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

In 2000, Li et al. introduced dual-cube networks, denoted by DC n for n ⩾ 1 , using the hypercube family Q n and showed the vertex symmetry and some fault-tolerant hamiltonian properties of DC n . 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 DC n . 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.