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A094087 Domination number of the Cartesian product of two n-cycles. 0
1, 2, 3, 4, 5, 8, 12, 16, 18, 20, 27, 32, 38, 42, 45, 56, 64, 71, 76, 80, 95, 104, 114, 120 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

1/5 <= a(n)/n^2 <= 1/4 for n>=4; it is conjectured that a(5n-1)=5n^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

Table of n, a(n) for n=1..24.

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.

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

Cf. A295428, A302406, A303334.

Sequence in context: A065428 A059747 A254328 * A225132 A240216 A017821

Adjacent sequences:  A094084 A094085 A094086 * A094088 A094089 A094090

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

STATUS

approved

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Last modified December 3 12:45 EST 2021. Contains 349463 sequences. (Running on oeis4.)