On the Spanning Cyclability of k-ary n-cube Networks

Abstract

Embedding cycles into a network topology is crucial for a network simulation. In particular, embedding Hamiltonian cycles is a major requirement for designing good interconnection networks. A graph G is called r-spanning cyclable if, for any r distinct vertices v1,v2,…,vr of G, there exist r cycles C1,C2,…,Cr in G such that vi is on Ci for every i, and every vertex of G is on exactly one cycle Ci. If r=1, this is the classical Hamiltonian problem. In this paper, we focus on the problem of embedding spanning disjoint cycles in bipartite k-ary n-cubes. Let k≥4 be even and n≥2. It is shown that the n-dimensional bipartite k-ary n-cube Qnk is m-spanning cyclable with m≤2n−1. Considering the degree of Qnk, the result is optimal.