cp's OEIS Frontend

A094087 Domination number of the Cartesian product of two n-cycles.

%I A094087 #35 Feb 16 2025 08:32:53
%S A094087 1,2,3,4,5,8,12,16,18,20,27,32,38,42,45,56,64,71,76,80,95,104,114,120,
%T A094087 125,144,155
%N A094087 Domination number of the Cartesian product of two n-cycles.
%C A094087 1/5 <= a(n)/n^2 <= 1/4 for n >= 4; it is conjectured that a(5n-1) = 5*n^2 - n and a(5n+1) = 5n^2 + 4n - 1 for n >= 1. - _Richard Bean_, Sep 08 2006 [Assadian proves that the both conjectured formulas give the upper bounds. - _Andrey Zabolotskiy_, Dec 23 2019]
%C A094087 The Cartesian product of two cycles is also called the torus grid graph. - _Andrew Howroyd_, Feb 29 2020
%H A094087 Navid Assadian, <a href="https://dspace.library.uvic.ca/bitstream/handle/1828/10716/Assadian_Navid_MSc_2019.pdf">Dominating Sets of the Cartesian Products of Cycles</a>, M. Sc. project, University of Victoria, 2019.
%H A094087 S. Klavžar and N. Seifter, <a href="https://doi.org/10.1016/0166-218X(93)E0167-W">Dominating Cartesian products of cycles</a>, Discrete Applied Mathematics, Vol. 59 (1995), no. 2, pp. 129-136.
%H A094087 Stephan Mertens, <a href="https://arxiv.org/abs/2408.08053">Domination Polynomials of the Grid, the Cylinder, the Torus, and the King Graph</a>, arXiv:2408.08053 [math.CO], 2024. See p. 15.
%H A094087 Zehui Shao, Jin Xu, S. M. Sheikholeslami, and Shaohui Wang, <a href="https://doi.org/10.1155/2018/3041426">The Domination Complexity and Related Extremal Values of Large 3D Torus</a>, Complexity, 2018, 3041426.
%H A094087 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DominationNumber.html">Domination Number</a>
%H A094087 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TorusGridGraph.html">Torus Grid Graph</a>
%F A094087 a(5n) = 5n^2. - _Richard Bean_, Jun 08 2006
%Y A094087 Cf. A295428, A302406, A303334.
%K A094087 nonn,more
%O A094087 1,2
%A A094087 _Richard Bean_, May 01 2004
%E A094087 More terms from _Richard Bean_, Sep 08 2006
%E A094087 a(22) from _Richard Bean_, Jul 24 2018
%E A094087 a(23)-a(24) from Shao et al. added by _Andrey Zabolotskiy_, Dec 23 2019
%E A094087 a(25)-a(27) from _Richard Bean_, Apr 03 2022