论文标题
预期的子树数字指数在随机聚苯乙烯和螺旋链中
The expected subtree number index in random polyphenylene and spiro chains
论文作者
论文摘要
图$ g $的子树编号索引$ \ emph {stn}（g）$是$ g $的非空子树的数量。这是一个基于结构和计数的拓扑指数，近年来一直受到越来越多的关注。在本文中，我们首先获得了随机聚苯二苯和螺旋链的子树量指数的预期值的精确公式，这些链是一类无支柱的多尖分分子和多环芳族烃的分子图。此外，我们建立了随机聚苯乙烯的子树数量指数的期望值与其相应的六边形挤压之间的关系。我们还提供了与$ N $ hexagons的所有聚苯和螺旋链的集合相对于子树数量指数的平均值。
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.
