We extensively discuss a new interconnection network topology, denoted by ϒ(n,r). Firstly, the ϒ(n,2) network is shown to provide average cost 3 log 2 n while providing superior fault tolerance characteristics. It is defined over any natural number of nodes n using 2n-3 edges for an average degree of 4 and has diameter no greater than k=⌈ log 2n⌉ with average diameter as small as [Formula: see text]. The network is planar and has cyclomatic number n-2. For n=2t the unbounded maximum degree is 2 log 2 n-1 believed indicative of generally a maximum unbounded degree O( log 2n). The bisection width ranges from 3 when n=2t to t+1 when n=2t+1. Secondly, we provide the ϒ*(n,r) network of bounded degree 2r. For n=rt the ϒ*(n,r) network has asymptotically better average cost than the general deBruijn(r,t) network while also maintaining planarity and cyclomatic property of ϒ(n,2). The ϒ family exhibits unique extremal properties of both theoretical interest and practical importance.
Comments on "A new family of Cayley graph interconnection networks of constant degree four"