论文标题
部分可观测时空混沌系统的无模型预测
Counting the numbers of paths of all lengths in dendrimers and its applications
论文作者
论文摘要
对于正整数$ n $和$ k $，dendrimer $ t_ {n，k} $定义为半径$ n $的根树，其距离的所有顶点均低于root的距离$ n $。树枝状聚合物是围绕着中心核心的分支单元的重复迭代，是呈刺的有机大分子。树枝状聚合物用于多种领域，包括化学，纳米技术，生物学。在本文中，对于任何正整数$ \ ell $，我们计算$ t_ {n，k} $的长度$ \ ell $的路径数。由于我们的主要结果，我们获得了$ t_ {n，k} $的平均距离，我们可以为$ t_ {n，k} $的维也纳索引建立替代证明。此外，我们概括了由Vargör和Dündar在2011年推出的中等统治的概念，该概念为$ t_ {n，k} $。
For positive integers $n$ and $k$, the dendrimer $T_{n, k}$ is defined as the rooted tree of radius $n$ whose all vertices at distance less than $n$ from the root have degree $k$. The dendrimers are higly branched organic macromolecules having repeated iterations of branched units that surroundes the central core. Dendrimers are used in a variety of fields including chemistry, nanotechnology, biology. In this paper, for any positive integer $\ell$, we count the number of paths of length $\ell$ of $T_{n, k}$. As a consequence of our main results, we obtain the average distance of $T_{n, k}$ which we can establish an alternate proof for the Wiener index of $T_{n, k}$. Further, we generalize the concept of medium domination, introduced by Vargör and Dündar in 2011, of $T_{n, k}$.
