Conditional fault diameter of crossed cubes

The conditional connectivity and the conditional fault diameter of a crossed cube are studied in this work. The conditional connectivity is the connectivity of an interconnection network with conditional faults, where each node has at least one fault-free neighbor. Based on this requirement, the conditional connectivity of a crossed cube is shown to be 2n−2$2n-2$. Extending this result, the conditional fault diameter of a crossed cube is also shown to be D(C_Qn)+3$D\left(C{Q}_n\right)+3$ as a set of 2n−3$2n-3$ node failures. This indicates that the conditional fault diameter of a crossed cube is increased by three compared to the fault-free diameter of a crossed cube. The conditional fault diameter of a crossed cube is approximately half that of the hypercube. In this respect, the crossed cube is superior to the hypercube.