Fault-Tolerance Research Of Path-embedding And Edge-pancyclicity In Crossed Cubes

In the study of network topology, using graph theory is a common method to build the model. And embedded path and generic circle is inevitable content when fault tolerance research network topology, thus more and more get the attention of people. Improve the fault tolerance of network can improve the fault resistance of large networks.As the deformation of the hypercube Qn network structure, the crossed cube CQn than in cubeg Qn.There are a lot of better performance. Although the crossed cube CQn and ordinary hypercube Qn has the same number of vertices and the same node degree, but the diameter of the crossed cube CQn is about half of the ordinary hypercube Qn. So CQn not only has the advantages existing, but also improved the shortcomings of Qn, And fault tolerance is the study of factors must be considered in the network topology, a large network, after all, there is always at run time nldes and lines or separate or problems at the same time. Based on this, considering the network fault tolerance is very important for a large network. fv to show for the errors in the point, fe expressed as errors in the number of edges. Based search when n is hours using computer program and when n is bigger, the two methods, mathematical induction fault-tolerant embedded path problem is studied and edge circle fault-tolerant properties of CQn, obtained the following results:(1) For any n(n?5), F(?)V(CQn)?E(CQn)when|F|?-2for any of the two correct.points (with degrees except for 2 vertex adjacent pair) in CQn-F existed in a long l path connecting these two right.points, among them, meet.2n-1-1?l?2n-fv-1(2) Proved that for any side e=(u,v)?E(CQn),when0?fv+fe?n-2,n?5, for any of the right side e, can exist for a long and contains the edge e right circle ia CQ_n.