The CompleteBinaryTree(n) command constructs the complete binary tree with depth n.

The CompleteKaryTree(k,n) command constructs the complete k-ary tree with depth n for a given k.

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

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

$G≔\mathrm{CompleteBinaryTree}\left(2\right)$

$G≔\mathrm{Graph\; 1:\; an\; undirected\; unweighted\; graph\; with\; 7\; vertices\; and\; 6\; edge(s)}$

$\mathrm{Edges}\left(G\right)$

$\left\{\left\{1\,2\right\}\,\left\{1\,5\right\}\,\left\{2\,3\right\}\,\left\{2\,4\right\}\,\left\{5\,6\right\}\,\left\{5\,7\right\}\right\}$

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

$H≔\mathrm{CompleteKaryTree}\left(3\,2\right)$

$H≔\mathrm{Graph\; 2:\; an\; undirected\; unweighted\; graph\; with\; 13\; vertices\; and\; 12\; edge(s)}$

$\mathrm{Edges}\left(H\right)$

$\left\{\left\{1\,2\right\}\,\left\{1\,6\right\}\,\left\{1\,10\right\}\,\left\{2\,3\right\}\,\left\{2\,4\right\}\,\left\{2\,5\right\}\,\left\{6\,7\right\}\,\left\{6\,8\right\}\,\left\{6\,9\right\}\,\left\{10\,11\right\}\,\left\{10\,12\right\}\,\left\{10\,13\right\}\right\}$

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