A230014
Triangle E(n,k), 1<=k<=n, giving the cardinality of optimal binary covering codes of empty spheres of length n and radius k.
Original entry on oeis.org
2, 2, 4, 4, 4, 8, 4, 4, 4, 16, 8, 6, 6, 8, 32, 14, 8, 6, 8, 14, 64, 24, 8, 8, 8, 8, 24, 128, 32, 16, 8, 8, 8, 16, 32, 256, 64, 24, 12, 10, 10, 12, 24, 64, 512, 124
Offset: 1
Triangle starts:
01: 2,
02: 2, 4,
03: 4, 4, 8,
04: 4, 4, 4, 16,
05: 8, 6, 6, 8, 32,
06: 14, 8, 6, 8, 14, 64,
07: 24, 8, 8, 8, 8, 24, 128,
08: 32, 16, 8, 8, 8, 16, 32, 256,
09: 64, 24, 12, 10, 10, 12, 24, 64, 512,
10: 124, ...
Related to
A060438, which has a code consisting of filled spheres instead of empty spheres.
Related to
A238305, the triangle giving the cardinality of optimal ternary covering codes of empty spheres.
The first column is equal to 2*
A000983.
A247181
Total domination number of the n-hypercube graph.
Original entry on oeis.org
2, 2, 4, 4, 8, 14, 24, 32, 64, 124
Offset: 1
a(1) = 2 since the complete graph on two vertices can only be totally dominated by taking both vertices.
- 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
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