The RooksGraph(m,n) command creates the m by n rook's graph on m*n vertices. This is the graph which represents all legal moves of the rook chess piece (also known as the castle) on an m by n chessboard.

When n and m are equal, the rook's graph is strongly regular.

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

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

$R≔\mathrm{RooksGraph}\left(4\,6\right)$

$R≔\mathrm{Graph\; 1:\; an\; undirected\; graph\; with\; 24\; vertices\; and\; 96\; edge(s)}$

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

$\mathrm{false}$

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

$6$

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

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

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