Math 3614: Study Guide 3 (9/30-10/9)

(Your group will be evaluated on this material on 10/9)

Sections 7.4-7.6

Objectives:

Learn the following terms:
- path of length n
- connected graph (undirected)
- strongly connected graph (directed)
- weakly connected graph (directed)
- connected components
- cut vertex
- cut edge
- Euler circuit
- Euler path
- Hamilton path
- Hamilton circuit
- weighted graph
- shortest path
Become comfortable working the following types of problems:
1. Determine whether a given graph is connected.
2. Determine the connected components of an undirected graph.
3. Determine the number of paths of a given length connecting two vertices of a given graph.
4. Determine whether an Euler path or Euler circuit exists for a given graph.
5. Determine whether a Hamilton path or Hamilton circuit exists for a given graph.
6. Given a small weighted graph, determine the shortest path connecting two nodes.
Problem List:Learn to work the following problems:
1. Section 7.4: 11, 23, 25
2. Section 7.5: 3, 5, 10, 12, 17, 41, 49
3. Section 7.6: 1, 7

Evaluation:

On Wednesday, October 9, the above objectives will be evaluated with a short quiz. You will take the quiz individually, and your group will be given the average score achieved by the members of your group.