computations clearly illustrate the book's many graphs. Samples of the book's source code can be found at github.com/springer-math/adventures-in-graph-theory. The text is geared towards advanced undergraduate and graduate students and is particularly useful for those who want to settle on a dissertation topic. This book, however, is also beneficial as a reference to anyone interested in how graph theory can be applied to other areas of mathematics.