Abstract
The path length of a tree, that is, the sum of the lengths of all root-leaf paths, is an important measure of efficiency of the tree. The fringe of a tree is the difference between the lengths of the longest path and the shortest path in the tree. The minimal and the maximal path length of trees with N leaves and given fringe have been well studied. In this paper, we initiate the study of the expected path length of the class of trees with N leaves and fringe Δ by giving a closed expression for the expected path length when Δ = 2.
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