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arXiv · 1406.4079

Leaf-to-leaf distances and their moments in finite and infinite m-ary tree graphs

Andrew M. Goldsborough·S. Alex Rautu·Rudolf A. Römer
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Abstract

We study the leaf-to-leaf distances on full and complete m-ary graphs using a recursive approach. In our formulation, leaves are ordered along a line. We find explicit analytical formulae for the sum of all paths for arbitrary leaf-to-leaf distance r as well as the average path lengths and the moments thereof. We show that the resulting explicit expressions can be recast in terms of Hurwitz-Lerch transcendants. Results for periodic trees are also given. For incomplete random binary trees, we provide first results by numerical techniques; we find a rapid drop of leaf-to-leaf distances for large r.

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Andrew M. Goldsborough, S. Alex Rautu, Rudolf A. Römer. 2015-04-17. Leaf-to-leaf distances and their moments in finite and infinite m-ary tree graphs. https://doi.org/10.1103/physreve.91.042133

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