On the mean subtree order of trees under edge contraction

For a tree T, the mean subtree order of T is the average order of a subtree of T. In 1984, Jamison conjectured that the mean subtree order of T decreases by at least 1/3 after contracting an edge in T. In this article we prove this conjecture in the special case that the contracted edge is a pendant edge. From this result, we have a new proof of the established fact that the path Pn has the minimum mean subtree order among all trees of order n. Moreover, a sharp lower bound is derived for the difference between the mean subtree orders of a tree T and a proper subtree S (of T), which is also used to determine the tree with second-smallest mean subtree order among all trees of order n