This course continues the journey into graph theory, offering an in-depth exploration of key advanced topics that build upon the fundamentals. Students will begin by studying graph isomorphisms, focusing on the structural equivalence of graphs and their practical implications in various applications. Through solved problems, we reinforce core concepts and provide hands-on experience with foundational techniques, ensuring a solid understanding of the basics while bridging the gap to more advanced topics.

We delve into the study of subgraphs and derived graphs, examining their properties, types, and relationships with the larger graphs they are part of. This segment highlights how smaller graph components contribute to the overall structure and behavior of graphs in theoretical and real-world contexts. Furthermore, the course covers operations on graphs, exploring how transformations such as union, intersection, and Cartesian products affect graph properties and applications.

Each topic is complemented by examples, illustrations, and problem-solving exercises, enabling students to grasp complex concepts intuitively. By the end of the course, participants will have a comprehensive understanding of these advanced graph theory topics and the skills to apply them in theoretical studies, algorithm design, and other practical areas. Whether you are a student, researcher, or professional, this course will significantly enhance your expertise in graph theory.