Link-Connectivities of Extended Double Loop Networks

Abstract

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.

This research was supported in part by a grant from NSA no. MDA904–90-H-1021. Part of the work was done when this author was visiting AT&T Bell Laboratories, Murray Hill, NJ.