Fault-Tolerant Pancyclicity Of Crossed Cubes

For sample graph G=(V,E),F is a subset which is fualty in G.|F| is the order of F. The problem of fault-tolerant pancyclicity is to get the maximum number of |F| stilly keep the communication between any nodes or edge effective.For rhe graph it is to find cycles of length from the girth to number of|V| in the subgraph which is abstracted from the subnet.The fault-tolerant pancyclicity problem has received intense research interest for its applications in various fields. For example, removal of some component to save resource; keep high performance of the communication in the multitask of the distributed system and so on.Failures of links and nodes in an interconnection network are inevitable,for its theoretical and practical value, this paper explores the Edge-fault-tolerant Node-pancyclicity of Crossed Cubes and Fault-tolerant Node-pancyclicity of Crossed Cubes with the help of the combination of computer and mathematics,and give the upper bound of the the number of faulty componets of crossed cube network structure after removal of which if can can ensure correct normal communication of the system.Letting fe be the numbers of faulty edges and fv be the numbers of faulty nodes in CQn, we show that for any u∈V(CQn) and any integer 6≤l≤2n, there exists cycle C of length l in CQn such that u is in C if the number of faulty edges do not eceed (n-3)。We show that for any u∈V(CQn) and any integer 8≤l≤2n-fv, there exists cycle C of length l in CQn such that u is in C if the sum of faulty edges and faulty nodes do not eceed (n-3)。...