On the Degree-Ratio Sombor Index: Corrections and New Bounds

Abstract

The degree-ratio Sombor index (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 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 DRSO and other classical indices, including the Diminished Sombor index, the Sombor index, the Randi´c index, the harmonic index, and the first Zagreb index.