Usman Muhammad, Javaid Muhammad
Department of Mathematics, School of Science, University of Management and Technology, Lahore, 54770, Pakistan.
Curr Org Synth. 2023 Aug 23. doi: 10.2174/1570179421666230823141758.
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.
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.
Theoretical applications of topological indices were described in detail.
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.
拓扑指数（TIs）是应用于数学化学领域的数学公式，用于预测各种化学结构的物理和化学性质。在本研究中，借助基于不同连接数的 Zagreb 指数，对三种不同类型的多环芳烃结构（PAHs）（即六并六苯并蔻、十二苯并环蔻和六邻位六苯并蔻）进行了研究。
ϑ = (V(ϑ),E(ϑ)) 用作图，其中 V(ϑ) 是顶点集，E(ϑ) 是边集。对于顶点 y ∈ V(ϑ)，度 d_ϑ (y) 是与 y 距离为 1 的顶点数量，连接数 ρ_ϑ (y) 是与顶点 y 距离为 2 的此类顶点数量。
详细描述了拓扑指数的理论应用。
最后，我们得到了第一和第二 Zagreb 连接以及修正的第一、第二、第三和第四 Zagreb 连接指数，这些指数是针对三种不同类型（六并六苯并蔻、十二苯并环蔻和六邻位六苯并蔻）的多环芳烃结构计算得出的。
