name = Knight's graph
image_caption = 8x8 Knight's graph
vertices = "nm"
edges = 4"mn"-6("m"+"n")+8
girth = 4 (if "n"≥3, "m"≥ 5)
properties = In
graph theory, a knight's tour graph is a graph that represents all legal moves of the knight chesspiece on a chessboardwhere each vertex represents a square on a chessboard and each edge is a legal move.More specifically, an knight's tour graph is a knight's tour graph of an chessboard.
For a knight's tour graph the total number of vertices is simply "nm".
For a knight's tour graph the total number of vertices is simply "n2" and the total number of edges is "4(n–2)(n–1)".Additionally, the number of edges for various "n" is identified as OEIS2C|id=A033996 in the
On-Line Encyclopedia of Integer Sequences.
Hamiltonian pathon the knight's tour graph is a knight's tour
The following Knight's graph shows the number of possible moves that can be made from each position on an 8×8 chessboard.
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