Queens on Hexagonal Boards

A queen on a hexagonal board with hexagonal cells is defined as a piece that moves along three lines, namely along the cells in the same row, up diagonal, or down diagonal. A queen dominates a cell if the cell is in the same line as the queen.
We show that hexagonal boards with \(n \geq 1\) rows and diagonals, where \(n \equiv 3 \pmod{4}\), have only two types of minimum dominating sets. We also determine the irredundance numbers of the boards with \(5\) and \(7\) rows.