## 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 ${K_{6}}$.