A set Formula: see text is a dominating set of a graph Formula: see text if every vertex of Formula: see text is adjacent to some vertex in Formula: see text. The domination number Formula: see text is the minimum cardinality among all dominating sets of Formula: see text The subdivision graph Formula: see text of a graph Formula: see text is a graph obtained from Formula: see text by replacing each edge Formula: see text of Formula: see text by a vertex Formula: see text and edges Formula: see text and Formula: see text. Esteban De Jesús Sánchez et. al On the (total) domination in subdivision graphs, Discret. Appl. Math. 384 (2026) 201–210. proved that for every tree Formula: see text of order Formula: see text with Formula: see text leaves, Formula: see text. In this note, we provide a constructive characterization of extremal trees attaining these two bounds.
Chellali et al. (Fri,) studied this question.