I'll be teaching graph theory this fall for the first time. The only undergraduate graph theory book I am familiar with is Doug West's book, which I like. But I'd like to consult some other undergraduate books as I prepare. Any suggestions?
I use "Introductory Graph Theory" by Gary Chartrand (Dover, 1985) because it is heavy on applications and introduces some of the concepts only after presenting examples that would need them. (A warning though, some of its definitions are not the same as those used by other authors.)
There is a newer book, "The Fascinating World of Graph Theory" by Arthur Benjamin, Gary Chartrand, and Ping Zhang (Princeton University Press, 2015) but I haven't tried using it in class yet.
For completeness, I do recommend several "Moore method"/inquiry-based sets of notes found at the Journal of Inquiry-Based Learning in Mathematics website. I have successfully used a pastiche of these resources for a first course, needing only basic sets and induction as background. Graph theory is very ideally suited to such presentation.
I've had success with Graphs, Colourings and the Four Colour Theorem (R.A. Wilson)
If you have a predetermined list of graph theory topics to cover it might not work for you, but it does a good job of stretching away from just 4CT-related material into wider topics.