# What is the name of this function of a tree?

I've written a recursive function of a tree, and I would like to know what it's called! It's not quite the same as the height or the width of a tree, but it seems kind of like a width.

Assuming the tree $T$ is binary, we can define the function $f(T)$ as follows. If $T$ has a only a single node, let $f(T) = 1$. Otherwise, let $T_0$ and $T_1$ be the two trees rooted at the child nodes $T$'s root. If $f(T_0) = f(T_1)$, then let $F(T) = F(T_0) + 1$; otherwise, let $f(T) = \max(f(T_0), f(T_1))$.

The function $f$ is generalized as follows to trees that are not necessarily binary. As before, let $f(T) = 1$ when $T$ has no edges. Otherwise, let $T_0, \dots, T_k$ be the $k+1$ subtrees rooted at the child nodes of $T$'s root, sorted by descending values of $f$. Then let $f(T) = \max_i(f(T_i) + i)$.

This is basically the Strahler number, which is great because now I can call my function ComputeStrahlerNumber instead of keeping the profane function name I was using as a placeholder.