超级Mbius立方体──一类最优容错的小直径互连网络

THE SUPER MBIUS CUBES A KIND OF OPTIMALLY FAULT TOLERANT INTERCONNECTION NETWORKS WITH LITTLE DIAMETERS

文中将具有２ｎ个顶点的Ｍｏｂｉｕｓ立方体的拓扑结构加以改变，得到了包含任意个顶点的互连网络——超级Ｍｏｂｉｕｓ立方体，并证明它保持了Ｍｏｂｉｕｓ立方体的高连通度、对数级的直径和顶点度数等优良性质，并且当顶点个数Ｎ＝２ｎ＋２ｎ－１时，０－型超级Ｍｏｂｉｕｓ立方体是一个（ｎ＋１）－正则图；更进一步地，由于它包含任意个顶点，所以其升级只需增加任意个顶点，从而克服了Ｍｏｂｉｕｓ立方体的升级必须成倍增加其顶点个数的缺点．

The Mbius cube is a hypercube variant. It has some superior properties to the hypercube. However, like the hypercube, it is also an n regular graph with 2 n nodes. So, it is necessary to double the number of nodes to upgrade the Mbius cube. In order to solve this problem, the topological structure of the Mbius cube with 2 n nodes is modified and the interconnection network the super Mbius cube is obtained, which contains arbitrary number of nodes. It is proved that the super Mbius cube preserves such fine properties as high connectivity, logarithm diameter,and node degree,and that when its number of nodes N is equal to 2 n +2 n-1 , the 0 type super Mbius cube is an ( n +1) regular graph; further more, because the super Mbius cube has arbitrary number of nodes, it needs only to add arbitrary number of nodes to upgrade itself, thus overcoming the shortcoming of the Mbius cube that it is necessary to double the number of nodes to upgrade it.