

A094087


Domination number of the Cartesian product of two ncycles.


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
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OFFSET

1,2


COMMENTS

1/5 <= a(n)/n^2 <= 1/4 for n>=4; it is conjectured that a(5n1)=5n^2n and a(5n+1)=5n^2+4n1 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. 129136.
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



