One-to-One Disjoint Path Covers on WK-Networks

Abstract

The WK-recursive network has received much attention due to its many attractive properties. In this paper, we consider the one-to-one disjoint path covers 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 u and v , there exist d -1 node-disjoint paths whose union covers all vertices of K(d , t) for d ≥ 3 and t ≥ 1. The results is optimal for vertices in different K j ( d , t − 1) for t ≥ 2, since each K j ( d , t − 1) with 1 ≤ j ≤ d has d − 1 open edges.