(n-3)-edge-fault-tolerant Weak-pancyclicity of (n, K)-star Graphs

The (n, k)-star graph is a generalized version of the n-star graph, which belongs to the class of Cayley graphs, and has been recognized as an attractive alternative to an n-cube for building massively parallel computers. Recently, Chen et al. showed that an (n, k)-star graph is 6-weak-vertex-pancyclic for k < n–1, that is, each vertex of an (n, k)-star graph is contained in a cycle of length ranged from 6 to n!/(n–k)!. This work demonstrates that an (n, k)-star graph remains 6-weak-pancyclic, even if there are up to n3 edge faults, where n  4 and 1  k < n. Since an (n, k)-star graph is regular of degree n–1, the result of this work is optimal with respect to the number of edge faults tolerated.