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The Fibonacci cube of dimension n, denoted as Γ n , is the subgraph of n-cube Q n induced by vertices with no consecutive 1's. We study the maximum number of disjoint subgraphs in Γ n isomorphic to Q k , and denote this number by q k (n). We prove several recursive results for q k (n), in particular we prove that q k (n) = q k−1 (n − 2) + q k (n − 3). We also prove a closed formula in which q k (n) is given in terms of Fibonacci numbers, and finally we give the generating function for the sequence {q k (n)} ∞ n=0 .

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Abstract:Hanoi graphs H model the Tower of Hanoi game with pegs and discs. Sierpiński graphs S arose in investigations of universal topological spaces and have meanwhile been studied extensively. It is proved that S embeds as a spanning subgraph into H if and only if is odd or, trivially, if = 1. MSC:05C60