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...

that the graph is associated with a symmetric BIBD. The Shrikhande graph shares these parameters with exactly one other graph, the 4×4 rook's graph, i.e....

Johnson graph is locally grid, meaning that the induced subgraph of the neighbors of any vertex is a rook's graph. More precisely, in the Johnson graph J (...

which is the complete graph Kq H(2,q), which is the lattice graph Lq,q and also the rook's graph H(d,1), which is the singleton graph K1 H(d,2), which is...

Every Paley graph is self-complementary. For example, the 3 × 3 rook's graph (the Paley graph of order nine) is self-complementary, by a symmetry that keeps...

The rook's graph (the graph that represents all legal moves of the rook chess piece on a chessboard) is also sometimes called the lattice graph, although...

then the m × n rook's graph (a graph that has a vertex for each square of an m × n chessboard and an edge for each two squares that a rook can move between...

4} knight's graph is the same as the four-dimensional hypercube graph. King's graph Queen's graph Rook's graph Bishop's graph Lattice graph Averbach, Bonnie;...

a pairing strategy. King's graph Knight's graph Rook's graph Bishop's graph Chess portal Weisstein, Eric W. "Queen Graph". MathWorld. Averbach, Bonnie;...

Knight's graph Queen's graph Rook's graph Bishop's graph Lattice graph Chess portal Chang, Gerard J. (1998), "Algorithmic aspects of domination in graphs", in...

The complement graph of a 2n-vertex crown graph is the Cartesian product of complete graphs K2 ▢ Kn, or equivalently the 2 × n rook's graph. In etiquette...

is the Cartesian product graph K2□Cn. The rook's graph is the Cartesian product of two complete graphs. If a connected graph is a Cartesian product, it...

not if both sides are odd. A component of the bishop's graph can be treated as a rook's graph on a diamond if the original board is square and has sides...

perfect matching). The tensor product of a complete graph with itself is the complement of a Rook's graph. Its vertices can be placed in an n-by-n grid, so...

unions of isomorphic complete graphs, the Turán graphs formed as the complement graphs of mKn, the 3 × 3 rook's graph, and the 5-cycle. The only countably...

neighbourhood is an induced matching. The Johnson graphs are locally grid, meaning that each neighborhood is a rook's graph. For a set A of vertices, the neighbourhood...

bipartite graphs. Every line graph of a bipartite graph is an induced subgraph of a rook's graph. Because line graphs of bipartite graphs are perfect...

not a distance-transitive graph. The n × n square rook's graph, i.e., the line graph of a balanced complete bipartite graph Kn,n, is an srg(n2, 2n − 2...

represented as a Cayley graph of the abelian group Z n 4 {\displaystyle Z_{n}^{4}} . The Sudoku graph contains as a subgraph the rook's graph, which is defined...

in random graphs. The Paley graph of order 9 is a locally linear graph, a rook's graph, and the graph of the 3-3 duoprism. The Paley graph of order 13...

special case of these graphs are the rook's graphs, line graphs of complete bipartite graphs. Like the line graphs of complete graphs, they can be characterized...

Grassmann graphs. The Hamming Graphs (including Hypercube graphs). The folded cube graphs. The square rook's graphs. The Livingstone graph. After introducing...

(2005). The rook's graphs are, equivalently, the line graphs of complete bipartite graphs, so the well-covered property of rook's graphs is equivalent...

two complete graphs, the rook's graphs, are integral. Similarly, the hypercube graphs, as Cartesian products of any number of complete graphs K 2 {\displaystyle...

described as the optimal colorings of rook's graphs, or as optimal edge colorings of complete bipartite graphs. An example of a 3 × 5 Latin rectangle...

× 3 {\displaystyle 3\times 3} Rook's graph and the Games graph, it is one of only three possible strongly regular graphs whose parameters have the form...

graph of a rook's graph, and each of its simplices represents a placement of rooks on an m × n chess board such that no two of the rooks attack each...

Turán graphs, 3 × 3 rook's graphs, and the 5-cycle. The infinite Rado graph is countably ultrahomogeneous. There are only two connected graphs that are...

queens puzzle Futoshiki Magic square Problems in Latin squares Rook's graph, a graph that has Latin squares as its colorings Sator Square Vedic square...

matching complex of the (m, n)-complete bipartite graph, or the independence complex of the m-by-n rook's graph. For any two positive integers m and n, the...