Abstract: The embedding of paths or cycles in the crossed cube has been attracting much research interest, and the fault-tolerance of the crossed cube has been a major concern of relevant studies as well. In order to study the crossed cube further, it constructs a kind of dimension preserving automorphism, and proves that it can be a group with synthetic operation.

Key words: crossed cube; Hypercube; interconnection networks; dimension preserving automorphism; dimension preserving automorphism group