关于超立方体与Mbius立方体的连接

A link between the hypercube and the Mbius cube

新型并行计算系统的研制依赖于对新型互连网络结构及其性质的研究.超立方体及其变型——Mbius立方体两者都具有优点,也具有缺点.本文给出了在超立方体与Mbius立方体的顶点之间的一种连接,从而得到一种称为HMm-立方体的新型网络,证明了HMn-立方体不仅保持了超立方体和Mbius立方体的低顶点度数和高连通度以及其直径至多比Mbius立方体大2的性质,而且它克服了超立方体对圈模拟能力的不足.

A new parallel system of computations depends on the study of the topological structure and properties of a new interconnection network.Both the hypercube and its variant the Mobius cube MQn have their own advantages and disadvantages.In this paper,we give a link between the hypercube and the Mobius cube and get a new interconnection network HMn cube.Also we show that the HMn not only keeps some of attractive properties of the hypercube and the Mobius cube,but has the property that its diameter is not more than two of the sum of the Mobius cube.Moreover,we prove that the HMn cube has Hamilton-connectivity which the hypercube does not possess this property.Both the hypercube and the Mobius cube are the sub-graphs of the HMn cube,so it has the function of both of them.