On domination number of Cartesian product of directed cycles

Let gamma(G) denote the domination number of a digraph G and let C-m square C-n denote the Cartesian product of C-m and C-n, the directed cycles of length m, n >= 2. In this paper, we determine the exact values: gamma(C-2 square C-n) = n; gamma(C-3 square C-n) = n if n equivalent to 0 (mod 3), otherwise, gamma(C-3 square C-n) = n + 1: gamma(C-4 square C-n) = 3n/2 if n equivalent to 0 (mod 8), otherwise, gamma(C-4 square C-n) = n + inverted right perpendicularn+1/2inverted left perpendicular. (C) 2009 Elsevier B.V. All rights reserved.