BishopsGraph(m,n) creates the m by n bishop's graph on m*n vertices. This is the bipartite graph representing all legal moves of a bishop chess piece on an m by n chessboard.

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

BishopsGraph(m,n,"white") command creates the m by n white bishop's graph on m*n vertices. BishopsGraph(m,n,"black") similarly creates a black bishop's graph.

These are the graphs representing the legal moves of the white or black bishop chess piece, respectively, on an m by n chessboard.

The white and black bishop's graphs correspond to the two connected components of the bishop's graph.

An m by n white or black bishop's graph has $2mn-3m-3n\+4$ edges when m and n are both greater than 1, and zero edges otherwise.

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

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

$B≔\mathrm{BishopsGraph}\left(4\,6\right)$

$B≔\mathrm{Graph\; 1:\; an\; undirected\; graph\; with\; 24\; vertices\; and\; 52\; edges}$

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

$\mathrm{false}$

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

$\mathrm{false}$

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

$\left[\left[''1:1''\,''1:3''\,''1:5''\,''2:2''\,''2:4''\,''2:6''\,''3:1''\,''3:3''\,''3:5''\,''4:2''\,''4:4''\,''4:6''\right]\,\left[''1:2''\,''1:4''\,''1:6''\,''2:1''\,''2:3''\,''2:5''\,''3:2''\,''3:4''\,''3:6''\,''4:1''\,''4:3''\,''4:5''\right]\right]$

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

$\mathrm{WB}≔\mathrm{BishopsGraph}\left(4\,6\,''white''\right)$

$\mathrm{WB}≔\mathrm{Graph\; 2:\; an\; undirected\; graph\; with\; 24\; vertices\; and\; 26\; edges}$

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

The GraphTheory[SpecialGraphs][BishopsGraph] command was introduced in Maple 2023.

For more information on Maple 2023 changes, see Updates in Maple 2023.