Hamiltonian Connectedness of Recursive Dual-Net

Recursive Dual-Net (RDN) was proposed recently as an effective, high-performance interconnection network for supercomputers with millions of nodes. A Recursive DualNet RDN(B) is recursively constructed on a base symmetric network B. At each iteration, the network is extended through dual-construction. The dual-construction extends a symmetric graph G into a symmetric graph G with size 2n2 and node-degree d + 1, where n and d are the size and the node-degree of G, respectively. Therefore, a k-level Recursive Dual-Net RDNk (B) contains (2n0)2k /2 nodes with a node degree of d0 + k, where n0 and d0 are the size and the node-degree of the base network B, respectively. In this paper, we show that, if the base network B is hamiltonian, RDNk (B) is hamiltonian. We give an efficient algorithm for constructing a hamiltonian cycle in RDNk (B) for k > 0. We also show that if the base network is hamiltonian connected, RDNk (B) is hamiltonian connected for any k > 0.

• Type: Journal
• Year: 2009
• Where: IEEECIT
• Authors: Yamin Li, Shietung Peng, Wanming Chu
• Keywords: Base Network, IEEECIT 2009, Information Technology, Recursive Dual-net, Symmetric Graph