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

✍ Scribed by Shih-Yan Chen; Shin-Shin Kao

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
784 KB
Volume
36
Category
Article
ISSN
0045-7906

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✦ Synopsis

In 2000, Li et al. introduced dual-cube networks, denoted by DC n for n P 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 DCENðGÞ. Given any arbitrary graph G, DCENðGÞ is generated from G using the similar structure of DC n . We show that if G is a nonbipartite and hamiltonian connected graph, then DCENðGÞ 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 DCENðGÞ preserves the same property. Furthermore, we prove that the similar results hold when G is a bipartite graph.

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