The structure of $k$-Lucas cubes

Fibonacci cubes and Lucas have been studied as alternatives for the classical hypercube topology interconnection networks. These families of graphs interesting graph theoretic enumerative properties. Among many generalization are $k$-Fibonacci cubes, which same number vertices but edge sets determined by a parameter $k$. In this work, we consider $k$-Lucas obtained subgraphs in way that from cubes. We obtain useful decomposition property allows calculation basic properties class: edges, average degree vertex, hypercubes they contain, diameter radius.