More Results on the Domination Number of Cartesian Product of Two Directed Cycles

Let gamma(D) denote the domination number of a digraph D and let C-m square C-n denote the Cartesian product of C-m and C-n, the directed cycles of length n >= m >= 3. Liu et al. obtained the exact values of gamma(C-m square C-n) for in up to 6 [Domination number of Cartesian products of directed cycles, Inform. Process. Lett. 111 (2010) 36-39]. Shao et al. determined the exact values of gamma(Cm square Cn) for m - 6, 7 [on the domination number of Cartesian product of two directed cycles, Journal of Applied Mathematics, Volume 2013, Article ID 6196951. Mollard obtained the exact values of gamma(C-m square C-n) for nt 3k + 2 [M. Mollard, On domination of Cartesian product of directed cycles: Results for certain equivalence classes of lengths, Discuss. Math. Graph Theory 33(2) (2013) 387-394.]. In this paper, we extend the current known results on C-m square C-n with m up to 21. Moreover, the exact values of gamma(C-n square C-n) with n up to 31 are determined.