One-to-Many Node Disjoint Path Covers on WK-Recursive Networks

Abstract

The WK-recursive network denoted by K(d, t) has received much attention due to its many favorable properties. We use Oi to denote the open vertex set of Ki(d, t−1) with 1 ≤ i ≤ d and let OI = {Oi|1 ≤ i ≤ d}. We prove that given any node μ and a set of distinct destination nodes T = {tj|1 ≤ j ≤ d−1} where tj ∉ OI, and μ, tj are not in the same subgraph, there exist d−1 node-disjoint paths between μ and T whose union covers all the vertices of K(d, t) where d≥4 and t≥1.