Written by two of the most prominent figures in the field of graph theory, this comprehensive text provides a remarkably student-friendly approach. Geared toward undergraduates taking a first course in graph theory, its sound yet accessible treatment emphasizes the history of graph theory and offers unique examples and lucid proofs. 2004 edition.
Generally easy to read and well-organized. A standard text in graph theory, there is a lot more in here that would be covered in a one-semester course, but the beauty in that is once you've covered the basics there's wiggle room to either touch on special topics or let the students choose something for a project. My second book by Chartrand, but definitely my favorite.