For a graph , a wide range of transformations are possible. A graph can be converted into a new graph by adding vertices or edges following certain criteria. A graph derived from the parent graph by inserting a new vertex into each of its edge is known as subdivision graph and can be denoted as . The transformation graph of a graph can be defined as a graph whose vertex set is union of the vertex set and edge set of and whose edge set is defined under certain conditions. Structure descriptors are widely used now-a-days to model the physico-chemical, structural and electronic properties of chemical compounds and networks. A structure descriptor of a transformation graph reflects different structural features than a structure descriptor of the original graph . By determining various structure descriptors of the transformation graphs of a molecule, wide range of structural properties of the underlying molecule could be modelled. In this study, the concept of transformation graph is applied on subdivision graph and further the structural properties of those graphs are studied via structure descriptors. The expressions for first Zagreb index and forgotten index of transformation graphs of subdivision graphs are determined in terms of parameters of the parental graph. Further, applying the determined results, a structural analysis was also carried out on a chemical graph.

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通过结构描述符对细分图的变换进行结构分析

对于图来说，可以进行多种变换。通过按照一定条件添加顶点或边，可以将图转换为新图。通过将新顶点插入到其每条边中而从父图导出的图称为细分图，可以表示为 。图的变换图可以定义为这样的图，其顶点集是 的顶点集和边集的并集，并且其边集是在一定条件下定义的。结构描述符如今被广泛用于模拟化合物和网络的物理化学、结构和电子特性。变换图的结构描述符反映了与原始图的结构描述符不同的结构特征。通过确定分子变换图的各种结构描述符，可以对基础分子的各种结构特性进行建模。在本研究中，变换图的概念应用于细分图，并进一步通过结构描述符研究这些图的结构特性。根据父图的参数确定细分图变换图的第一萨格勒布索引和遗忘索引的表达式。此外，应用测定结果，还在化学图谱上进行结构分析。