Graph Theory: A Problem Oriented Approach by Daniel A. Marcus is widely regarded as a top-tier resource for students who prefer active learning over passive reading. Rather than presenting theorems and proofs in a standard lecture format, the book uses approximately 360 strategically placed problems to lead you toward discovering the principles of graph theory yourself. Why It Is Highly Recommended

A problem-oriented approach to graph theory involves learning through solving problems. This approach helps students develop a deep understanding of graph theory concepts by applying them to real-world problems. The following are some key concepts in graph theory that can be learned through a problem-oriented approach:

Vertices, edges, and representations

"Introduction to Graph Theory" by Richard J. Trudeau: Perhaps the most "friendly" book on the subject, focusing on visual intuition and classic puzzles.

  1. Investigation: The student is presented with a simple-looking problem (often involving puzzles like the Königsberg bridges or map coloring).
  2. Exploration: Through a series of guided problems, the student discovers properties of graphs on their own.
  3. Formalization: Only after the student has "discovered" a rule does the book introduce the standard theorem or definition associated with it.

Example