The KnightsGraph(m,n) command creates the m by n knight's graph on m*n vertices. This is the bipartite graph which represents all legal moves of the knight chess piece on an m by n chessboard.

An m by n knight's graph has $4mn-6m-6n\+8$ edges when m and n are both greater than 1, and zero edges otherwise.

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

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

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

$R≔\mathrm{Graph\; 1:\; an\; undirected\; graph\; with\; 24\; vertices\; and\; 44\; edge(s)}$

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

$\mathrm{false}$

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

$2$

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

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

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