In graph theory, a knight's graph, or 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 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 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.
Famous quotes containing the words knight and/or graph:
“The Knight of the Doleful Countenance.”
—Miguel De Cervantes (1547–1616)
“When producers want to know what the public wants, they graph it as curves. When they want to tell the public what to get, they say it in curves.”
—Marshall McLuhan (1911–1980)