Maximum Diminished Sombor Index of Molecular Trees with a Perfect Matching

TL;DR

This paper investigates the maximum diminished Sombor index in molecular trees with perfect matchings, characterizes extremal structures, and explores its relevance for predicting properties of octane isomers.

Contribution

It determines the maximum DSO index for molecular trees with perfect matchings and characterizes the extremal trees, linking graph theory to chemical property prediction.

Findings

Identified the maximum DSO index among molecular trees with perfect matchings.

Characterized all extremal trees achieving the maximum DSO.

Explored the chemical applicability of DSO for octane isomers.

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.