Hamiltonian connectivity and globally 3*-connectivity of dual-cube extensive networks

In 2000, Li et al. introduced dual-cube networks, denoted by DCn for n >= 1, using the hypercube family Q(n) and showed the vertex symmetry and some fault-tolerant hamiltonian properties of DCn. In this article, we introduce a new family of interconnection networks called dual-cube extensive networks, denoted by DCEN(G). Given any arbitrary graph G, DCEN(G) is generated from G using the similar structure of DCn. We show that if G is a nonbipartite and hamiltonian connected graph, then DCEN(G) is hamiltonian connected. In addition, if G has the property that for any two distinct vertices u, v of G, there exist three disjoint paths between u and v such that these three paths span the graph G, then DCEN(G) preserves the same property. Furthermore, we prove that the similar results hold when G is a bipartite graph. (C) 2009 Elsevier Ltd. All rights reserved.