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:
“Nae living man I’ll love again,
Since that my lovely knight is slain.
Wi ae lock of his yellow hair
I’ll chain my heart for evermair.”
—Unknown. The Lament of the Border Widow (l. 25–28)
“In this Journal, my pen is a delicate needle point, tracing out a graph of temperament so as to show its daily fluctuations: grave and gay, up and down, lamentation and revelry, self-love and self-disgust. You get here all my thoughts and opinions, always irresponsible and often contradictory or mutually exclusive, all my moods and vapours, all the varying reactions to environment of this jelly which is I.”
—W.N.P. Barbellion (1889–1919)