Szeged, PI and Mostar indices are some of the most investigated distance-based molecular descriptors. Recently, many different variations of these topological indices appeared in the literature and sometimes they are all together called Szeged-like topological indices. In this paper, we formally introduce the concept of a general Szeged-like topological index, which includes all mentioned indices and also infinitely many other topological indices that can be defined in a similar way. As the main result of the paper, we provide a cut method for computing a general Szeged-like topological index for any strength-weighted graph. This greatly generalizes various methods known for some of the mentioned indices and therefore rounds off such investigations. Moreover, we provide applications of our main result to benzenoid systems, phenylenes, and coronoid systems, which are well-known families of molecular graphs. In particular, closed-form formulas for some subfamilies of these graphs are deduced.

中文翻译：

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用于计算 Szeged 类拓扑指数的通用切割方法并应用于分子图

Szeged、PI 和 Mostar 指数是一些研究最多的基于距离的分子描述符。最近，这些拓扑指数的许多不同变体出现在文献中，有时它们统称为 Szeged 类拓扑指数。在本文中，我们正式介绍了一般 Szeged 类拓扑索引的概念，它包括所有提到的索引以及可以以类似方式定义的无限多个其他拓扑索引。作为论文的主要结果，我们提供了一种切割方法，用于计算任何强度加权图的一般 Szeged 类拓扑指数。这极大地概括了针对某些提到的指数已知的各种方法，因此完善了此类调查。此外，我们将我们的主要结果应用于苯类系统、亚苯基、和冠状系统，它们是众所周知的分子图家族。特别地，推导出了这些图的一些子族的封闭式公式。