A247181 Total domination number of the n-hypercube graph.
2, 2, 4, 4, 8, 14, 24, 32, 64, 124
Offset: 1
Examples
a(1) = 2 since the complete graph on two vertices can only be totally dominated by taking both vertices.
Links
- 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
Extensions
a(10) from Jernej Azarija, Jun 30 2016
Comments