If you are looking for a free or open-source alternative to "Introduction to Graph Theory" by Douglas B. West, there are several options available:
One of the defining characteristics of West’s writing is his classification of proof methods. He explicitly teaches students how to think about graph theory proofs, categorizing them into standard techniques such as extremality, induction, and contradiction. This makes the book not just a reference for graph theory, but a primer on mathematical reasoning itself.
If you decide to take on this book, a bit of preparation can make the experience much smoother: introduction to graph theory by douglas b west pdf
Whether you are studying for an exam or conducting research, this book provides the structure and insight needed to master the topic.
Advanced topics include Eulerian circuits (traversing every edge once) and Hamiltonian cycles (visiting every vertex once). The text analyzes the structural conditions required for these paths to exist, linking back to the classic Traveling Salesperson Problem (TSP). Tips for Studying Introduction to Graph Theory If you are looking for a free or
Visiting every vertex exactly once (the basis for the Traveling Salesperson Problem).
: West does not skip steps in proofs, teaching readers how to think like mathematicians. This makes the book not just a reference
: Cuts, k-connected graphs, Menger’s theorem, and network flow. Coloring of Graphs : Vertex coloring, chromatic number, and structural bounds. Planar Graphs