20.500.12556/DKUM-80902 More results on the domination number of Cartesian product of two directed cycles Let γ(D) denote the domination number of a digraph D and let C$_m$□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 γ(C$_m$□C$_n$) for m 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 γ(C$_m$□C$_n$) for m = 6, 7 [On the domination number of Cartesian product of two directed cycles, Journal of Applied Mathematics, Volume 2013, Article ID 619695]. Mollard obtained the exact values of γ(C$_m$□C$_n$) for m = 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$_m$□C$_n$ with m up to 21. Moreover, the exact values of γ(C$_n$□C$_n$) with n up to 31 are determined. domination number Cartesian product directed cycle true true false Angleški jezik Ni določen Članek v reviji 2021-11-11 04:58:48 2022-09-02 12:48:31 2022-09-02 12:48:32 0000-00-00 00:00:00 2019 0 0 Str. 1-9 ǂno. ǂ2 ǂVol. ǂ7 2019 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 519.1 24462088 10.3390/math7020210 2227-7390 http://dx.doi.org/10.3390/math7020210 1 acfe0b89-42a3-11ec-bd00-00155d000105 https://dk.um.si/Dokument.php?lang=slv&id=155363 Fakulteta za naravoslovje in matematiko 0 0 0