Abstract
We study a recursively defined two-parameter family of graphs which generalizes Fibonacci cubes and determine their basic structural and enumerative properties. In particular, we show that all of them are induced subgraphs of hypercubes and present their canonical decomposition. Further, we compute their metric invariants and establish some Hamiltonicity properties. We show that the new family inherits many useful properties of the Fibonacci cubes and hence could be interesting for potential applications. We also compute the degree distribution, opening thus the way for computing many degree-based topological invariants. Several possible directions of further research are discussed in the concluding section.
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