Abstract
The graph-theoretic study of combinatorial chessboard problems can be extended to the study of line graphs of graphs of combinatorial designs. In particular, the determination of optimal placements of rooks on a chessboard corresponds to the determination of domination parameters of graphs of block designs. The determination of one such parameter, the independence number, is shown to follow directly from classical results in design theory. Additionally, the domination number of graphs of finite projective planes is discussed.
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