Domination by queens on a square beehive (Q1377840)

A game board \(B_n\) analogous to the chessboard is considered. It consists of \(n^2\) hexagonal cells forming a square and is called the square beehive. A queen moves on this board analogously as on the chessboard (obviously in six directions). For the square beehive \(B_n\) various numerical characteristics are introduced, namely upper domination number, upper independence number, lower domination number, lower independence number, etc. Equalities and inequalities for them in terms of \(n\) are stated.