The diminished Sombor index of a graph \( G \) with edge set \( E \) is defined as \[ DSO(G)=\sum_{uv \in E} \frac{\sqrt{d_u^2+d_v^2}}{d_u+d_v}, \] in which \( d_u \) and \( d_v \) are the degrees of the adjacent vertices \( u \) and \( v \), respectively.
In this note, we determine the unique tricyclic graph of a given order maximizing DSO, and characterize some structural properties of this graph.