Abstract: The crossed cube which is a topological structure of the network has received much attention from scholars worldwide, and studies of its faulttolerance are also a major concern. In the situation of conditional node fault (each faultfree node is adjacent to at least two other faultfree nodes), it  discusses that  while n≥4, the Hamiltonian cycles exist in a n dimensional crossed cube, even if the number of faulty nodes is up to 2n-7.

Key words: crossed cube; conditional node fault; Hamiltonian cycle; fault tolerance