Graph Theory

1. Looking at the graph above, answer the following:
a. Identify the number of odd vertices.
b. Identify the number of even vertices.
c. Does it have a Euler circuit? Does it have a Euler path? Explain your answers

2. Looking at the graph above, answer the following:
a. Identify the number of odd vertices.
b. Identify the number of even vertices.
c. Does it have a Euler circuit? Does it have a Euler path? Explain your answers.

3. Find 3 different Hamilton circuits in the graph above

4. How many distinct Hamilton circuits does the graph above have? List them using A as the starting vertex.

5. How many edges are in K17, the complete graph with 17 vertices?

6. Explain why the graph below has no Hamilton circuit but does have a Hamilton path

Submit your answers to the questions above by downloading and completing the Graph Theory and Travelling Salesman Problem worksheet.