Background: Topological indices (TIs) are mathematical formulas that are applied in mathematical chemistry to predict the physical and chemical properties of various chemical structures. In this study, three different types of polycyclic aromatic hydrocarbon structures (PAHs) (i.e., Hexa-peri-hexabenzocoronene, Dodeca-benzo-circumcoronene, and Hexa-cata- hexabenzocoronene) are studied with the help of the different connection number-based Zagreb indices. Materials and Methods: ϑ = (V(ϑ),E(ϑ)) is used as a graph, where V(ϑ) is a collection of vertices and E(ϑ) is a collection of edges. For a vertex y, ∈V(ϑ), the degree d_ϑ (y), is the number of those vertices that are at a distance of 1 from y and the connection number ρ_ϑ (y) is the number of such vertices that are at a distance of 2 from vertex y. Results: Theoretical applications of topological indices were described in detail. Conclusion: Finally, we obtained the first and second Zagreb connections as well as the modified first, second, third, and fourth Zagreb connection indices, which were calculated for three different types (Hexa-peri-hexabenzocorone, Dodeca-benzo-circumcoronene, and Hexa-cata-hexabenzocoronene) of polycyclic aromatic hydrocarbon structures.

中文翻译：

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基于连接的多环芳烃结构萨格勒布指数

背景：拓扑指数（TI）是数学化学中应用的数学公式，用于预测各种化学结构的物理和化学性质。在这项研究中，借助基于不同连接数的Zagreb，研究了三种不同类型的多环芳烃结构（PAH）（即Hexa-peri-六苯并苯、Dodeca-苯并环苯和Hexa-cata-六苯并苯）指数。材料和方法： ϑ = (V(ϑ),E(ϑ)) 用作图，其中 V(ϑ) 是顶点的集合，E(ϑ) 是边的集合。对于顶点 y，εV(ϑ)，度 d_ϑ (y) 是距 y 距离为 1 的顶点的数量，连接数 ρ_ϑ (y) 是位于 y 的顶点的数量距顶点 y 的距离为 2。结果：详细描述了拓扑指数的理论应用。结论：最后，我们获得了第一和第二萨格勒布连接以及修改后的第一、第二、第三和第四萨格勒布连接指数，这些指数是针对三种不同类型（Hexa-peri-六苯并酮、Dodeca-苯并环晕烯和六-催化-六苯并苯）的多环芳烃结构。