The two-equal-disjoint path cover problem of Matching Composition Network

Abstract

Embedding of paths have attracted much attention in the parallel processing. Many-to-many communication is one of the most central issues in various interconnection networks. A graph G is globally two-equal-disjoint path coverable if for any two distinct pairs of vertices ( u , v ) and ( w , x ) of G, there exist two disjoint paths P and Q satisfied that (1) P ( Q, respectively) joins u and v ( w and x, respectively), (2) | P | = | Q | , and (3) V ( P ∪ Q ) = V ( G ) . The Matching Composition Network (MCN) is a family of networks which two components are connected by a perfect matching. In this paper, we consider the globally two-equal-disjoint path cover property of MCN. Applying our result, the Crossed cube CQ n , the Twisted cube TQ n , and the Möbius cube MQ n can all be proven to be globally two-equal-disjoint path coverable for n ⩾ 5 .