  The hypercube of dimension n is the graph whose vertices are the 2^n binary
words of length n, and there is an edge between two of them if they have
Hamming distance 1. We consider an edit distance based on swaps and mismatches,
to which we refer as tilde-distance, and define the tilde-hypercube with edges
linking words at tilde-distance 1. Then, we introduce and study some isometric
subgraphs of the tilde-hypercube obtained by using special words called
tilde-isometric words. The subgraphs keep only the vertices that avoid a given
tilde-isometric word as a factor. In the case of word 11, the subgraph is
called tilde-Fibonacci cube, as a generalization of the classical Fibonacci
cube. The tilde-hypercube and the tilde-Fibonacci cube can be recursively
defined; the same holds for the number of their edges. This allows an
asymptotic estimation of the number of edges in the tilde-Fibonacci cube, in
comparison to the total number in the tilde-hypercube.
