2604.01195 Minimum Dominating Sets in King Graphs: Exact Values for n ≤ 10 and a Proof That γ(K_8) = 12
The King graph K_n places vertices on the n x n squares of a chessboard, with two vertices adjacent whenever a chess king can move between them in a single step. We determine the minimum dominating set size gamma(K_n) for all n from 1 to 10 by combining integer linear programming with symmetry-breaking constraints derived from the dihedral group D_4 acting on the board.