Embedding spanning disjoint cycles in augmented cube networks with prescribed vertices in each cycle

One of the important issues in evaluating an interconnection network is to study the Hamiltonian cycle embedding problems. For a positive integer k, a graph G is said to be spanning k-cyclable if for k prescribed vertices , there exist k disjoint cycles such that the union of spans G, and each contains exactly one vertex of . According to the definition, the problem of finding hamiltonian cycle focuses on k = 1. The notion of spanning cyclability can be applied to the problem of identifying faulty processors and other related issues in interconnection networks. The n-dimensional augmented cube is an important node-symmetric variant of the n-dimensional hypercube . In this paper, we prove that with is spanning k-cyclable for .