1. Graph Theory
Unit 2

2. 2.09 Path of Optimal Value

3. Definition
On a graph, the Path of Minimum Value corresponds to the DISTANCE between two vertices
The Path of Maximum Value corresponds to the simple path that travels the maximum amount of edges
On a network, the Path of Optimal Value corresponds to the WEIGHT of the path between two vertices

4. Example 1: Find the Paths of Minimum value between A and P
If there is an overwhelming number of ways to try, then you can use the strategy of labelling each vertex.

5. Example 2: Robert Bourassa Dam
This facility generates approximately 5328MW of electricity, which is transmitted via high-tension lines to Quebec’s main urban centers. Transmission lines lose some power depending on state of repair and other factors. The engineering crew has to find the path of least power loss at any given time from the Dam to M.

6. Example 3:Outdoor Medicine
A doctor must visit several villages in the Far North. He lives in village E and travels by snowmobile. The graph shows the villages he must visit. He usually spends 1 h in each village.

7. Questions
Give a path that the doctor can follow to visit all of the villages without passing through the same village twice and without returning home after his trip

8. Questions
Give a path that the doctor can take to visit every village without repeating and return home after.
How long does this path take him?

9. Questions
Why is it pointless to look for the leave value of an Euler path or circuit?

10. 2.09 Practice
Visions Book 2
Page 52
#4, 6, 8, 9, 10