This lecture covers the properties and representations of graphs, focusing on topics such as graph definition, orientation, weighting, and complete graphs. It also delves into special types of graphs like trees and binary trees, as well as different graph representations like adjacency matrices and adjacency lists. The lecture further explores algorithms for graph traversal, including Breadth-First Search (BFS) and Depth-First Search (DFS), emphasizing the importance of data structures like queues and stacks in these algorithms.