Paths in Möbius cubes and crossed cubes

The Möbius cube MQn and the crossed cube CQn are two important variants of the hypercube Qn. This paper shows that for any two different vertices u and v in G∈{MQn,CQn} with n⩾3, there exists a uv-path of every length from dG(u,v)+2 to n2−1 except for a shortest uv-path, where dG(u,v) is the distance between u and v in G. This result improves some known results.