Research On The Fault-Tolerant Edge-Pancyclicity Of Two Kinds Of Variants Of Hypercubes

The graph theory plays a very significant and prominent role as a method in construction of interconnection networks topology.By application,in the field of interconnection network,it has greatly increased its scope in driving different scholars towards itself.In addition,Fault-tolerant edge pancyclicity and path embedding have also involved the scholars to gather the usefulness of these criteria in measurement of fault-tolerant of network.The n-dimensional Mobius Cube MQ_n and n-dimensional Crossed Cube CQ_n play important role as the variants of the hypercube.They contain some of the superior properties to that of hypercube.Many massive networks,involving number of multiple connections,are prone to fail due to unexpected faults in them.This research inspects and explores inside the Fault-Tolerant Edge-Pancyclicity of MQ_n.It finds out that if,mostly n-3 faulty vertices and/or edges are contained in MQ_n(n ? 3)then,for any fault-free edge e in MQ_n and any integer l with 6 ? l ? 2~n-fv,there is a fault-free cycle of length l containing the edge e in MQ_n where number of faulty vertices is denoted by fv.It also investigates the Fault-Tolerant Edge-Pancyclicity of CQ_n that if,mostly n-2 faulty vertices and/or edges are contained in CQ_n(n?5)then,for any fault-free edge uv in CQ_n and any integer l with 6 ? l ? 2~n-fv except l = 7,there is a fault-free cycle of length l containing the edge uv in CQ_n where number of faulty vertices is denoted by fv.Our results prove that when a massive topological structure of a large scale parallel computing system is framed on both Mobius cube MQ_n and crossed cube CQ_n,the system has greater capability of applying ring structured parallel algorithm in communication efficient manner in the hybrid presence of failures of edges and vertices than that of the hypercube network.