Knight's graph

infobox graph
name = Knight's graph


image_caption = 8x8 Knight's graph
vertices = "nm"
edges = 4"mn"-6("m"+"n")+8
chromatic_number =
chromatic_index =
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 chess piece on a chessboard where each vertex represents a square on a chessboard and each edge is a legal move.More specifically, an n imes m knight's tour graph is a knight's tour graph of an n imes m chessboard.

For a n imes m knight's tour graph the total number of vertices is simply "nm".

For a n imes n 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.

A Hamiltonian path on 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.

ee also

* Knight's tour
* King's graph
* Rook's graph


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