Applied combinatorics: graph theory non-isomorphic trees help please?
Hi I wonder if someone can help me with the following questions:
(a) List all non-isomorphic trees (not rooted) on 12 vertices with each vertex of degree either 1 or 3.
I get only one such tree with 5 internal vertices of degree 3 and 7 leaves (of degree 1) I think this is correct but if I'm missing something please let me know.
The question I'm having trouble with is this one:
(b)Explain why your list in (a) contains no repetition (i.e. why the trees are all non-isomorphic), as well as why your list contains all such trees.
I used trial and error to find the tree so how do explain that it is unique?
Any help would be greatly appreciated.
Thanks in advance.