Leaper graphs

  title={Leaper graphs},
  author={Donald Ervin Knuth},
  • D. Knuth
  • Published 1 November 1994
  • Mathematics
An {r, s}-leaper [1, p. 130; 2, p. 30; 3] is a generalized knight that can jump from (x, y) to (x±r, y±s) or (x ± s, y ± r) on a rectangular grid. The graph of an {r, s}-leaper on an m × n board is the set of mn vertices (x, y) for 0 ≤ x < m and 0 ≤ y < n, with an edge between vertices that are one {r, s}-leaper move apart. We call x the rank and y the file of board position (x, y). George P. Jelliss [4, 5] raised several interesting questions about these graphs, and established some of their… 
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