***ANSWER IN PYTHON PLEASE***

1. Construct random trees on =10,11,12 nodes (one each is enough). For each such tree, draw it, compute its Prfer code and then convert the code back into a tree. Do you get your old tree back?

2. For a few randomly chosen Prfer codes, construct the corresponding tree, draw it if you want, and convert it back into a Prfer code. Do you get your old code back?

3. Which labelled tree on n nodes {0,1,,n1} corresponds to the Prfer code [0,1,2,,n3]?

4. Which labelled tree on n nodes {0,1,,n1} corresponds to a Prfer code which has n2 identical entries?

3. Random Trees The nx. randon_tree (n) command can be used to generate a random tree on the n vertices represented in python by range( (n) (in order). Such a tree can be converted into a sequence of n2 numbers, its Prufer code by the python function pruefer_code, defined as follows: Conversely, the following function tree_pruefer constructs a tree from a Prer code. Conversely, the following function tree_pruefer constructs a tree from a Prfer code