Speaker
Description
Let $G$ be a simple connected graph. A vertex-degree-based topological index is defined as $$TI_f(G) = \sum_{uv \in E(G)} f(d_u, d_v),$$ where $f(x, y)$ is a symmetric real function. In theoretical chemistry, these indices serve as essential numerical molecular descriptors in QSAR/QSPR models. In this work, we investigate the extremal properties of $TI_f + RTI_f$, defined as the sum of a topological index and its reciprocal. Focusing on the first Zagreb index ($f(x, y) = x + y$), the second Zagreb index ($f(x, y) = xy$), and the forgotten index ($f(x, y) = x^2 + y^2$), we characterize the graphs that achieve the maximum and minimum values of $TI_f + RTI_f$ among all trees. Furthermore, we extend our analysis to the extremal problem for $TI_f + RTI_f$ of $k$-uniform hypergraphs.