ocw.mit.edu
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MIT OpenCourseWare provides free, openly licensed course materials from MIT courses, allowing self-paced study without enrollment. You can access lecture notes, assignments, exams, and reading lists across many subjects—including graph theory and other math and CS topics.
More resources on Graph Theory
mathworld.wolfram.com
MathWorld is an extensive online mathematics encyclopedia from Wolfram Research offering detailed, encyclopedia-style articles on graph theory topics—including definitions, theorems, algorithms, and examples—with diagrams and links to related concepts for study and reference.
Graph Theory and Combinatorics
Coursera course: Trees and Graphs: Basics
Introduction to Graph Theory
We invite you to a fascinating journey into Graph Theory — an area which connects the elegance of painting and the rigor of mathematics; is simple, but not unsophisticated. Graph Theory gives us, both an easy way to pictorially represent many major mathematical results, and insights into the deep theories behind them. In this online course, among other intriguing applications, we will see how GPS systems find shortest routes, how engineers design integrated circuits, how biologists assemble genomes, why a political map can always be colored using a few colors. We will study Ramsey Theory which proves that in a large system, complete disorder is impossible! By the end of the course, we will implement an algorithm which finds an optimal assignment of students to schools. This algorithm, developed by David Gale and Lloyd S. Shapley, was later recognized by the conferral of Nobel Prize in Economics. As prerequisites we assume only basic math (e.g., we expect you to know what is a square or how to add fractions), basic programming in python (functions, loops, recursion), common sense and curiosity. Our intended audience are all people that work or plan to work in IT, starting from motivated high school students.
khanacademy.org
Khan Academy is a free online learning platform offering high-quality video lessons, practice problems, and quizzes across numerous subjects, including math topics like graph theory.