OFFSET

1,2

COMMENTS

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]

The Cartesian product of two cycles is also called the torus grid graph. - Andrew Howroyd, Feb 29 2020

LINKS

Navid Assadian, Dominating Sets of the Cartesian Products of Cycles, M. Sc. project, University of Victoria, 2019.

S. Klavžar and N. Seifter, Dominating Cartesian products of cycles, Discrete Applied Mathematics, Vol. 59 (1995), no. 2, pp. 129-136.

Stephan Mertens, Domination Polynomials of the Grid, the Cylinder, the Torus, and the King Graph, arXiv:2408.08053 [math.CO], 2024. See p. 15.

Zehui Shao, Jin Xu, S. M. Sheikholeslami, and Shaohui Wang, The Domination Complexity and Related Extremal Values of Large 3D Torus, Complexity, 2018, 3041426.

Eric Weisstein's World of Mathematics, Domination Number

Eric Weisstein's World of Mathematics, Torus Grid Graph

FORMULA

a(5n) = 5n^2. - Richard Bean, Jun 08 2006

CROSSREFS

KEYWORD

nonn,more

AUTHOR

Richard Bean, May 01 2004

EXTENSIONS

More terms from Richard Bean, Sep 08 2006

a(22) from Richard Bean, Jul 24 2018

a(23)-a(24) from Shao et al. added by Andrey Zabolotskiy, Dec 23 2019

a(25)-a(27) from Richard Bean, Apr 03 2022

STATUS

approved