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Title:
On the Degree-Ratio Sombor Index: Corrections and New Bounds
Authors:
Zhoujian Shao
Akbar Jahanbani ORCID iD 0000-0002-2800-4420
Volume
97
Issue
2
Year
2027
Pages
657-675
Abstract

The degree-ratio Sombor index (\( \operatorname{DRSO} \)) is a recently introduced geometric degree-based topological invariant. First, we correct an erroneous lower bound involving the Sombor index and rectify the characterization of extremal graphs from the original work on this index [11]. Subsequently, we investigate the relationship between the \( \operatorname{DRSO} \) index and the spectral radius of a graph. Sharp upper and lower bounds involving the graph's order, size, minimum and maximum degree are obtained. Finally, we establish several relations between \( \operatorname{DRSO} \) and other classical indices, including the Diminished Sombor index, the Sombor index, the Randić index, the harmonic index, and the first Zagreb index.