无规聚亚苯基和螺环链的期望子树数指数
The expected subtree number index in random polyphenylene and spiro chains
摘要：
图$G$的子树数索引$\emph{STN}(G)$是$G$的非空子树的数目。它是一种基于结构和计数的拓扑指数，近年来受到越来越多的关注。本文首先给出了一类无支链多螺环分子和多环芳烃的分子图--无规聚苯撑链和螺环链的子树数指数的期望值的精确公式。此外，我们还建立了无规聚亚苯基的子树数指数的期望值与其相应的六角压缩之间的关系。我们还提出了子树数指数的平均值相对于所有的聚亚苯基和螺链与$n$六边形。
英文摘要：
Subtree number index $\emph{STN}(G)$ of a graph $G$ is the number of nonempty subtrees of $G$. It is a structural and counting based topological index that has received more and more attention in recent years. In this paper we first obtain exact formulas for the expected values of subtree number index of random polyphenylene and spiro chains, which are molecular graphs of a class of unbranched multispiro molecules and polycyclic aromatic hydrocarbons. Moreover, we establish a relation between the expected values of the subtree number indices of a random polyphenylene and its corresponding hexagonal squeeze. We also present the average values for subtree number indices with respect to the set of all polyphenylene and spiro chains with $n$ hexagons.
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