In graph theory, a king's graph is a graph that represents all legal moves of the king chess piece on a chessboard where each vertex represents a square on a chessboard and each edge is a legal move. More specifically, an king's graph is a king's graph of an chessboard.
For a king's graph the total number of vertices is simply .
For a king's graph the total number of vertices is simply and the total number of edges is . Additionally, the number of edges for various is identified as A002943 in the On-Line Encyclopedia of Integer Sequences.
Neighbourhood in the king's graph corresponds to the Moore neighborhood for cellular automata.
The logic puzzle game Hidato is based on King's graph.
Famous quotes containing the words king and/or graph:
“The old Romans all wished to have a king over them because they had not yet tasted the sweetness of freedom.”
—Titus Livius (Livy)
“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)