  A spanning tree of an unweighted graph is a minimum average stretch spanning
tree if it minimizes the ratio of sum of the distances in the tree between the
end vertices of the graph edges and the number of graph edges. We consider the
problem of computing a minimum average stretch spanning tree in polygonal
2-trees, a super class of 2-connected outerplanar graphs. For a polygonal
2-tree on $n$ vertices, we present an algorithm to compute a minimum average
stretch spanning tree in $O(n \log n)$ time. This algorithm also finds a
minimum fundamental cycle basis in polygonal 2-trees.
