TreeHeight returns the height of the tree T with the vertex r as root. In other words it returns the maximum distance of the vertices of T from r.

If the root r is omitted, TreeHeight returns the diameter of G.

$\mathrm{with}\left(\mathrm{GraphTheory}\right)\:$

$T≔\mathrm{Graph}\left(\left\{\left\{1\,2\right\}\,\left\{2\,3\right\}\,\left\{2\,4\right\}\,\left\{4\,5\right\}\right\}\right)$

$T≔\mathrm{Graph\; 1:\; an\; undirected\; unweighted\; graph\; with\; 5\; vertices\; and\; 4\; edge(s)}$

$\mathrm{TreeHeight}\left(T\,1\right)$

$3$

$\mathrm{TreeHeight}\left(T\,4\right)$

$2$

$\mathrm{DrawGraph}\left(T\right)$

The GraphTheory[TreeHeight] command was updated in Maple 2021.