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 king said, -Divide the living boy in two; then give half to the one, and half to the other. But the woman whose son was alive said to the king -because compassion for her son burned within her - -Please, my lord, give her the living boy; certainly do not kill him! The other said, -It shall be neither mine nor yours; divide it. Then the king responded: -Give the first woman the living boy; do not kill him. She is his mother.”
—Bible: Hebrew, 1 Kings. 3:25-37.
Solomon resolves a dispute between two women over a child. Solomon’s wisdom was proven by this story.
“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)