The Leech tree, introduced by John Leech in 1975, is a tree on n vertices with positive integer edge weights such that the weighted distances between pairs of vertices are exactly 1, 2,..., !n 2 " . Only five Leech trees are known and some nonexistence results have been presented through the years. Variations of Leech trees such as the minimal distinct distance trees and modular Leech trees have been considered. In this note we examine such Leech-type questions on distances between leaves. We also introduce some other labeling questions related to the original motivation for Leech trees.
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