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

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 v(1),v(2),& mldr;,v(r) of G, there exist r cycles C-1,C-2,& mldr;,C-r in G such that v(i) is on C-i for every i, and every vertex of G is on exactly one cycle C-i. 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 Q(n)(k) is m-spanning cyclable with m <= 2n - 1. Considering the degree of Q(n)(k), the result is optimal.