Link-Connectivities of Extended Double Loop Networks

  • Frank K. Hwang
  • Wen-Ching Winnie Li
Part of the Applied Optimization book series (APOP, volume 1)


The notion of extended double loop networks (EDLN) was introduced in [5]. Such a network, denoted by G(n; a, e; b, f), is a 2-regular digraph (each node has 2 inlinks and 2 outlinks) with n nodes labelled by the residues 0,1, ... , n-1, of integers modulo n, and 2n links i ai + e, i → bi + f, for i = 0,1, ... , n - 1. Many 2-regular digraphs popular as topologies for interconnecting networks are special EDLNs. For example, G(n; 2, 0; 2, 1) is the generalized de Bruijn network [6],[9], G(n; -2, -1; -2, -2) is the Imase-Itoh network [7], G(n;1, e; 1, f) is the usual double loop network [3], and G(n;1,1;1, f) is the FLBH (forward loop backward hop) network [9],[11]. EDLNs are interesting not only because they are a natural generalization of the networks well studied before, but also because their graph structures, despite simple linking patterns, are reasonably complicated due to the “noncommutative” nature of the two types of links (that is, the two paths of length two starting from a node using both types of links do not usually terminate at the same node) and the fact that they are not necessarily Cayley graphs [5]. Our ultimate goal is to investigate various properties of EDLNs to see if certain EDLNs will serve as good interconnection networks. In this paper we study the connectivities of such networks.


Cayley Graph Line Graph Small Positive Integer Residue Modulo Link Connectivity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media Dordrecht 1996

Authors and Affiliations

  • Frank K. Hwang
    • 1
  • Wen-Ching Winnie Li
    • 2
  1. 1.AT&T Bell LaboratoriesMurray HillUSA
  2. 2.Department of MathematicsPennsylvania State UniversityUniversity ParkUSA

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