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White Bishop Graph


A white bishop graph is a graph formed from possible moves of a bishop chess piece, which may make diagonal moves of any length on a chessboard (or any other board), when starting from a white square on the board. To form the graph, each chessboard square is considered a vertex, and vertices connected by allowable bishop moves are considered edges.

The (m,n)-white bishop graph is therefore a connected component of the general (m,n)-bishop graph. It is isomorphic to the (m,n)-black bishop graph unless both m and n are odd.

Special cases are summarized in the following table.

(m,n)graph
(1,n)empty graph K^__(|_n/2_|)
(2,n)path graph P_n
(3,3)square graph C_4
(n,n+1)n-triangular honeycomb bishop graph

See also

Bishop Graph, Black Bishop Graph, King Graph, Knight Graph, Rook Graph

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Cite this as:

Weisstein, Eric W. "White Bishop Graph." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/WhiteBishopGraph.html

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