1. UNIT 3 THINKING MATHEMATICALLY BY BLITZER Hamilton Paths and Hamilton Circuits

2. We have studied paths and circuits that covered every edge of a graph. Using every edge of a graph is helpful for garbage collection, curb sweeping, or snow removal. What about a UPS driver trying to find the best way to deliver packages around town? In this situation a driver is only concerned about finding a path that passes through each vertex of the graph only once. Thus, it is not important to use every road or edge between the delivery locations. Thinking mathematically by Blitzer Pg: 842

3. Hamilton Path A path that passes all the vertices of a graph exactly once (must include all vertices).

4. Hamilton Circuit Starts at a vertex and visits each vertex once and only once, returning to where it started.

5. The number of Hamilton circuits in a complete graph If you have a graph that is complete and has a Hamilton circuit it has multiple sequences that will produce the same Hamilton circuit. In order to avoid a duplication you can start and end at vertex A. How many unique Circuits can you get from a complete Hamilton graph with four vertices? AB CD

6. The number of Hamilton circuits in a complete graph The number of Hamilton circuits in a complete graph with n vertices. (n-1)! Determine the number of Hamilton circuits in a complete graph with: a) Four vertices b) Five Vertices c) Eight Vertices

7. Weighted Graph Is when we assign numbers to the edges of a graph.