Sharp Bounds on Diminished Sombor Index

Meysam Taheri-Dehkordi; Amir Hossein Nokhodkar; Gholam Hossein Fath-Tabar

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arXiv · 2607.20562

Sharp Bounds on Diminished Sombor Index

Meysam Taheri-Dehkordi·Amir Hossein Nokhodkar·Gholam Hossein Fath-Tabar

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Abstract

The Diminished Sombor index $(DSO)$ of a simple graph $G$ is a recently introduced degree-based topological index, defined as \[ DSO(G)= \sum_{uv\in E(G)} \frac{\sqrt{d_u^2+d_v^2}} {d_u+d_v} \] In this paper, we establish a collection of new sharp bounds for the $DSO$ index in terms of several fundamental graph parameters and well-known topological indices. In all cases, the proposed bounds rigorously specify the equality conditions, thereby providing a complete characterization of the extremal graphs. These findings deepen the theoretical understanding of the $DSO$ index and provide powerful analytical tools for interdisciplinary applications in mathematical chemistry.

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BibTeX RIS

Meysam Taheri-Dehkordi, Amir Hossein Nokhodkar, Gholam Hossein Fath-Tabar. 2026-07-19. Sharp Bounds on Diminished Sombor Index. https://arxiv.org/abs/2607.20562

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