Problem2A

Problem2A: Find the six nonisomorphic trees on {6} vertices, and for each compute the number of distinct spanning trees in { K_{6}} isomorphic to it.

Solution: There are six nonisomorphic trees on {6} vertices, drawn as follows.

There are {6!/2}, {6!/2}, {6!/2}, {6!/8}, {6!/3!}, and {6!/5!} labeled trees isomorphic to the {6} spanning trees respectively. So in total, there are { 1296=6^{4}} distinct spanning trees in {K_{6}}.

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