The Disjoint Paths Covers Of Torus

With the progress of society,the rapid development of computer technology has made the large-scale,high-complexity interconnection networks become a reality,these interconnection networks have become broadcast networks,local area networks,Communication network and other distributed computer systems are the core of the design,and play an indispensable role in large-scale parallel systems,determine the security,practicability and reliability of the whole system.As a topology of interconnection network,Torus has many excellent proper ties and is the most widely used distributed computer system interconnection net work.Finding disjoint paths between vertices of interconnected networks is one of the classical problems in the study of network topology,because the problem of non-routing is closely related to the data transmission of networks.In this paper,the main research is the disjoint paths covers of Torus.We consider the ont-to-many disjoint paths covers of two-dimensional network first.Proved that there has a one-to-many m-disjont paths cover in Torus?k ₁,k₂?,whilek₁,k₂?5 and all is odd,1?m?3.And then proved it there has a one-to-many 3-disjont paths cover in bipartiteTorus?k ₁,k₂?,whilek₁,k₂?6 and all is even.We think about the many-to-many disjoint paths cover of two-dimensional network.Proved that there has an unpaired many-to-many 3-disjont paths cover in Torus?k ₁,k₂?,wherek₁,k₂?6 and all is even.Finally,we studied the disjoint paths cover of k-ary n-cube,which is one of the Torus networks.Proved that there has an unpaired many-to-many m-disjont paths cover in Faulty k-ary n-cube,where k?4 is even,n?2,1?m?2n-1,f?2n-m-1.