A247181 Total domination number of the n-hypercube graph.

2, 2, 4, 4, 8, 14, 24, 32, 64, 124

Offset

1,1

Comments

a(n) = size of smallest subset S of vertices of the n-cube Q_n such that every vertex of Q_n has a neighbor in S.

Proof for first formula can be found in the Verstraten link. - Kamiel P.F. Verstraten, Jun 10 2015

Links

Table of n, a(n) for n=1..10.

J. Azarija, M. A. Henning and S. Klavžar (Total) Domination in Prisms, arXiv:1606.08143 [math.CO], 2016.

Jernej Azarija, S. Klavzar, Y. Rho, and S. Sim, On domination-type invariants of Fibonacci cubes and hypercubes, Preprint 2016; See Table 4.

Jernej Azarija, S. Klavzar, Y. Rho, and S. Sim, On domination-type invariants of Fibonacci cubes and hypercubes, Ars Mathematica Contemporanea, 14 (2018) 387-395. See Table 4.

M. Henning and A. Yeo, Total domination in graphs, Springer, 2013.

Kamiel P. F. Verstraten, A Generalization of the Football Pool Problem, Master's Thesis, Tilburg University, 2014.

Eric Weisstein's World of Mathematics, Hypercube Graph

Eric Weisstein's World of Mathematics, Total Domination Number

Formula

a(n) = 2*A000983(n-1), at least if 2<=n<=9. - Omar E. Pol, Nov 22 2014. This formula is true for all n>=2 (see Azarija-Henning-Klavžar paper). - Omar E. Pol, Jul 01 2016

a(n) = A230014(n,1), at least if 1<=n<=9. - Omar E. Pol, Nov 23 2014. This formula is true for all n>=1 (in accordance with the above comment). - Omar E. Pol, Jul 01 2016

Example

a(1) = 2 since the complete graph on two vertices can only be totally dominated by taking both vertices.

Crossrefs

Cf. A000983 (half), A323515 (number of sets).

Sequence in context: A063776 A287135 A276063 * A118406 A355811 A357214

Adjacent sequences: A247178 A247179 A247180 * A247182 A247183 A247184

Keyword

nonn,more,hard

Author

Jernej Azarija, Nov 22 2014

Extensions

a(10) from Jernej Azarija, Jun 30 2016

Status

approved