 Any two nonadjacent vertices may be transformed into any other two nonadjacent vertices by a symmetry of the graph.When the rook's graph is not square, the pairs of adjacent vertices fall into two orbits of the symmetry group according to whether they are adjacent horizontally or vertically, but when the graph is square any two adjacent vertices may also be mapped into each other by a symmetry and the graph is therefore distance-transitive.When formula_29 and formula_30 are relatively prime, the symmetry group formula_31 of the rook's graph contains as a subgroup the cyclic group formula_32 that acts by cyclically permuting the formula_2 vertices; therefore, in this case, the rook's graph is a circulant graph.