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Introduction

Part of a Staunton chess set
Left to right: white king, black rook, black queen, white pawn, black knight, white bishop

Chess is a board game for two players. It is sometimes called international chess or Western chess to distinguish it from related games such as xiangqi (Chinese chess) and shogi (Japanese chess).

Chess is an abstract strategy game that involves no hidden information and no elements of chance. It is played on a chessboard with 64 squares arranged in an 8×8 grid. The players, referred to as "White" and "Black", each control sixteen pieces: one king, one queen, two rooks, two bishops, two knights, and eight pawns. White moves first, followed by Black. The game is typically won by checkmating the opponent's king, i.e. threatening it with inescapable capture. There are several ways a game can end in a draw.

The recorded history of chess goes back at least to the emergence of a similar game, chaturanga, in seventh-century India. After its introduction in Persia, it spread to the Arab world and then to Europe. The rules of chess as they are known today emerged in Europe at the end of the 15th century, with standardization and universal acceptance by the end of the 19th century. Today, chess is one of the world's most popular games and is played by millions of people worldwide. (Full article...)

8x8 Rook's graph

In graph theory, a rook's graph is an undirected graph that represents all legal moves of the rook chess piece on a chessboard. Each vertex of a rook's graph represents a square on a chessboard, and there is an edge between any two squares sharing a row (rank) or column (file), the squares that a rook can move between. These graphs can be constructed for chessboards of any rectangular shape. Although rook's graphs have only minor significance in chess lore, they are more important in the abstract mathematics of graphs through their alternative constructions: rook's graphs are the Cartesian product of two complete graphs, and are the line graphs of complete bipartite graphs. The square rook's graphs constitute the two-dimensional Hamming graphs.

Rook's graphs are highly symmetric, having symmetries taking every vertex to every other vertex. In rook's graphs defined from square chessboards, more strongly, every two edges are symmetric, and every pair of vertices is symmetric to every other pair at the same distance in moves (making the graph distance-transitive). For rectangular chessboards whose width and height are relatively prime, the rook's graphs are circulant graphs. With one exception, the rook's graphs can be distinguished from all other graphs using only two properties: the numbers of triangles each edge belongs to, and the existence of a unique 4-cycle connecting each nonadjacent pair of vertices. (Full article...)

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Chess from A to Z

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