Abstract The quantitative structures activity relationships (QSAR) and quantitative structures property relationships (QSPR) between the chemical compounds are studied with the help of topological indices (TI’s) which are the fixed real numbers directly linked with the molecular graphs. Gutman and Trinajstic (1972) defined the first degree based TI to measure the total π-electrone energy of a molecular graph. Recently, Ali and Trinajstic (2018) restudied the connection based TI’s such as first Zagreb connection index, second Zagreb connection index and modified first Zagreb connection index to find entropy and accentric factor of the octane isomers. In this paper, we study the modified second Zagreb connection index and modified third Zagreb connection index on the T-sum (molecular) graphs obtained by the operations of subdivision and product on two graphs. At the end, as the applications of the obtained results for the modified Zagreb connection indices of the T-sum graphs of the particular classes of alkanes are also included. Mainly, a comparision among the Zagreb indices, Zagreb connection indices and modified Zagreb connection indices of the T-sum graphs of the particular classes of alkanes is performed with the help of numerical tables, 3D plots and line graphs using the statistical tools.

中文翻译：

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T-sum 图的修改萨格勒布连接索引

摘要 借助与分子图直接相关的固定实数拓扑指数（TI's），研究了化合物之间的定量结构活性关系（QSAR）和定量结构性质关系（QSPR）。Gutman 和 Trinajstic (1972) 定义了基于一阶的 TI 来测量分子图的总 π 电子能量。最近，Ali 和 Trinajstic (2018) 重新研究了基于连接的 TI，例如第一萨格勒布连接指数、第二萨格勒布连接指数和修改后的第一萨格勒布连接指数，以找到辛烷值异构体的熵和重音因子。在本文中，我们在两个图上通过细分和乘积运算得到的T-sum（分子）图上研究了修正的第二萨格勒布连接指数和修正的第三萨格勒布连接指数。最后，还包括所得结果对特定烷烃类的 T 和图的修正萨格勒布连接指数的应用。主要是在数值表、3D 绘图和使用统计工具的线图的帮助下，对特定类别烷烃的 T 和图的萨格勒布指数、萨格勒布连接指数和修改的萨格勒布连接指数进行了比较。