Abstract Nanosheets are two-dimensional polymeric materials, which are among the most active areas of investigation of chemistry and physics. Many diverse physicochemical properties of compounds are closely related to their underlying molecular topological descriptors. Thus, topological indices are fascinating beginning points to any statistical approach for attaining quantitative structure–activity (QSAR) and quantitative structure–property (QSPR) relationship studies. Irregularity measures are generally used for quantitative characterization of the topological structure of non-regular graphs. In various applications and problems in material engineering and chemistry, it is valuable to be well-informed of the irregularity of a molecular structure. Furthermore, the estimation of the irregularity of graphs is helpful for not only QSAR/QSPR studies but also different physical and chemical properties, including boiling and melting points, enthalpy of vaporization, entropy, toxicity, and resistance. In this article, we compute the irregularity measures of graphene nanosheet, H-naphtalenic nanosheet, SiO 2 {\text{SiO}}_{2} nanosheet, and the nanosheet covered by C 3 {C}_{3} and C 6 {C}_{6} .

中文翻译：

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测量纳米片的不规则性

摘要 纳米片是二维高分子材料，是化学和物理学研究最活跃的领域之一。化合物的许多不同的物理化学性质与其潜在的分子拓扑描述符密切相关。因此，拓扑指数是获得定量结构-活性 (QSAR) 和定量结构-性质 (QSPR) 关系研究的任何统计方法的引人入胜的起点。不规则性度量通常用于对非正则图的拓扑结构进行定量表征。在材料工程和化学的各种应用和问题中，充分了解分子结构的不规则性是很有价值的。此外，图形不规则性的估计不仅有助于 QSAR/QSPR 研究，而且有助于不同的物理和化学性质，包括沸点和熔点、汽化焓、熵、毒性和电阻。在本文中，我们计算了石墨烯纳米片、H-萘纳米片、SiO 2 {\text{SiO}}_{2} 纳米片以及被 C 3 {C}_{3} 和 C 6 覆盖的纳米片的不规则性度量{C}_{6} .