This document discusses bi-connected components in graphs. It defines an articulation point as a vertex in a connected graph whose removal would disconnect the graph. A bi-connected component is a maximal subgraph that contains no articulation points. The document presents algorithms for identifying articulation points and bi-connected components in a graph using depth-first search (DFS). It introduces the concepts of tree edges, back edges, forward edges and cross edges in a DFS tree and explains how to use these edge types to determine if a vertex is an articulation point based on the minimum discovery time of its descendant vertices.