I have written a new textbook in graph theory, published by the American Mathematical Society. It is now available for purchase:
Fundamentals of Graph Theory-AMS
Fundamentals of Graph Theory-Amazon
Fundamentals of Graph Theory-Google Books
Reviews: London Math Society (p. 61) MAA
DESCRIPTION:
Graph theory is a fascinating and inviting branch of mathematics. Many problems are easy to state and have natural visual representations, inviting exploration by new students and professional mathematicians. The goal of this textbook is to present the fundamentals of graph theory to a wide range of readers. The book contains many significant recent results in graph theory, presented using up-to-date notation. The author included the shortest, most elegant, most intuitive proofs for modern and classic results while frequently presenting them in new ways. Major topics are introduced with practical applications that motivate their development, and which are illustrated with examples that show how to apply major theorems in practice. This includes the process of finding a brute force solution (case-checking) when an elegant solution is not apparent. With over 1200 exercises, internet resources (e.g., the OEIS for counting problems), helpful appendices, and a detailed guide to different course outlines, this book provides a versatile and convenient tool for the needs of instructors at a large variety of institutions.
ADDITIONAL SECTIONS:
The Pigeonhole Principle
Uniquely Colorable Graphs
Allan Bickle, PhD 