On conditional diagnosability and reliability of the BC networks

An n-dimensional bijective connection network (in brief, BC network), denoted by X n , is an n-regular graph with 2 n nodes and n2 n?1 edges. Hypercubes, crossed cubes, twisted cubes, and Mobius cubes all belong to the class of BC networks (Fan and He in Chin. J. Comput. 26(1):84---90, [2003]). We prove that the super connectivity of X n is 2n?2 for n?3 and the conditional diagnosability of X n is 4n?7 for n?5. As a corollary of this result, we obtain the super connectivity and conditional diagnosability of the hypercubes, twisted cubes, crossed cubes, and Mobius cubes.