The Fibonacci cube is an isometric subgraph of the hypercube having a Fibonacci number of vertices. The Fibonacci cube was originally proposed by W-J. Hsu as an interconnection network and like the hypercube it has very attractive topological properties but with a more moderated growth. Among these properties, we discuss the hamiltonicity in the Fibonacci cube and also in the Lucas cube which is obtained by removing all the strings that begin and end with 1 from the Fibonacci cube. We give also the eccentricity sequences of the Fibonacci and the Lucas cubes. Finally, we present a study of both cubes from the domination and the 2-packing points of view.
