Lecture 27

Learning objectives

After this class, you should be able to:

1. Define a graph (undirected and directed), a vertex/node, and an edge.
2. Given the figure of a graph, give its set of vertices and set of edges.
3. Given the set of vertices and set of edges of a graph, draw a figure to show the graph.
4. Given a graph, show its representations using an adjacency list, and adjacency matrix, and an incidence matrix. Also give the space required for each of those representations.
5. Given a graph, show the order in which which nodes are visited in the following traversals: (i) depth first search and (ii) breadth first search. Also give the time complexities for the traversals.

Reading assignment

1. Chapter 8, up to (and including) section 8.2, class notes.

Exercises and review questions

• Exercises and review questions on current lecture's material
  1. Give the set of vertices and edges for graph 2 shown in class.
  2. Give the adjacency list, adjacency matrix, and incidence matrix representations for graph 1 shown in class.
  3. Show the orders in which nodes are visited in (i) depth first and (ii) breadth first traversals of graph 1. When multiple neighbors of a node may be traversed, choose the smaller-numbered neighbor first.

• Questions on next lecture's material
  1. None. Start preparing for the final exam.