Research on Topological Properties and Embedding Issues of the Exchanged Hypercube

As a new variant of the hypercube,the exchanged hypercube reduces the cost of topology connecting when the scale of networks increases.According to the graphic definition of Exchanged Hypercube,in this paper,we obtain its formulized definition,prove that the subgraphs of exchanged hypercube are isomorphic to hypercubes,propose the concepts of EHS(s,t) and EHT(s,t),and on the basis of these concepts,prove that there are only even circles with length no more than 4,and that the vertex connectivity and edge connectivity of exchanged hypercube are both min{s+1,t+1}.To enlarge the application range of the exchanged hypercube,we put forwards three strategies embedding hypercubes into exchanged hypercubes as well,and prove that,when n=s+t+1,Qn-1 can be embedded into the exchanged hypercube EH(s,t) homeomorphically.