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About: Rook's graph     Goto   Sponge   NotDistinct   Permalink

An Entity of Type : yago:WikicatRegularGraphs, within Data Space : dbpedia.demo.openlinksw.com associated with source document(s)

Type: softwareyago:WikicatMathematicalChessProblemsyago:Abstraction100002137yago:Attribute100024264yago:Communication100033020yago:Condition113920835yago:Difficulty114408086yago:Graph107000195yago:Problem114410605yago:State100024720yago:VisualCommunication106873252yago:WikicatPerfectGraphsyago:WikicatRegularGraphs New Facet based on Instances of this Class

In graph theory, a rook's graph is a graph that represents all legal moves of the rook chess piece on a chessboard. Each vertex of a rook's graph represents a square on a chessboard, and each edge connects two squares on the same row (rank) or on the same column (file) as each other, the squares that a rook can move between. These graphs can be constructed for chessboards of any rectangular shape, and can be defined mathematically as the Cartesian product of two complete graphs, as the two-dimensional Hamming graphs, or as the line graphs of complete bipartite graphs.