The edge-pancyclicity of dual-cube extensive networks
Shih-Yan Chen, Shin-Shin Kao · International Conference on Computer Engineering and Applications · 2008
The hypercube family Qn is one of the most well-known interconnection networks in parallel computers, e.g. see [3, 6]. Using Qn, Li et al. introduced dual-cube networks DC(n) and show the vertex symmetry and some fault-tolerant hamiltonian properties of DC(n) [7, 8]. By replacing Qn with any arbitrary graph G in DC(n), a new family of interconnection networks called dual-cube extensive networks, denoted by DCEN(G), was introduced recently [4]. It is proved in [4] that DCEN(G) the hamiltonian connectivity and the globally-3*-connectivity of G. In this article, we prove that DCEN(G) preserves the edge-pancyclicity of G as well. More precisely, suppose that every edge G lies on a cycle of length l, where l is an arbitrary integer with 3 ≤ l ≤ |G|. Then for any edge e of DCEN(G), there exists a cycle in DCEN(G), denoted by Cl, such that e ∈ Cl and the length of Cl is l for every lmin ≤ l ≤ |DCEN(G)|, where lmin ∈ {3, 8}. The result is shown to be optimal. Furthermore, we prove that the similar results hold when G is a bipartite graph.