Abstract Graph theory served in different fields of sciences, especially in chemistry in which creating complex structures and studying their enormous properties. Graph operation is a tool to construct complex chemical structures using basic graphs. While studying their properties, topological descriptors are a well-known methodology introduced by chemists, and even after half of a century past, it is still serving. Formally, a topological descriptor or index is a numerical value corresponding to a chemical structure. This numerical value can be easily accessed by a particular equation, for example, the second Zagreb index, the first reformulated Zagreb, and also from the forgotten topological descriptor. In this particular work, we generalized two existing graph operations, and by using these newly developed graph operations, we created two complex structures by using two graph operations, namely, the corona product and double graph operation. Furthermore, to evaluate the chemical properties of these newly generated structures, we used the methodology of topological descriptors, particularly the first and second Zagreb, the first reformulated Zagreb, and forgotten topological descriptors. Moreover, we also presented the closed formulas of the first and second Zagreb co-indices for these newly generated structures.

中文翻译：

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由两个图操作及其拓扑描述符的泛化设计的结构

摘要 图论服务于不同的科学领域，尤其是在创造复杂结构和研究其巨大性质的化学领域。图运算是一种利用基本图构造复杂化学结构的工具。在研究它们的性质时，拓扑描述符是化学家引入的一种众所周知的方法，即使在过去的半个世纪之后，它仍然在起作用。形式上，拓扑描述符或索引是对应于化学结构的数值。这个数值可以很容易地通过一个特定的方程来访问，例如，第二个萨格勒布指数、第一个重新表述的萨格勒布指数，以及被遗忘的拓扑描述符。在这项特定的工作中，我们概括了两个现有的图操作，并通过使用这些新开发的图操作，我们使用两个图操作创建了两个复杂的结构，即电晕积和双图操作。此外，为了评估这些新生成结构的化学性质，我们使用了拓扑描述符的方法，特别是第一个和第二个萨格勒布，第一个重新制定的萨格勒布，以及被遗忘的拓扑描述符。此外，我们还为这些新生成的结构提出了第一和第二萨格勒布协指数的封闭公式。