Rook's Graph

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High Quality Content by WIKIPEDIA articles! Rook's graphs are vertex-transitive and (n + m 2)-regular; they are the only regular graphs formed from the moves of standard chess pieces in this way (Elkies). When m n, the symmetries of the rook's graph are formed by independently permuting the rows and columns of the graph. When n = m the graph has additional symmetries that swap the rows and columns; the rook's graph for a square chessboard is symmetric. Any two vertices in a rook's graph are either at distance one or two from each other, according to whether they are adjacent or nonadjacent respectively. Any two nonadjacent vertices may be transformed into any other two nonadjacent vertices by a symmetry of the graph. When the rook's graph is not square, the pairs of adjacent vertices fall into two orbits of the symmetry group according to whether they are adjacent horizontally or vertically, but when the graph is square any two adjacent vertices may also be mapped into each other by a symmetry and the graph is therefore distance-transitive.
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Weitere Informationen

  • Allgemeine Informationen
    • GTIN 09786131174278
    • Editor Lambert M. Surhone, Miriam T. Timpledon, Susan F. Marseken
    • Genre Sport
    • Anzahl Seiten 68
    • EAN 9786131174278
    • Format Fachbuch
    • Titel Rook's Graph
    • Herausgeber Betascript Publishing

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