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This is a Quantitative Study study.

October 16, 2025Open Access

Diminished Sombor index and its relationship with topological indices

Key Points

The diminished sombor index relates closely to various classical topological indices in graph theory.
Sharp bounds for the diminished sombor index are established using indices such as Zagreb and Randić.
Characterizations of extremal graphs are provided for equality conditions between diminished sombor and topological indices.
In-depth analysis of inequalities enhances understanding of the connections among different graph indices.

Abstract

In this paper, we investigate the Diminished Sombor index (DSO), a recently introduced degree-based topological index for a simple graph G, defined as \ DSO (G) = ₔₕ ₄ dᵤ²+dᵥ²dᵤ+dᵥ, \ where dᵤ denotes the degree of a vertex u V. We establish several sharp bounds for this index in terms of classical topological indices such as the Zagreb, Albertson, Harmonic, Randić, and geometric-arithmetic indices. The relationships and inequalities between DSO and these indices are analyzed thoroughly, with characterizations of extremal graphs achieving equality conditions.

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Fateme Movahedi (Sun,) studied this question.

synapsesocial.com/papers/68f12bfb2107091eab27a39a https://doi.org/https://doi.org/10.48550/arxiv.2508.06532