A topological invariant is a numerical parameter associated with molecular graph and plays an imperative role in the study and analysis of quantitative structure activity/property relationships (QSAR/QSPR). The correlation between the entire -electron energy and the structure of a molecular graph was explored and understood by the first Zagreb index. Recently, Liu et al. (2019) calculated the first general Zagreb index of the -sum graphs. In the same paper, they also proposed the open problem to compute the general Randić index of the -sum graphs, where and denote the valency of the vertex in the molecular graph . Aim of this paper is to compute the lower and upper bounds of the general Randić index for the -sum graphs when . We present numerous examples to support and check the reliability as well as validity of our bounds. Furthermore, the results acquired are the generalization of the results offered by Deng et al. (2016), who studied the general Randić index for exactly .

中文翻译：

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F-和图的一般Randić指数的界线

拓扑不变量是与分子图相关的数值参数，在定量结构活性/性质关系（QSAR / QSPR）的研究和分析中起着至关重要的作用。整个之间的相关性-电子能量和分子图的结构进行了探讨，并通过所述第一萨格勒布索引理解。最近，刘等。（2019）计算出的第一一般萨格勒布索引-总和的曲线图。在同一篇论文中，他们还提出了开放问题以计算一般的兰迪奇指数对的-和图形，其并表示分子图中顶点的价。本文的目的是为-和图计算通用Randić指数的上下界。我们提供了许多示例来支持和检查边界的可靠性和有效性。此外，获得的结果是Deng等人提供的结果的概括。（2016），他研究了Randić指数。