NationMaster - Encyclopedia: Knight's tour graph

In graph theory, a knight's tour graph is a graph that represents all legal moves of the knight piece on a chessboard where each vertex represents a square on a chessboard and each edge is a legal move. More specifically, an $n times m$ knight's tour graph is a knight's tour graph of an $n times m$ chessboard. A labeled graph with 6 vertices and 7 edges. ... The knight moves in an L shape. ... A chessboard is often painted or engraved on a chess table. ...

For a $n times m$ knight's tour graph the total number of vertices is simply $n m$ .

For a $n times n$ knight's tour graph the total number of vertices is simply $n 2$ and the total number of edges is $4(n - 2)(n - 1)$ . Additionally, the number of edges for for various $n$ is identified as A033996 in the On-Line Encyclopedia of Integer Sequences. The On-Line Encyclopedia of Integer Sequences (OEIS) is an extensive searchable database of integer sequences, freely available on the Web. ...

See also