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Goldsborough, Andrew M.; Rautu, S. Alex; Römer, Rudolf A. (2014)
Publisher: IOP Publishing Ltd.
Languages: English
Types: Preprint
Subjects: Q1, QA, QC, Mathematical Physics

Classified by OpenAIRE into

arxiv: Quantitative Biology::Tissues and Organs
We study the leaf-to-leaf distances on full and complete m-ary graphs\ud 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.
  • The results below are discovered through our pilot algorithms. Let us know how we are doing!

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