# Harrison Chapman

## Math 301: Trees, II

Class date: Friday, November 22, 2019
1. Explain why the Prufer code 01274 is invalid.

2. Write the Extended Prufer code and draw the corresponding tree:

1. 01264

2. 02020

3. 54321

4. 7634244

5. 333333

3. Write the Prufer code for the trees on the side whiteboard.

4. Use a random number generator (ex: Google “roll a die”) to draw a random labeled tree with 10 vertices. Justify why your tree really is random.

5. Show that a graph $$G$$ is a tree if and only if it contains no cycles, but adding any new edge creates a cycle.