The domination number of Cartesian product of two directed paths

摘要

Let γ (P_m?P_n) be the domination number of the Cartesian product of directed paths P_m and P_n for m,n ≥ 2. Liu et al. in (J. Comb. Optim. 22(4):651-662, 2011) determined the value of γ (P_m?P_n) for arbitrary n and m ≤ 6. In this work we give the exact value of γ (P_m?P_n) for any m,n and exhibit dominating sets of minimum cardinality.