Embedding spanning disjoint cycles in enhanced hypercube networks with prescribed vertices in each cycle

Abstract

Embedding cycles into a network topology is crucial for the network simulation. In particular, embedding Hamiltonian cycles is a major requirement for designing good interconnection networks. A graph G is called k-spanning cyclable if, for any k distinct vertices v1,v2,…,vk of G, there exist k cycles C1,C2,…,Ck in G such that vi is on Ci for every i, and every vertex of G is on exactly one cycle Ci. If k=1, this is the classical Hamiltonian problem. In this study, we focus on embedding spanning disjoint cycles in enhanced hypercube networks and show that the n-dimensional enhanced hypercube Qn,m is k-spanning cyclable if k≤n and n≥4, and k-spanning cyclable if k≤n−1 and n=2,3. Moreover, the results are optimal with respect to the degree of Qn,m, and some experimental examples are provided to verify the theoretical results.