Geodesic
On domination-type invariants of Fibonacci cubes and hypercubes
Ars Mathematica Contemporanea, Tome 14 (2018) no. 2, pp. 387-395.

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The Fibonacci cube Γn is the subgraph of the n-dimensional cube Qn induced by the vertices that contain no two consecutive 1s. Using integer linear programming, exact values are obtained for γt(Γn), n ≤ 12. Consequently, γt(Γn) ≤ 2Fn − 10 + 21Fn − 8 holds for n ≥ 11, where Fn are the Fibonacci numbers. It is proved that if n ≥ 9, then γt(Γn) ≥ ⌈(Fn + 2−11)/(n−3)⌉ − 1. Using integer linear programming exact values for the 2-packing number, connected domination number, paired domination number, and signed domination number of small Fibonacci cubes and hypercubes are obtained. A conjecture on the total domination number of hypercubes asserting that γt(Qn)=2n − 2 holds for n ≥ 6 is also disproved in several ways.
DOI : 10.26493/1855-3974.1172.bae
Keywords: Total domination number, Fibonacci cube, hypercube, integer linear programming, covering codes 
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Jernej Azarija; Sandi Klavžar; Yoomi Rho; Seungbo Sim. On domination-type invariants of Fibonacci cubes and hypercubes. Ars Mathematica Contemporanea, Tome 14 (2018) no. 2, pp. 387-395. doi : 10.26493/1855-3974.1172.bae. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.1172.bae/

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