Inequalities are a useful method to investigate and compare topological indices of graphs relatively. A large collection of graph associated numerical descriptors have been used to examine the whole structure of networks. In these analysis, degree related topological indices have a significant position in theoretical chemistry and nanotechnology. Thus, the computation of degree related indices is one of the successful topic of research. Given a molecular graph H , the general Randić connectivity index is interpreted as Rα(H)=∑ℛ∈E(H)(degH(a)degH(b))α, with α is a real quantity. Also a graph transformation of H provides a comparatively simpler isomorphic structure with an ease to work on different chemical properties. In this article, we determine the sharp bounds of general Randić index of numerous graph transformations, such that semi-total-point, semi-total-line, total and eight individual transformations Hfgh , where f, g, h ∈ {+ , -} of graphs by using combinatorial inequalities.

中文翻译：

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变换图的一般Randić索引的清晰边界

不等式是一种有用的方法，可以相对地研究和比较图的拓扑指标。图相关的数字描述符的大量收集已用于检查网络的整体结构。在这些分析中，与度相关的拓扑指数在理论化学和纳米技术中具有重要地位。因此，学位相关指标的计算是研究的成功课题之一。给定一个分子图H，一般的Randić连接性指数被解释为Rα（H）= ∑ℛ∈E（H）（degH（a）degH（b））α，其中α为实数。同样，H的图转换提供了相对简单的同构结构，易于处理不同的化学性质。在本文中，我们确定了众多图变换的一般Randić索引的尖锐边界，例如半总点，