RVCCC: A new variational network of cube-connected cycles and its topological properties

Variational networks of cube-connected cycles are recursive cubes of rings

“…1 of [10]. In order to get an appreciation of the edges of a recursive cubes of rings, let us consider Q The variational networks of cube-connected cycles were recently proposed in [17] as extensions of the well-known cube-connected cycles from [11]. Before we define these graphs, let us define two automorphisms of the group (Z 2 ) r :…”

“…The graph RV CCC 3 can be visualized as in Fig. 2 of [17]. Looking at Definitions 1 and 2, it might appear that recursive cubes of rings and variational networks of cube-connected cycles are structurally very different.…”

“…As illustrations of recently proposed interconnection networks, we point to the recursive cubes of rings (see [10], building on [13]) and the variational networks of cube-connected cycles [17]. The purpose of this short note is to point out that the variational networks of cube-connected cycles are, in fact, isomorphic to particular recursive cubes of rings; consequently, the algorithm to find a shortest path joining any two nodes of a variational network of cube-connected cycles and the derivation of the diameter of the network in [17] are actually subsumed by the optimal routing algorithm and derivations in [10].…”