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

Let Γn and Λn be the n-dimensional Fibonacci cube and Lucas cube, respectively. The domination number γ of Fibonacci cubes and Lucas cubes is studied. In particular it is proved that γ(Λn) is bounded below by Ln−2n n−3 , where Ln is the n-th Lucas number. The 2-packing number ρ of these cubes is also studied. It is proved that ρ(Γn) is bounded below by 22 lg n 2 −1 and the exact values of ρ(Γn) and ρ(Λn) are obtained for n ≤ 10. It is also shown that Aut(Γn) Z2. Key words: Fibonacci cubes; Lucas cubes; domination number; 2-packing number; automorphism group Math. Subj. Class. (2010): 05C69, 05C25 ∗ Corresponding author 1 

• Type: Journal
• Year: 2011
• Where: CMA
• Authors: Aline Castro, Sandi Klavzar, Michel Mollard, Yoomi Rho
• Keywords: CMA 2011, Distributed And Parallel Computing, Domination Number, Exact Values, Lucas Number