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

  • Authors:
  • Pao-Lien Lai;Hong-Chun Hsu

  • Affiliations:
  • Department of Computer Science and Information Engineering, National Dong Hwa University, Shoufeng, Hualien, Taiwan 97401, ROC;Department of Medical Informatics, Tzu Chi University, Hualien, Taiwan 970, ROC

  • Venue:
  • Information Processing Letters
  • Year:
  • 2008

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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 Mobius cube MQ"n can all be proven to be globally two-equal-disjoint path coverable for n=5.