The HaarGraph(n) function creates the nth Haar graph.

The nth Haar graph is a bipartite graph on m = 2*ilog[2](i)+2 vertices in which the vertices u[i] and v[j] are adjacent if the kth digit in the binary expansion of n is nonzero, where k = irem(j-i,m).

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

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

$W≔\mathrm{HaarGraph}\left(7\right)$

$W≔\mathrm{Graph\; 1:\; an\; undirected\; graph\; with\; 6\; vertices\; and\; 9\; edge(s)}$

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

$\left\{\left\{0\,1\right\}\,\left\{0\,3\right\}\,\left\{0\,5\right\}\,\left\{1\,2\right\}\,\left\{1\,4\right\}\,\left\{2\,3\right\}\,\left\{2\,5\right\}\,\left\{3\,4\right\}\,\left\{4\,5\right\}\right\}$

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

The GraphTheory[SpecialGraphs][HaarGraph] command was introduced in Maple 2020.

For more information on Maple 2020 changes, see Updates in Maple 2020.