vertexorder=breadthfirst or depthfirst

Specifies whether the order of vertices in the graph should follow a breadth-first or depth-first traversal of the tree. The default is depthfirst.

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.

The CompleteKaryArborescence(k,n) command constructs the complete k-ary arborescence with depth n.

The CompleteKaryAntiArborescence(k,n) command constructs the complete k-ary anti-arborescence with depth n.

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

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

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

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

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

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

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

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

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

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

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

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

$\mathrm{CA}≔\mathrm{CompleteKaryArborescence}\left(3\,2\right)$

$\mathrm{CA}≔\mathrm{Graph\; 3:\; a\; directed\; graph\; with\; 13\; vertices\; and\; 12\; arc(s)}$

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

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

$\mathrm{CAA}≔\mathrm{CompleteKaryAntiArborescence}\left(3\,2\right)$

$\mathrm{CAA}≔\mathrm{Graph\; 4:\; a\; directed\; graph\; with\; 13\; vertices\; and\; 12\; arc(s)}$

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

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

The vertexorder option was introduced in Maple 2019.

For more information on Maple 2019 changes, see Updates in Maple 2019.

The GraphTheory[SpecialGraphs][CompleteKaryArborescence] and GraphTheory[SpecialGraphs][CompleteKaryAntiArborescence] commands were introduced in Maple 2022.

For more information on Maple 2022 changes, see Updates in Maple 2022.