... D(GS,r) ≤25r for r even,2r5r2− 2r +1 for r odd. For the triangular lattice:26r +3≤ D(GT,r) ≤12r +4 for r ≡ 0mod4,12r +2 for r ≡ 1, 2or3 mod4.When ... ≤8r − 89r2− 16r for r ≡ 0mod4,89r − 25 for r ≡ 1mod4,89r − 34 for r ≡ 2mod4,8r − 16(r − 3)(9r − 43) for r ≡ 3mod4. For the square lattice:the electronic journal ... (Theorems 4–8) bounds obtainedhere, plus the upper bound established in [13] in the case of the square lattice, we obtainthe following results. For the brick wall grid: for r even,25r +3 for r odd,25r...