Explain why the Prufer code 01274 is invalid.
Write the Extended Prufer code and draw the corresponding tree:
01264
02020
54321
7634244
333333
Write the Prufer code for the trees on the side whiteboard.
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.
Show that a graph \(G\) is a tree if and only if it contains no cycles, but adding any new edge creates a cycle.