Super spanning connectivity on WK-recursive networks

Abstract

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 use K(d,t) to denote the WK-recursive network of level t, each of which basic modules is a d-vertex complete graph, where d>1 and t≥1. We prove that for any two distinct vertices μ and ν, there exist m node disjoint paths whose union covers all the vertices of K(d,t) for d≥4, t≥1 and 1≤m≤d−1. Since the connectivity of K(d,t) is d−1, the result is optimal in the worst case.