GraphTheory[SpecialGraphs]
BishopsGraph
construct bishop's graph
Calling Sequence
Parameters
Description
Examples
Compatibility
BishopsGraph(m,n)
BishopsGraph(m,n, player)
m, n
-
positive integers
player
string, one of "white", "black", or "both"
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 4⁢m⁢n−6⁢m−6⁢n+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 2⁢m⁢n−3⁢m−3⁢n+4 edges when m and n are both greater than 1, and zero edges otherwise.
with⁡GraphTheory:
with⁡SpecialGraphs:
B≔BishopsGraph⁡4,6
B≔Graph 1: an undirected graph with 24 vertices and 52 edges
IsPlanar⁡B
false
IsConnected⁡B
The two connected components of the bishop's graph correspond to the squares reachable by the white bishop and the black bishop.
ConnectedComponents⁡B
1:1,1:3,1:5,2:2,2:4,2:6,3:1,3:3,3:5,4:2,4:4,4:6,1:2,1:4,1:6,2:1,2:3,2:5,3:2,3:4,3:6,4:1,4:3,4:5
DrawGraph⁡B
With the third parameter we can specify that the graph contain only the moves of the white or black bishop.
WB≔BishopsGraph⁡4,6,white
WB≔Graph 2: an undirected graph with 24 vertices and 26 edges
DrawGraph⁡WB
The GraphTheory[SpecialGraphs][BishopsGraph] command was introduced in Maple 2023.
For more information on Maple 2023 changes, see Updates in Maple 2023.
See Also
ChromaticNumber
IsPlanar
KingsGraph
KnightsGraph
QueensGraph
RooksGraph
SpecialGraphs
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