A black 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 black 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 -black bishop graph is therefore a connected component of the general -bishop graph. It is isomorphic to the -white bishop graph unless both and are odd.
Special cases are summarized in the following table.
graph | |
empty graph | |
path graph | |
butterfly graph | |
-triangular honeycomb bishop graph |
Stan Wagon (pers. comm., Dec. 5, 2018) considered the set of graphs with vertices corresponding to all subsets of the integers 1, ..., of size and with edges between vertices that agree as vectors in exactly one position. Wagon noted that the graphs with correspond to the -black bishop graphs.