Abstract:Graph Theory
International audience
If f is a binary word and d a positive integer, then the generalized Fibonacci cube Qd(f) is the graph obtained from the d-cube Qd by removing all the vertices that contain f as a factor, while the generalized Lucas cube Qd(lucas(f)) is the graph obtained from Qd by removing all the vertices that have a circulation containing f as a factor. The Fibonacci cube Γd and the Lucas cube Λd are the graphs Qd(11) and Qd(lucas(11)), respectively. It is proved that… Show more
The Fibonacci cube Γ n is obtained from the n-cube Q n by removing all the vertices that contain two consecutive 1s. It is proved that Γ n admits a perfect code if and only if n ≤ 3.
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