On the mean subtree order of trees under edge contraction

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