Abstract
AbstractFor a tree , the mean subtree order of is the average order of a subtree of . In 1984, Jamison conjectured that the mean subtree order of decreases by at least 1/3 after contracting an edge in . 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 has the minimum mean subtree order among all trees of order . Moreover, a sharp lower bound is derived for the difference between the mean subtree orders of a tree and a proper subtree (of ), which is also used to determine the tree with second‐smallest mean subtree order among all trees of order .
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