Connection-Based Zagreb Indices of Polycyclic Aromatic Hydrocarbons Structures.

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.

Method: 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.