Super spanning connectivity on WK-recursive networks

摘要

The WK-recursive network has received much attention due to its many favorable properties such as small diameter, large connectivity, and high degree of scalability and expandability. In this paper, we consider the super spanning connectivity properties of the WK-recursive network. We useK(d,t)to denote the WK-recursive network of levelt, each of which basic modules is ad-vertex complete graph, whered>1andt≥1. We prove that for any two distinct verticesμandν, there existmnode disjoint paths whose union covers all the vertices ofK(d,t)ford≥4,t≥1and1≤m≤d?1. Since the connectivity ofK(d,t)isd?1, the result is optimal in the worst case.