Paths in Möbius cubes and crossed cubes

The Mobius cube MQ"n and the crossed cube CQ"n are two important variants of the hypercube Q"n. This paper shows that for any two different vertices u and v in [email protected]?{MQ"n,CQ"n} with n>=3, there exists a uv-path of every length from d"G(u,v)+2 to 2^n-1 except for a shortest uv-path, where d"G(u,v) is the distance between u and v in G. This result improves some known results.

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