High Quality Content by WIKIPEDIA articles! 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 n times m king's graph is a king's graph of an n times m chessboard. For a n times m king's graph the total number of vertices is simply nm. For a n times n king's graph the total number of vertices is simply n2 and the total number of edges is (2n ? 2)(2n ? 1). Additionally, the number of edges for various n is identified as A002943 in the On-Line Encyclopedia of Integer Sequences.

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