On the domination number and the 2-packing number of Fibonacci cubes and Lucas cubes
Let ?n ? n and ?n ? n be the n n -dimensional Fibonacci cube and Lucas cube, respectively. The domination number ? ? of Fibonacci cubes and Lucas cubes is studied. In particular it is proved that ?(?n) ? ( ? n ) is bounded below by ? L n ? 2 n n ? 3 ? , where Ln L n is the n n th Lucas number. The 2-packing number ? ? of these cubes is also studied. It is proved that ?(?n) ? ( ? n ) is bounded below by 2 2 ? lg n ? 2 ? 1 and the exact values of ?(?n) ? ( ? n ) and ?(?n) ? ( ? n ) are obtained for n?10 n ? 10 . It is also shown that Aut ( ? n ) ? Z 2 .
domination number 2-packing number fibonacci cubes lucas cubes automorphism group