The m×n rook graph (confusingly called the m×n grid by Brouwer et al. 1989, p. 440) and also sometimes known as a lattice graph (e.g., Brouwer) is the graph Cartesian product K_m square K_n of complete graphs, which is equivalent to the line graph L(K_(m, n)) of the complete bipartite graph K_(m, n). This is the definition adopted for example by Brualdi and Ryser, although restricted to the case m = n. This definition corresponds to the connectivity graph of a rook chess piece (which can move any number of spaces in a straight line-either horizontally or vertically, but not diagonally) on an m×n chessboard.
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