Computing the Neighbourhood Multiple Topological Indices of Dendritic Graphs

In this article, we extend the traditional multiple degree-based topological indices (TIs) to neighborhood multiple degree-based TIs with the aim of studying the branching and generation of three distinct dendrimers namely, poly (propyl ether imine) (PETIM), zinc porphyrin, and porphyrin. We defined and computed six existing neighborhood versions of multiple degree-based TIs for the dendrimers. The computational analysis revealed that our TIs display exponential or linear growth as the dendrimer generations increase. Our findings reveal that the extended TIs such as the second Zagreb index (Γ_MM₂(G)) and forgotten index (Γ_MF(G)) effectively capture the highest structural complexity, showing rapid exponential growth with each generation. In contrast, TIs; atom bond connectivity index (Γ_MABC(G)) and Randíc index (Γ_MR(G)) exhibit more moderate or linear growth, indicating their focus on more localized structural characteristics. These results contribute to a broader understanding of the dendrimer’s structural complexity and connectivity highlighting their potential in drug delivery applications. The research also reveals critical insights on the neighborhood multiple degree-based TI’s role as an efficient molecular descriptor that can characterize connectivity patterns of complex graphs. The analytical results have a further implication on the quantitative structure-property relationship (QSPR) modeling of these dendrimers.