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Table of Contents
Chapter 3: Graphs
3.1 Basic Definitions and Applications
3.2 Graph Connectivity and Graph Traversal
3.3 Implementing Graph Traversal Using Queues and Stacks
3.4 Testing Bipartiteness: An Application of Breadth-First Search
3.5 Connectivity in Directed Graphs
3.6 Directed Acyclic Graphs and Topological Ordering
DAGs are directed graphs that do not contain cycles. G is a DAG ⇔ G has a topological ordering. Despite DAGs having no cycles, they can contain nC2 nodes. To find a topological ordering, recursively find nodes with no incoming edges and order them next in the ordering. (Once you order a node, delete it and all of its outgoing edges; this will cause there to be at least one new node that does not have an incoming edge.) Such an algorithm can run in time O(m+n).
