有限和无限m元树图的叶间距离及其矩
Leaf-to-leaf distances and their moments in finite and infinite m-ary tree graphs
摘要：
本文利用递归方法研究了满图和完全图上的叶间距离。在我们的公式中，叶子沿着一条线排列。我们发现明确的分析公式的总和的所有路径为任意叶到叶的距离r以及平均路径长度和时刻。我们表明，由此产生的显式表达式可以重铸的Hurwitz-Lerch超越。周期树的结果也给出了。对于不完全随机二叉树，我们提供了第一个结果的数值技术，我们发现一个快速下降的叶到叶的距离大r。
英文摘要：
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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