Abstract

The random polyphenyl chains with n hexagons are the special graphs of unbranched polycyclic aromatic hydrocarbons. The Randić (R) index and first Zagreb (M₁) index are two well-studied topological indices and found to be useful tools in QSPR and QSAR investigations. In this paper, we further establish simple explicit formulae for expected values of the Randić and first Zagreb indices in random polyphenyl chains and present the average values of these indices with respect to the set of all polyphenyl chains with n hexagons. Based on these formulae, we make comparisons between expected values of the Randić and first Zagreb indices in random polyphenyl chains.

摘要

具有n个六边形的无规多苯基链是无支链多环芳烃的特殊图。Randić ( R ) 指数和第一萨格勒布 ( M ₁ ) 指数是两个经过充分研究的拓扑指数，被发现是 QSPR 和 QSAR 调查中的有用工具。在本文中，我们进一步建立了随机多苯基链中 Randić 指数和第一萨格勒布指数期望值的简单显式公式，并给出了这些指数相对于具有n 个六边形的所有多苯基链的集合的平均值。基于这些公式，我们比较了随机多苯基链中 Randić 和第一个萨格勒布指数的预期值。