Link-Connectivities of Extended Double Loop Networks
The notion of extended double loop networks (EDLN) was introduced in . 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 ,, G(n; -2, -1; -2, -2) is the Imase-Itoh network , G(n;1, e; 1, f) is the usual double loop network , and G(n;1,1;1, f) is the FLBH (forward loop backward hop) network ,. 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 . 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.
KeywordsCayley Graph Line Graph Small Positive Integer Residue Modulo Link Connectivity
Unable to display preview. Download preview PDF.
- Y. Cheng, F. K. Hwang, I. F. Akyildiz and D. F. Hsu, “Routing Algorithms for Double Loop Networks,” Inter. J. Found. Comput. Sci. Google Scholar
- M. A. Fiol, M. Valero, J. L. A. Yebra, I. Alegre and T. Lang, “Optimization of Double-Loop Structures for Local Networks,” Proc. XIX Int. Symp. MIMI ‘82, Paris, 1982, pp. 37–41.Google Scholar
- F. K. Hwang and W.-C. W. Li, “Hamiltonian Circuits for 2-Regular Interconnection Networks,” in Networks Optimization, Ed: D. Z. Du and P. Pardalos, World Scientific, River Edge, NJ.Google Scholar
- D. E. Knuth, The Art of Computer Programming, Vol. 2, Addison-Wesley, Reading, MA 1972.Google Scholar
- S. M. Reddy, D. K. Pradhan and J. G. Kuhl, “Direct Graphs with Minimum Diameter and Maximal Connectivity,” School of Eng., Oakland Univ. Tech. Rep., July 1980.Google Scholar