On the domination number and the 2-packing number of Fibonacci cubes and Lucas cubes

Let ΓnΓn and ΛnΛn be the nn-dimensional Fibonacci cube and Lucas cube, respectively. The domination number γγ of Fibonacci cubes and Lucas cubes is studied. In particular it is proved that γ(Λn)γ(Λn) is bounded below by ⌈Ln−2nn−3⌉, where LnLn is the nnth Lucas number. The 2-packing number ρρ of these cubes is also studied. It is proved that ρ(Γn)ρ(Γn) is bounded below by 22⌊lgn⌋2−1 and the exact values of ρ(Γn)ρ(Γn) and ρ(Λn)ρ(Λn) are obtained for n≤10n≤10. It is also shown that Aut(Γn)≃Z2.