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In [A Note on Path Embedding in Crossed Cubes with Faulty Vertices, Information Processing Letters 121 (2017) pp. 34--38], Chen et al. conjectured that $\\text{Orb}(\\text{CQ}_n)=2^{\\lceil\\frac{n}{2}\\rceil-2}$ for $n\\geqslant 3$, where $\\text{CQ}_n$ denotes an $n$-dimensional crossed cube. 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