故障二维环面网络的点二元泛圈性

Vertex bipancyclity of the Torus with faulty elements

二维环面是一类重要的互联网络,被广泛应用到大型并行分布式系统的网络拓扑中.近年来,人们开始对具有故障元的二维环面进行研究.圈嵌入问题是研究互联网络并行计算中最重要问题之一,本文研究了带有故障元的二维环面以及其子网络的圈嵌入问题并得到如下结果.在具有至多一个故障点或一条故障边的二维环面Torus(m,n)以及子网络Row-Torus(m,n)中(m,n≥3),每个顶点在长从4到mn的无故障偶圈中。

Recently, two-dimensional Torus has been drawing considerable attention as topologies for parallel and distributed multiprocessor interconnection networks. This paper studies the problem of embedding cycles in the two-dimensional Torus with faulty elements and gets the following result. Given two integers m, n 〉 3, for any healthy vertex of the Torus （m, n） with at most one faulty vertex or one faulty edge, there is a cycle of every even length from 4 to mn containing this vertex.