Domination number of toroidal grid digraphs

Abstract

Let G = (D, A) be a digraph of order n. A subset S of vertex set V(D) is a dominating set of D if for each vertex vε D - S there exists a vertex uε S such that (u, v) is an arc of D. The domination number of D, γ(D), is the order of a smallest dominating set of D. In this paper we calculate the domination number of the cartesian product of two directed cycles C_m and C_n for m = 3, 4, 5, 6 and arbitrary n.