Rook Complement Graph
RookComplementGraph
The m×n rook complement graph K_m square K_n^_ is the graph complement of the m×n rook graph. It has vertex count mn and edge count [画像:2(m; 2)(n; 2)], where (n; k) is a binomial coefficient.
Special cases are summarized in the following table.
(m,n) K_m square K_n^_
(1,n) empty
graph K^__n
(2,2) ladder
rung graph 2P_2
(2,3) cycle
graph C_6
(2,4) cubical
graph Q_3
(2,n) n-crown graph
(3,3) generalized quadrangle GQ(2,1)
(n,n+1) circulant
graph
(n,2n+/-1) circulant
graph
See also
Crown Graph, Graph Complement, Rook GraphExplore with Wolfram|Alpha
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Cite this as:
Weisstein, Eric W. "Rook Complement Graph." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/RookComplementGraph.html