A numeric parameter which studies the behaviour, structural, toxicological, experimental, and physicochemical properties of chemical compounds under several graphs’ isomorphism is known as topological index. In 2018, Ali and Trinajstić studied the first Zagreb connection index to evaluate the value of a molecule. This concept was first studied by Gutman and Trinajstić in 1972 to find the solution of -electron energy of alternant hydrocarbons. In this paper, the first Zagreb connection index and coindex are obtained in the form of exact formulae and upper bounds for the resultant graphs in terms of different indices of their factor graphs, where the resultant graphs are obtained by the product-related operations on graphs such as tensor product, strong product, symmetric difference, and disjunction. At the end, an analysis of the obtained results for the first Zagreb connection index and coindex on the aforesaid resultant graphs is interpreted with the help of numerical values and graphical depictions.

中文翻译：

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第一Zagreb连接索引和结果图的共索引的计算分析

在几个图的同构下研究化合物的行为，结构，毒理学，实验和物理化学性质的数值参数被称为拓扑指数。2018年，Ali和Trinajstić研究了第一个Zagreb连接指数以评估分子的价值。该概念最早由Gutman和Trinajstić于1972年研究，目的是寻找以下方面的解决方案：交替碳氢化合物的电子能。本文以因子图的不同索引的形式，通过精确公式和结果图上限的形式获得了第一个Zagreb连接索引和共索引，其中结果图是通过图上的乘积相关操作获得的例如张量积，强积，对称差和析取。最后，借助于数值和图形描述来解释在上述结果图上对第一萨格勒布连接指数和共指数的获得结果的分析。