Australasian Journal Of Combinations
For each positive integer n, the toroidal queens graph may be described as a graph with vertex set Zn × Zn where every vertex is adjacent to those vertices in the directions (1, 0), (0, 1), (1, 1), (1,−1) from it. We here extend this idea, examining graphs with vertex set F × F, where F is a finite field, and any four directions are used to define adjacency. The automorphism groups and isomorphism classes of such graphs are found.
William D. Weakley (2013).
Toroidal Queens Graphs Over Finite Fields. Australasian Journal Of Combinations.57, 21–38.