The Research Of Properties Of The Crossed Cube Connected Cycles Networks And It's Variant

Interconnection network is an important part of super computers.When design and select a topological structure for an interconnection network,hamiltonian and fault tolerance is a significant index for evaluating the performance of network,while the conditional connectivity and the restricted connectivity offer metric parameters to measure the reliability of networks.In this paper,we consider the crossed cube connected cycles networks and the crossed cube connected cycles n-tuples cartesian product networks,which obtains the following results:1.The main results about the crossed cube connected cycles networks:(1)We proved the crossed cube connected cycles network is neither vertex-transitive,nor edge-transitive;(2)We proved CQCC(n)isn't Cayley graph;(3)We gave one algorithm to calculate diameter and the upper(lower)bound of the diameter of CQCC(n);(4)We gave the conditional vertex connectivity and restricted vertex-connectivity of CQCC(n).2.In addition the following results are obtained:(1)In 2010,Haizhong Shi pro-posed a conjecture:for any integer n ? 3,CQCC(n)is an union of edge-disjoint a hamiltonian cycles and a perfect matching.we proved this conjecture is true by discussing the situation when n is even or odd.In other words,we proved the crossed cube connected cycles network is the chordal ring network;(2)We gave the edge-disjoint hamiltonian cycle and perfect matching of CQCC(n)when n = 3,4,5,6.3.Haizhong Shi designed an interconnection network——the crossed cube con-nected cycles n-tuples cartesian product networks CQCC(d1,d2,…,dn).In this pa-per,(1)we gave the main properties of CQCC(d1,d2,…,dn);(2)We gave the condi-tional vertex connectivity and restricted vertex-connectivity of the CQCC(d1,d2,…,dn).