Maximum Diminished Sombor Index of Molecular Trees with a Perfect Matching

Abstract: The diminished Sombor index $(DSO)$ of a graph $G$, introduced by Rajathagiri, is defined as $$DSO(G)=\sum_{uv\in E}\frac{\sqrt{d_u^2+d_v^2}}{d_u+d_v},$$ where $d_u$ and $d_v$ are the degrees of vertices $u$ and $v$. A graph $G$ is a molecular graph if $d_G(u)\leq 4$ for all $u\in V(G)$. In this paper, we examine the chemical applicability of the $DSO$ index for predicting physicochemical properties of octane isomers. We also determine the maximum value of the diminished Sombor index among all molecular trees of order $n$ with perfect matching and characterize all the corresponding extremal trees.