Article
Weighted multiconnected loop networks.
Department of Mathematics, University of Bergen, Allégt. 55, N5007 Bergen, Norway
Discrete Mathematics (Impact Factor: 0.58). 01/1996; 148:161173. DOI: 10.1016/0012365X(94)00239F Source: DBLP

Article: Equivalent doubleloop networks
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ABSTRACT: Hwang and Xu defined equivalent doubleloop networks and gave one such result showing that the Lshapes of the two equivalent networks are recombinations of three rectangles. Recently, Rödseth gave an elegant algebraic theorem for equivalent multiloop networks. We show that its doubleloop version yields equivalent networks of the 3rectangle version. We also show that other seemingly different geometric recombinations also all turn out to be special cases of the 3rectangle version.TAIWANESE JOURNAL OF MATHEMATICS 01/2001; 4:661668. · 0.67 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Recently, Chen, Hwang and Liu [S.K. Chen, F.K. Hwang, Y.C. Liu, Some combinatorial properties of mixed chordal rings, J. Interconnection Networks 1 (2003) 3–16] introduced the mixed chordal ring network as a topology for interconnection networks. In particular, they showed that the amount of hardware and the network structure of the mixed chordal ring network are very comparable to the (directed) doubleloop network, yet the mixed chordal ring network can achieve a better diameter than the doubleloop network. More precisely, the mixed chordal ring network can achieve diameter about 2N as compared to 3N for the (directed) doubleloop network, where N is the number of nodes in the network. One of the most important questions in interconnection networks is, for a given number of nodes, how to find an optimal network (a network with the smallest diameter) and give the construction of such a network. Chen et al. [S.K. Chen, F.K. Hwang, Y.C. Liu, Some combinatorial properties of mixed chordal rings, J. Interconnection Networks 1 (2003) 3–16] gave upper and lower bounds for such an optimization problem on the mixed chordal ring network. In this paper, we improve the upper and lower bounds as 2⌈N/2⌉+1 and ⌈2N−3/2⌉, respectively. In addition, we correct some deficient contexts in [S.K. Chen, F.K. Hwang, Y.C. Liu, Some combinatorial properties of mixed chordal rings, J. Interconnection Networks 1 (2003) 3–16].Inf. Process. Lett. 01/2009; 109:757762.
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