Article

# Weighted multi-connected loop networks.

Department of Mathematics, University of Bergen, Allégt. 55, N-5007 Bergen, Norway

Discrete Mathematics (Impact Factor: 0.58). 01/1996; 148:161-173. DOI: 10.1016/0012-365X(94)00239-F Source: DBLP

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**ABSTRACT:**Using a geometric interpretation of continued fractions, we give a new proof of Rødseth’s formula for Frobenius numbers.Proceedings of the Steklov Institute of Mathematics 04/2012; 276(1). · 0.28 Impact Factor -
##### Article: Equivalent double-loop networks

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**ABSTRACT:**Hwang and Xu defined equivalent double-loop networks and gave one such result showing that the L-shapes of the two equivalent networks are recombinations of three rectangles. Recently, Rödseth gave an elegant algebraic theorem for equivalent multi-loop networks. We show that its double-loop version yields equivalent networks of the 3-rectangle version. We also show that other seemingly different geometric recombinations also all turn out to be special cases of the 3-rectangle version.TAIWANESE JOURNAL OF MATHEMATICS 01/2001; 4:661-668. · 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) double-loop network, yet the mixed chordal ring network can achieve a better diameter than the double-loop network. More precisely, the mixed chordal ring network can achieve diameter about 2N as compared to 3N for the (directed) double-loop 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].Information Processing Letters 01/2009; 109:757-762. · 0.49 Impact Factor

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