Queen's graph

Summary

In mathematics, a queen's graph is an undirected graph that represents all legal moves of the queen—a chess piece—on a chessboard. In the graph, each vertex represents a square on a chessboard, and each edge is a legal move the queen can make; that is, a horizontal, vertical or diagonal move by any number of squares. If the chessboard has dimensions $m\times n$, then the induced graph is called the $m\times n$ queen's graph.