I am searching for a term that describes the following property of a rooted tree (or actually a DODAG, but that should not make a difference) and preferably for a publication that uses/introduces this term.

Given a tree $ T=(V,E)$ with a dedicated root $ v_0 \in V$ . The depth $ \delta(v)$ of a vertex $ v$ is the length of the (shortest) path to $ v_0$ . The depth of the tree is denoted as $ \delta_{max} = max_{v \in V}\,\,\delta(v)$ . The set of vertices with the same depth is denoted as $ L(d) = \{ v \,|\, \delta(v) = d\}$ . What is an appropriate term for the maximum number of elements in the $ L(d)$ , that is $ W = max_{d \in [0,\delta_{max}]}\, |L(d)|$ ?

In the above example, the number would be $ W=5$ , because there are 5 vertices with depth 3. Potential terms that came to my mind where tree width, but that is actually 1 for all trees (with at least two vertices) or fan-out, but that is defined per vertex and the fan-out of a tree is the maximum over all fan-outs of the vertices (3 in the above example).