Symmetric properties and two variants of shuffle-cubes
share
Li et al. in [Inf. Process. Lett. 77 (2001) 35–41] proposed the shuffle cube SQ_n as an attractive interconnection network topology for massive parallel and distributed systems. By far, symmetric properties of the shuffle cube remains unknown. In this paper, we show that SQ_n is not vertex-transitive for all n>2, which is not an appealing property in interconnection networks. To overcome this limitation, two novel vertex-transitive variants of the shuffle-cube, namely simplified shuffle-cube SSQ_n and balanced shuffle cube BSQ_n are introduced. Then, routing algorithms of SSQ_n and BSQ_n for all n>2 are given respectively. Furthermore, we show that both SSQ_n and BSQ_n possess Hamiltonian cycle embedding for all n>2. Finally, as a by-product, we mend a flaw in the Property 3 in [IEEE Trans. Comput. 46 (1997) 484–490].
READ FULL TEXT