Dendrimers are highly defined hyperbranched artificial macromolecules, synthesised by convergent or divergent approach with specific applications in various fields. Dendrimers can be represented as graph models, from which a quantitative description can be drawn in relation with their structural properties. The distance-based and the degree-based descriptors have great importance and huge applications in structural chemistry. These indices together with entropy measures are found to be more effective and have found application in scientific fields. The idea of graph entropy is to characterise the complexity of graphs. The use of these graph invariants in quantitative structure property relationship and quantitative structure activity relationship studies has become of major interest in recent years. In this paper, the distance-based molecular descriptors of pyrene cored dendrimers are studied applying the technique of converting original graph into quotient graphs using -classes. It is to be noted that, since the pyrene cored dendrimer, is not a partial cube, usual cut method is not applicable. Further, various degree-based descriptors and their corresponding graph entropies of the pyrene cored dendrimers are also studied. Based on the obtained results, a comparative analysis as well as a regression analysis was carried out.

中文翻译：

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通过商图方法计算芘核树枝状聚合物的结构描述符及其图熵测量

树枝状聚合物是高度定义的超支化人工大分子，通过聚合或发散方法合成，在各个领域都有特定的应用。树枝状聚合物可以表示为图形模型，从中可以得出与其结构特性相关的定量描述。基于距离和基于度的描述符在结构化学中具有重要的重要性和巨大的应用。人们发现这些指数与熵度量一起更有效，并已在科学领域得到应用。图熵的思想是表征图的复杂程度。近年来，这些图不变量在定量结构属性关系和定量结构活动关系研究中的使用已成为人们的主要兴趣。本文利用类将原始图转换为商图的技术，研究了芘核树枝状聚合物的基于距离的分子描述符。需要指出的是，由于芘核树枝状聚合物不是部分立方体，因此通常的切割方法不适用。此外，还研究了芘核树枝状聚合物的各种基于度的描述符及其相应的图熵。根据所得结果，进行了比较分析和回归分析。