Abstract Metal-organic frameworks (MOFs) are porous materials formed by strong bonds between metal ions and organic ligands to represent very high surface area, large pore volume, excellent chemical stability and unique morphology. Work on synthesis, structures and characteristics of many MOFs shows the importance of these frameworks with versatile applications, such as energy storage devices of excellent electrode materials, gas storage, heterogeneous catalysis, environmental hazard, assessment of chemicals and sensing of different gases. A topological property or index is a numerical invariant that predicts the physicochemical properties of the chemical compounds of the underlying molecular graph or framework. Wiener (1947) created the practice of the topological indices (TI’s) in organic molecules with the reference of boiling point of paraffin. In this paper, we study the two different metal-organic frameworks with respect to the number of increasing layers with metal and organic ligands as well. We also compute the generalized Zagreb index and generalized Zagreb connection index of these frameworks. Moreover, the various indices and connection indices are obtained by using the aforesaid generalized versions. At the end, a comparison is also included between the indices and connection indices with the help of numerical values and their 3D plots.

中文翻译：

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金属有机骨架的拓扑性质

摘要 金属有机骨架（MOFs）是由金属离子与有机配体之间强键结合形成的多孔材料，具有极高的表面积、大孔容、优异的化学稳定性和独特的形貌。许多 MOF 的合成、结构和特性的工作表明这些框架具有多种应用的重要性，例如优良电极材料的储能装置、气体存储、多相催化、环境危害、化学品评估和不同气体的传感。拓扑性质或指数是预测潜在分子图或框架的化合物的物理化学性质的数值不变量。Wiener (1947) 以石蜡的沸点为参考，创建了有机分子中拓扑指数 (TI) 的实践。在本文中，我们还研究了两种不同的金属 - 有机框架，以及金属和有机配体的层数增加。我们还计算了这些框架的广义萨格勒布指数和广义萨格勒布连接指数。此外，各种索引和连接索引是通过使用上述广义版本获得的。最后，在数值及其 3D 绘图的帮助下，还包括索引和连接索引之间的比较。各种指标和连接指标是利用上述广义版本得到的。最后，在数值及其 3D 绘图的帮助下，还包括索引和连接索引之间的比较。各种指标和连接指标是利用上述广义版本得到的。最后，在数值及其 3D 绘图的帮助下，还包括索引和连接索引之间的比较。