BananaTree(n,k) creates an (n,k) banana tree.

The banana tree is a graph constructed by connecting a single leaf from n distinct copies of a k-star graph with a single vertex distinct from the star graphs.

Each such graph has n*(k+1)+1 vertices and (n+1)*k edges.

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

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

$B≔\mathrm{BananaTree}\left(4\,3\right)$

$B≔\mathrm{Graph\; 1:\; an\; undirected\; graph\; with\; 17\; vertices\; and\; 16\; edge(s)}$

$\mathrm{IsPlanar}\left(B\right)$

$\mathrm{true}$

$\mathrm{ChromaticNumber}\left(B\right)$

$2$

$\mathrm{DrawGraph}\left(B\,\mathrm{style}=\mathrm{planar}\right)$

The GraphTheory[SpecialGraphs][BananaTree] command was introduced in Maple 2021.

For more information on Maple 2021 changes, see Updates in Maple 2021.