RooksGraph - Maple Help

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GraphTheory[SpecialGraphs]

 RooksGraph
 construct rook's graph

 Calling Sequence RooksGraph(m,n)

Parameters

 m, n - positive integers

Description

 • 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 on an m by n chessboard.
 • When n and m are equal, the rook's graph is strongly regular.

Examples

 > $\mathrm{with}\left(\mathrm{GraphTheory}\right):$
 > $\mathrm{with}\left(\mathrm{SpecialGraphs}\right):$
 > $R≔\mathrm{RooksGraph}\left(4,6\right)$
 ${R}{≔}{\mathrm{Graph 1: an undirected unweighted graph with 24 vertices and 96 edge\left(s\right)}}$ (1)
 > $\mathrm{IsPlanar}\left(R\right)$
 ${\mathrm{false}}$ (2)
 > $\mathrm{ChromaticNumber}\left(R\right)$
 ${6}$ (3)
 > $\mathrm{DrawGraph}\left(R\right)$

Compatibility

 • The GraphTheory[SpecialGraphs][RooksGraph] command was introduced in Maple 2020.
 • For more information on Maple 2020 changes, see Updates in Maple 2020.

 See Also