Lecture
This lecture covers the concept of graph isomorphisms, where two graphs are considered identical if they have the same set of vertices and edges. The lecture explains the definition of isomorphic graphs, the notation used, and provides examples. It also discusses the computational complexity of determining graph isomorphisms and the number of isomorphism classes of graphs based on the vertices. The instructor highlights the difficulty in deciding whether graphs are isomorphic and the active research in finding efficient algorithms for this problem.